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Documents authored by Niedermeier, Rolf

Document
DOI: 10.4230/LIPIcs.STACS.2023.35
Parameterized Lower Bounds for Problems in P via Fine-Grained Cross-Compositions

Authors: Klaus Heeger, André Nichterlein, and Rolf Niedermeier

Published in: LIPIcs, Volume 254, 40th International Symposium on Theoretical Aspects of Computer Science (STACS 2023)

Abstract
We provide a general framework to exclude parameterized running times of the form O(l^β + n^γ) for problems that have polynomial running time lower bounds under hypotheses from fine-grained complexity. Our framework is based on cross-compositions from parameterized complexity. We (conditionally) exclude running times of the form O(l^{γ/(γ-1) - ε} + n^γ) for any 1 < γ < 2 and ε > 0 for the following problems: - Longest Common (Increasing) Subsequence: Given two length-n strings over an alphabet Σ (over ℕ) and l ∈ ℕ, is there a common (increasing) subsequence of length l in both strings? - Discrete Fréchet Distance: Given two lists of n points each and k ∈ N, is the Fréchet distance of the lists at most k? Here l is the maximum number of points which one list is ahead of the other list in an optimum traversal. - Planar Motion Planning: Given a set of n non-intersecting axis-parallel line segment obstacles in the plane and a line segment robot (called rod), can the rod be moved to a specified target without touching any obstacles? Here l is the maximum number of segments any segment has in its vicinity. Moreover, we exclude running times O(l^{2γ/(γ-1) - ε} + n^γ) for any 1 < γ < 3 and ε > 0 for: - Negative Triangle: Given an edge-weighted graph with n vertices, is there a triangle whose sum of edge-weights is negative? Here l is the order of a maximum connected component. - Triangle Collection: Given a vertex-colored graph with n vertices, is there for each triple of colors a triangle whose vertices have these three colors? Here l is the order of a maximum connected component. - 2nd Shortest Path: Given an n-vertex edge-weighted digraph, vertices s and t, and k ∈ ℕ, has the second longest s-t-path length at most k? Here l is the directed feedback vertex set number. Except for 2nd Shortest Path all these running time bounds are tight, that is, algorithms with running time O(l^{γ/(γ-1)} + n^γ) for any 1 < γ < 2 and O(l^{2γ/(γ -1)} + n^γ) for any 1 < γ < 3, respectively, are known. Our running time lower bounds also imply lower bounds on kernelization algorithms for these problems.
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Klaus Heeger, André Nichterlein, and Rolf Niedermeier. Parameterized Lower Bounds for Problems in P via Fine-Grained Cross-Compositions. In 40th International Symposium on Theoretical Aspects of Computer Science (STACS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 254, pp. 35:1-35:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{heeger_et_al:LIPIcs.STACS.2023.35,
  author =	{Heeger, Klaus and Nichterlein, Andr\'{e} and Niedermeier, Rolf},
  title =	{{Parameterized Lower Bounds for Problems in P via Fine-Grained Cross-Compositions}},
  booktitle =	{40th International Symposium on Theoretical Aspects of Computer Science (STACS 2023)},
  pages =	{35:1--35:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-266-2},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{254},
  editor =	{Berenbrink, Petra and Bouyer, Patricia and Dawar, Anuj and Kant\'{e}, Mamadou Moustapha},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2023.35},
  URN =		{urn:nbn:de:0030-drops-176876},
  doi =		{10.4230/LIPIcs.STACS.2023.35},
  annote =	{Keywords: FPT in P, Kernelization, Decomposition}
}
Document
DOI: 10.4230/LIPIcs.IPEC.2022.25
Applying a Cut-Based Data Reduction Rule for Weighted Cluster Editing in Polynomial Time

Authors: Hjalmar Schulz, André Nichterlein, Rolf Niedermeier, and Christopher Weyand

Published in: LIPIcs, Volume 249, 17th International Symposium on Parameterized and Exact Computation (IPEC 2022)

Abstract
Given an undirected graph, the task in Cluster Editing is to insert and delete a minimum number of edges to obtain a cluster graph, that is, a disjoint union of cliques. In the weighted variant each vertex pair comes with a weight and the edge modifications have to be of minimum overall weight. In this work, we provide the first polynomial-time algorithm to apply the following data reduction rule of Böcker et al. [Algorithmica, 2011] for Weighted Cluster Editing: For a graph G = (V,E), merge a vertex set S ⊆ V into a single vertex if the minimum cut of G[S] is at least the combined cost of inserting all missing edges within G[S] plus the cost of cutting all edges from S to the rest of the graph. Complementing our theoretical findings, we experimentally demonstrate the effectiveness of the data reduction rule, shrinking real-world test instances from the PACE Challenge 2021 by around 24% while previous heuristic implementations of the data reduction rule only achieve 8%.
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Hjalmar Schulz, André Nichterlein, Rolf Niedermeier, and Christopher Weyand. Applying a Cut-Based Data Reduction Rule for Weighted Cluster Editing in Polynomial Time. In 17th International Symposium on Parameterized and Exact Computation (IPEC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 249, pp. 25:1-25:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{schulz_et_al:LIPIcs.IPEC.2022.25,
  author =	{Schulz, Hjalmar and Nichterlein, Andr\'{e} and Niedermeier, Rolf and Weyand, Christopher},
  title =	{{Applying a Cut-Based Data Reduction Rule for Weighted Cluster Editing in Polynomial Time}},
  booktitle =	{17th International Symposium on Parameterized and Exact Computation (IPEC 2022)},
  pages =	{25:1--25:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-260-0},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{249},
  editor =	{Dell, Holger and Nederlof, Jesper},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2022.25},
  URN =		{urn:nbn:de:0030-drops-173816},
  doi =		{10.4230/LIPIcs.IPEC.2022.25},
  annote =	{Keywords: Correlation Clustering, Minimum Cut, Maximum s-t-Flow}
}
Document
DOI: 10.4230/LIPIcs.ESA.2022.53
There and Back Again: On Applying Data Reduction Rules by Undoing Others

Authors: Aleksander Figiel, Vincent Froese, André Nichterlein, and Rolf Niedermeier

Published in: LIPIcs, Volume 244, 30th Annual European Symposium on Algorithms (ESA 2022)

Abstract
Data reduction rules are an established method in the algorithmic toolbox for tackling computationally challenging problems. A data reduction rule is a polynomial-time algorithm that, given a problem instance as input, outputs an equivalent, typically smaller instance of the same problem. The application of data reduction rules during the preprocessing of problem instances allows in many cases to considerably shrink their size, or even solve them directly. Commonly, these data reduction rules are applied exhaustively and in some fixed order to obtain irreducible instances. It was often observed that by changing the order of the rules, different irreducible instances can be obtained. We propose to "undo" data reduction rules on irreducible instances, by which they become larger, and then subsequently apply data reduction rules again to shrink them. We show that this somewhat counter-intuitive approach can lead to significantly smaller irreducible instances. The process of undoing data reduction rules is not limited to "rolling back" data reduction rules applied to the instance during preprocessing. Instead, we formulate so-called backward rules, which essentially undo a data reduction rule, but without using any information about which data reduction rules were applied to it previously. In particular, based on the example of Vertex Cover we propose two methods applying backward rules to shrink the instances further. In our experiments we show that this way smaller irreducible instances consisting of real-world graphs from the SNAP and DIMACS datasets can be computed.
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Aleksander Figiel, Vincent Froese, André Nichterlein, and Rolf Niedermeier. There and Back Again: On Applying Data Reduction Rules by Undoing Others. In 30th Annual European Symposium on Algorithms (ESA 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 244, pp. 53:1-53:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{figiel_et_al:LIPIcs.ESA.2022.53,
  author =	{Figiel, Aleksander and Froese, Vincent and Nichterlein, Andr\'{e} and Niedermeier, Rolf},
  title =	{{There and Back Again: On Applying Data Reduction Rules by Undoing Others}},
  booktitle =	{30th Annual European Symposium on Algorithms (ESA 2022)},
  pages =	{53:1--53:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-247-1},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{244},
  editor =	{Chechik, Shiri and Navarro, Gonzalo and Rotenberg, Eva and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2022.53},
  URN =		{urn:nbn:de:0030-drops-169914},
  doi =		{10.4230/LIPIcs.ESA.2022.53},
  annote =	{Keywords: Kernelization, Preprocessing, Vertex Cover}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2022.21
Deepening the (Parameterized) Complexity Analysis of Incremental Stable Matching Problems

Authors: Niclas Boehmer, Klaus Heeger, and Rolf Niedermeier

Published in: LIPIcs, Volume 241, 47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022)

Abstract
When computing stable matchings, it is usually assumed that the preferences of the agents in the matching market are fixed. However, in many realistic scenarios, preferences change over time. Consequently, an initially stable matching may become unstable. Then, a natural goal is to find a matching which is stable with respect to the modified preferences and as close as possible to the initial one. For Stable Marriage/Roommates, this problem was formally defined as Incremental Stable Marriage/Roommates by Bredereck et al. [AAAI '20]. As they showed that Incremental Stable Roommates and Incremental Stable Marriage with Ties are NP-hard, we focus on the parameterized complexity of these problems. We answer two open questions of Bredereck et al. [AAAI '20]: We show that Incremental Stable Roommates is W[1]-hard parameterized by the number of changes in the preferences, yet admits an intricate XP-algorithm, and we show that Incremental Stable Marriage with Ties is W[1]-hard parameterized by the number of ties. Furthermore, we analyze the influence of the degree of "similarity" between the agents' preference lists, identifying several polynomial-time solvable and fixed-parameter tractable cases, but also proving that Incremental Stable Roommates and Incremental Stable Marriage with Ties parameterized by the number of different preference lists are W[1]-hard.
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Niclas Boehmer, Klaus Heeger, and Rolf Niedermeier. Deepening the (Parameterized) Complexity Analysis of Incremental Stable Matching Problems. In 47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 241, pp. 21:1-21:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{boehmer_et_al:LIPIcs.MFCS.2022.21,
  author =	{Boehmer, Niclas and Heeger, Klaus and Niedermeier, Rolf},
  title =	{{Deepening the (Parameterized) Complexity Analysis of Incremental Stable Matching Problems}},
  booktitle =	{47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022)},
  pages =	{21:1--21:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-256-3},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{241},
  editor =	{Szeider, Stefan and Ganian, Robert and Silva, Alexandra},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2022.21},
  URN =		{urn:nbn:de:0030-drops-168194},
  doi =		{10.4230/LIPIcs.MFCS.2022.21},
  annote =	{Keywords: Stable Marriage, Stable Roommates, adapting to changing preferences, NP-hardness, W\lbrack1\rbrack-hardness, XP, FPT, master lists, incremental algorithms}
}
Document
DOI: 10.4230/LIPIcs.CPM.2022.6
An FPT-Algorithm for Longest Common Subsequence Parameterized by the Maximum Number of Deletions

Authors: Laurent Bulteau, Mark Jones, Rolf Niedermeier, and Till Tantau

Published in: LIPIcs, Volume 223, 33rd Annual Symposium on Combinatorial Pattern Matching (CPM 2022)

Abstract
In the NP-hard Longest Common Subsequence problem (LCS), given a set of strings, the task is to find a string that can be obtained from every input string using as few deletions as possible. LCS is one of the most fundamental string problems with numerous applications in various areas, having gained a lot of attention in the algorithms and complexity research community. Significantly improving on an algorithm by Irving and Fraser [CPM'92], featured as a research challenge in a 2014 survey paper, we show that LCS is fixed-parameter tractable (FPT) when parameterized by the maximum number of deletions per input string. Given the relatively moderate running time of our algorithm (linear time when the parameter is a constant) and small parameter values to be expected in several applications, we believe that our purely theoretical analysis could finally pave the way to a new, exact and practically useful algorithm for this notoriously hard string problem.
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Laurent Bulteau, Mark Jones, Rolf Niedermeier, and Till Tantau. An FPT-Algorithm for Longest Common Subsequence Parameterized by the Maximum Number of Deletions. In 33rd Annual Symposium on Combinatorial Pattern Matching (CPM 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 223, pp. 6:1-6:11, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{bulteau_et_al:LIPIcs.CPM.2022.6,
  author =	{Bulteau, Laurent and Jones, Mark and Niedermeier, Rolf and Tantau, Till},
  title =	{{An FPT-Algorithm for Longest Common Subsequence Parameterized by the Maximum Number of Deletions}},
  booktitle =	{33rd Annual Symposium on Combinatorial Pattern Matching (CPM 2022)},
  pages =	{6:1--6:11},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-234-1},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{223},
  editor =	{Bannai, Hideo and Holub, Jan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2022.6},
  URN =		{urn:nbn:de:0030-drops-161338},
  doi =		{10.4230/LIPIcs.CPM.2022.6},
  annote =	{Keywords: NP-hard string problems, multiple sequence alignment, center string, parameterized complexity, search tree algorithms, enumerative algorithms}
}
Document
DOI: 10.4230/LIPIcs.SWAT.2022.29
Most Classic Problems Remain NP-Hard on Relative Neighborhood Graphs and Their Relatives

Authors: Pascal Kunz, Till Fluschnik, Rolf Niedermeier, and Malte Renken

Published in: LIPIcs, Volume 227, 18th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2022)

Abstract
Proximity graphs have been studied for several decades, motivated by applications in computational geometry, geography, data mining, and many other fields. However, the computational complexity of classic graph problems on proximity graphs mostly remained open. We study 3-Colorability, Dominating Set, Feedback Vertex Set, Hamiltonian Cycle, and Independent Set on the following classes of proximity graphs: relative neighborhood graphs, Gabriel graphs, and relatively closest graphs. We prove that all of the aforementioned problems remain NP-hard on these graphs, except for 3-Colorability and Hamiltonian Cycle on relatively closest graphs, where the former is trivial and the latter is left open. Moreover, for every NP-hard case we additionally show that no 2^{o(n^{1/4})}-time algorithm exists unless the Exponential-Time Hypothesis (ETH) fails, where n denotes the number of vertices.
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Pascal Kunz, Till Fluschnik, Rolf Niedermeier, and Malte Renken. Most Classic Problems Remain NP-Hard on Relative Neighborhood Graphs and Their Relatives. In 18th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 227, pp. 29:1-29:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{kunz_et_al:LIPIcs.SWAT.2022.29,
  author =	{Kunz, Pascal and Fluschnik, Till and Niedermeier, Rolf and Renken, Malte},
  title =	{{Most Classic Problems Remain NP-Hard on Relative Neighborhood Graphs and Their Relatives}},
  booktitle =	{18th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2022)},
  pages =	{29:1--29:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-236-5},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{227},
  editor =	{Czumaj, Artur and Xin, Qin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.SWAT.2022.29},
  URN =		{urn:nbn:de:0030-drops-161891},
  doi =		{10.4230/LIPIcs.SWAT.2022.29},
  annote =	{Keywords: Proximity Graphs, Relatively Closest Graphs, Gabriel Graphs, 3-Colorability, Dominating Set, Feedback Vertex Set, Hamiltonian Cycle, Independent Set, Exponential-Time Hypothesis}
}
Document
DOI: 10.4230/LIPIcs.SAND.2022.17
Temporal Connectivity: Coping with Foreseen and Unforeseen Delays

Authors: Eugen Füchsle, Hendrik Molter, Rolf Niedermeier, and Malte Renken

Published in: LIPIcs, Volume 221, 1st Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2022)

Abstract
Consider planning a trip in a train network. In contrast to, say, a road network, the edges are temporal, i.e., they are only available at certain times. Another important difficulty is that trains, unfortunately, sometimes get delayed. This is especially bad if it causes one to miss subsequent trains. The best way to prepare against this is to have a connection that is robust to some number of (small) delays. An important factor in determining the robustness of a connection is how far in advance delays are announced. We give polynomial-time algorithms for the two extreme cases: delays known before departure and delays occurring without prior warning (the latter leading to a two-player game scenario). Interestingly, in the latter case, we show that the problem becomes PSPACE-complete if the itinerary is demanded to be a path.
Cite as

Eugen Füchsle, Hendrik Molter, Rolf Niedermeier, and Malte Renken. Temporal Connectivity: Coping with Foreseen and Unforeseen Delays. In 1st Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 221, pp. 17:1-17:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{fuchsle_et_al:LIPIcs.SAND.2022.17,
  author =	{F\"{u}chsle, Eugen and Molter, Hendrik and Niedermeier, Rolf and Renken, Malte},
  title =	{{Temporal Connectivity: Coping with Foreseen and Unforeseen Delays}},
  booktitle =	{1st Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2022)},
  pages =	{17:1--17:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-224-2},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{221},
  editor =	{Aspnes, James and Michail, Othon},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.SAND.2022.17},
  URN =		{urn:nbn:de:0030-drops-159598},
  doi =		{10.4230/LIPIcs.SAND.2022.17},
  annote =	{Keywords: Paths and walks in temporal graphs, static expansions of temporal graphs, two-player games, flow computations, dynamic programming, PSPACE-completeness}
}
Document
DOI: 10.4230/LIPIcs.SAND.2022.19
Temporal Unit Interval Independent Sets

Authors: Danny Hermelin, Yuval Itzhaki, Hendrik Molter, and Rolf Niedermeier

Published in: LIPIcs, Volume 221, 1st Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2022)

Abstract
Temporal graphs have been recently introduced to model changes to a given network that occur throughout a fixed period of time. We introduce and investigate the Temporal Δ Independent Set problem, a temporal variant of the well known Independent Set problem. This problem is e.g. motivated in the context of finding conflict-free schedules for maximum subsets of tasks, that have certain (changing) constraints on each day they need to be performed. We are specifically interested in the case where each task needs to be performed in a certain time-interval on each day and two tasks are in conflict on a day if their time-intervals overlap on that day. This leads us to considering Temporal Δ Independent Set on the restricted class of temporal unit interval graphs, i.e., temporal graphs where each layer is unit interval. We present several hardness results for this problem, as well as two algorithms: The first is a constant-factor approximation algorithm for instances where τ, the total number of time steps (layers) of the temporal graph, and Δ, a parameter that allows us to model some tolerance in the conflicts, are constants. For the second result we use the notion of order preservation for temporal unit interval graphs that, informally, requires the intervals of every layer to obey a common ordering. We provide an FPT algorithm parameterized by the size of minimum vertex deletion set to order preservation.
Cite as

Danny Hermelin, Yuval Itzhaki, Hendrik Molter, and Rolf Niedermeier. Temporal Unit Interval Independent Sets. In 1st Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 221, pp. 19:1-19:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{hermelin_et_al:LIPIcs.SAND.2022.19,
  author =	{Hermelin, Danny and Itzhaki, Yuval and Molter, Hendrik and Niedermeier, Rolf},
  title =	{{Temporal Unit Interval Independent Sets}},
  booktitle =	{1st Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2022)},
  pages =	{19:1--19:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-224-2},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{221},
  editor =	{Aspnes, James and Michail, Othon},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.SAND.2022.19},
  URN =		{urn:nbn:de:0030-drops-159617},
  doi =		{10.4230/LIPIcs.SAND.2022.19},
  annote =	{Keywords: Temporal Graphs, Vertex Orderings, Order Preservation, Interval Graphs, Algorithms and Complexity}
}
Document
DOI: 10.4230/LIPIcs.STACS.2022.30
Delay-Robust Routes in Temporal Graphs

Authors: Eugen Füchsle, Hendrik Molter, Rolf Niedermeier, and Malte Renken

Published in: LIPIcs, Volume 219, 39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022)

Abstract
Most transportation networks are inherently temporal: Connections (e.g. flights, train runs) are only available at certain, scheduled times. When transporting passengers or commodities, this fact must be considered for the the planning of itineraries. This has already led to several well-studied algorithmic problems on temporal graphs. The difficulty of the described task is increased by the fact that connections are often unreliable - in particular, many modes of transportation suffer from occasional delays. If these delays cause subsequent connections to be missed, the consequences can be severe. Thus, it is a vital problem to design itineraries that are robust to (small) delays. We initiate the study of this problem from a parameterized complexity perspective by proving its NP-completeness as well as several hardness and tractability results for natural parameterizations.
Cite as

Eugen Füchsle, Hendrik Molter, Rolf Niedermeier, and Malte Renken. Delay-Robust Routes in Temporal Graphs. In 39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 219, pp. 30:1-30:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{fuchsle_et_al:LIPIcs.STACS.2022.30,
  author =	{F\"{u}chsle, Eugen and Molter, Hendrik and Niedermeier, Rolf and Renken, Malte},
  title =	{{Delay-Robust Routes in Temporal Graphs}},
  booktitle =	{39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022)},
  pages =	{30:1--30:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-222-8},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{219},
  editor =	{Berenbrink, Petra and Monmege, Benjamin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2022.30},
  URN =		{urn:nbn:de:0030-drops-158403},
  doi =		{10.4230/LIPIcs.STACS.2022.30},
  annote =	{Keywords: algorithms and complexity, parameterized complexity, time-varying networks, temporal paths, journeys}
}
Document
DOI: 10.4230/DagRep.11.3.16
Temporal Graphs: Structure, Algorithms, Applications (Dagstuhl Seminar 21171)

Authors: Arnaud Casteigts, Kitty Meeks, George B. Mertzios, and Rolf Niedermeier

Published in: Dagstuhl Reports, Volume 11, Issue 3 (2021)

Abstract
This report documents the program and the outcomes of Dagstuhl Seminar 121171 "Temporal Graphs: Structure, Algorithms, Applications". The seminar was organized around four core areas: models, concepts, classes; concrete algorithmic problems; distributed aspects; applications. Because of the ongoing pandemic crisis, the seminar had to be held fully online, with talk and open problems sessions focussing on afternoons. Besides 19 contributed talks and small-group discussions, there were lively open-problem sessions, and some of the problems and research directions proposed there are part of this document. Despite strongly missing the usual Dagstuhl atmosphere and personal interaction possibilities, the seminar helped to establish new contacts and to identify new research directions in a thriving research area between (algorithmic) graph theory and network science.
Cite as

Arnaud Casteigts, Kitty Meeks, George B. Mertzios, and Rolf Niedermeier. Temporal Graphs: Structure, Algorithms, Applications (Dagstuhl Seminar 21171). In Dagstuhl Reports, Volume 11, Issue 3, pp. 16-46, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@Article{casteigts_et_al:DagRep.11.3.16,
  author =	{Casteigts, Arnaud and Meeks, Kitty and Mertzios, George B. and Niedermeier, Rolf},
  title =	{{Temporal Graphs: Structure, Algorithms, Applications (Dagstuhl Seminar 21171)}},
  pages =	{16--46},
  journal =	{Dagstuhl Reports},
  ISSN =	{2192-5283},
  year =	{2021},
  volume =	{11},
  number =	{3},
  editor =	{Casteigts, Arnaud and Meeks, Kitty and Mertzios, George B. and Niedermeier, Rolf},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/DagRep.11.3.16},
  URN =		{urn:nbn:de:0030-drops-146892},
  doi =		{10.4230/DagRep.11.3.16},
  annote =	{Keywords: algorithm engineering, complex network analysis, distributed computing, models and classes, parameterized complexity analysis}
}
Document
DOI: 10.4230/LIPIcs.STACS.2021.47
Binary Matrix Completion Under Diameter Constraints

Authors: Tomohiro Koana, Vincent Froese, and Rolf Niedermeier

Published in: LIPIcs, Volume 187, 38th International Symposium on Theoretical Aspects of Computer Science (STACS 2021)

Abstract
We thoroughly study a novel but basic combinatorial matrix completion problem: Given a binary incomplete matrix, fill in the missing entries so that the resulting matrix has a specified maximum diameter (that is, upper-bounding the maximum Hamming distance between any two rows of the completed matrix) as well as a specified minimum Hamming distance between any two of the matrix rows. This scenario is closely related to consensus string problems as well as to recently studied clustering problems on incomplete data. We obtain an almost complete picture concerning the complexity landscape (P vs NP) regarding the diameter constraints and regarding the number of missing entries per row of the incomplete matrix. We develop polynomial-time algorithms for maximum diameter three, which are based on Deza’s theorem [Discret. Math. 1973, J. Comb. Theory, Ser. B 1974] from extremal set theory. In this way, we also provide one of the rare links between sunflower techniques and stringology. On the negative side, we prove NP-hardness for diameter at least four. For the number of missing entries per row, we show polynomial-time solvability when there is only one missing entry and NP-hardness when there can be at least two missing entries. In general, our algorithms heavily rely on Deza’s theorem and the correspondingly identified sunflower structures pave the way towards solutions based on computing graph factors and solving 2-SAT instances.
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Tomohiro Koana, Vincent Froese, and Rolf Niedermeier. Binary Matrix Completion Under Diameter Constraints. In 38th International Symposium on Theoretical Aspects of Computer Science (STACS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 187, pp. 47:1-47:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{koana_et_al:LIPIcs.STACS.2021.47,
  author =	{Koana, Tomohiro and Froese, Vincent and Niedermeier, Rolf},
  title =	{{Binary Matrix Completion Under Diameter Constraints}},
  booktitle =	{38th International Symposium on Theoretical Aspects of Computer Science (STACS 2021)},
  pages =	{47:1--47:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-180-1},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{187},
  editor =	{Bl\"{a}ser, Markus and Monmege, Benjamin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2021.47},
  URN =		{urn:nbn:de:0030-drops-136925},
  doi =		{10.4230/LIPIcs.STACS.2021.47},
  annote =	{Keywords: sunflowers, binary matrices, Hamming distance, stringology, consensus problems, complexity dichotomy, combinatorial algorithms, graph factors, 2-Sat, Hamming radius}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2020.43
Multistage s-t Path: Confronting Similarity with Dissimilarity in Temporal Graphs

Authors: Till Fluschnik, Rolf Niedermeier, Carsten Schubert, and Philipp Zschoche

Published in: LIPIcs, Volume 181, 31st International Symposium on Algorithms and Computation (ISAAC 2020)

Abstract
Addressing a quest by Gupta et al. [ICALP'14], we provide a first, comprehensive study of finding a short s-t path in the multistage graph model, referred to as the Multistage s-t Path problem. Herein, given a sequence of graphs over the same vertex set but changing edge sets, the task is to find short s-t paths in each graph ("snapshot") such that in the found path sequence the consecutive s-t paths are "similar". We measure similarity by the size of the symmetric difference of either the vertex set (vertex-similarity) or the edge set (edge-similarity) of any two consecutive paths. We prove that these two variants of Multistage s-t Path are already NP-hard for an input sequence of only two graphs and maximum vertex degree four. Motivated by this fact and natural applications of this scenario e.g. in traffic route planning, we perform a parameterized complexity analysis. Among other results, for both variants, vertex- and edge-similarity, we prove parameterized hardness (W[1]-hardness) regarding the parameter path length (solution size) for both variants, vertex- and edge-similarity. As a further conceptual study, we then modify the multistage model by asking for dissimilar consecutive paths. One of our main technical results (employing so-called representative sets known from non-temporal settings) is that dissimilarity allows for fixed-parameter tractability for the parameter solution size, contrasting the W[1]-hardness of the corresponding similarity case. We also provide partially positive results concerning efficient and effective data reduction (kernelization).
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Till Fluschnik, Rolf Niedermeier, Carsten Schubert, and Philipp Zschoche. Multistage s-t Path: Confronting Similarity with Dissimilarity in Temporal Graphs. In 31st International Symposium on Algorithms and Computation (ISAAC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 181, pp. 43:1-43:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{fluschnik_et_al:LIPIcs.ISAAC.2020.43,
  author =	{Fluschnik, Till and Niedermeier, Rolf and Schubert, Carsten and Zschoche, Philipp},
  title =	{{Multistage s-t Path: Confronting Similarity with Dissimilarity in Temporal Graphs}},
  booktitle =	{31st International Symposium on Algorithms and Computation (ISAAC 2020)},
  pages =	{43:1--43:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-173-3},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{181},
  editor =	{Cao, Yixin and Cheng, Siu-Wing and Li, Minming},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2020.43},
  URN =		{urn:nbn:de:0030-drops-133879},
  doi =		{10.4230/LIPIcs.ISAAC.2020.43},
  annote =	{Keywords: Temporal graphs, shortest paths, consecutive similarity, consecutive dissimilarity, parameterized complexity, kernelization, representative sets in temporal graphs}
}
Document
DOI: 10.4230/LIPIcs.CPM.2020.20
Parameterized Algorithms for Matrix Completion with Radius Constraints

Authors: Tomohiro Koana, Vincent Froese, and Rolf Niedermeier

Published in: LIPIcs, Volume 161, 31st Annual Symposium on Combinatorial Pattern Matching (CPM 2020)

Abstract
Considering matrices with missing entries, we study NP-hard matrix completion problems where the resulting completed matrix should have limited (local) radius. In the pure radius version, this means that the goal is to fill in the entries such that there exists a "center string" which has Hamming distance to all matrix rows as small as possible. In stringology, this problem is also known as Closest String with Wildcards. In the local radius version, the requested center string must be one of the rows of the completed matrix. Hermelin and Rozenberg [CPM 2014, TCS 2016] performed a parameterized complexity analysis for Closest String with Wildcards. We answer one of their open questions, fix a bug concerning a fixed-parameter tractability result in their work, and improve some running time upper bounds. For the local radius case, we reveal a computational complexity dichotomy. In general, our results indicate that, although being NP-hard as well, this variant often allows for faster (fixed-parameter) algorithms.
Cite as

Tomohiro Koana, Vincent Froese, and Rolf Niedermeier. Parameterized Algorithms for Matrix Completion with Radius Constraints. In 31st Annual Symposium on Combinatorial Pattern Matching (CPM 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 161, pp. 20:1-20:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{koana_et_al:LIPIcs.CPM.2020.20,
  author =	{Koana, Tomohiro and Froese, Vincent and Niedermeier, Rolf},
  title =	{{Parameterized Algorithms for Matrix Completion with Radius Constraints}},
  booktitle =	{31st Annual Symposium on Combinatorial Pattern Matching (CPM 2020)},
  pages =	{20:1--20:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-149-8},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{161},
  editor =	{G{\o}rtz, Inge Li and Weimann, Oren},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2020.20},
  URN =		{urn:nbn:de:0030-drops-121456},
  doi =		{10.4230/LIPIcs.CPM.2020.20},
  annote =	{Keywords: fixed-parameter tractability, consensus string problems, Closest String, Closest String with Wildcards}
}
Document
DOI: 10.4230/LIPIcs.CPM.2020.28
Faster Binary Mean Computation Under Dynamic Time Warping

Authors: Nathan Schaar, Vincent Froese, and Rolf Niedermeier

Published in: LIPIcs, Volume 161, 31st Annual Symposium on Combinatorial Pattern Matching (CPM 2020)

Abstract
Many consensus string problems are based on Hamming distance. We replace Hamming distance by the more flexible (e.g., easily coping with different input string lengths) dynamic time warping distance, best known from applications in time series mining. Doing so, we study the problem of finding a mean string that minimizes the sum of (squared) dynamic time warping distances to a given set of input strings. While this problem is known to be NP-hard (even for strings over a three-element alphabet), we address the binary alphabet case which is known to be polynomial-time solvable. We significantly improve on a previously known algorithm in terms of worst-case running time. Moreover, we also show the practical usefulness of one of our algorithms in experiments with real-world and synthetic data. Finally, we identify special cases solvable in linear time (e.g., finding a mean of only two binary input strings) and report some empirical findings concerning combinatorial properties of optimal means.
Cite as

Nathan Schaar, Vincent Froese, and Rolf Niedermeier. Faster Binary Mean Computation Under Dynamic Time Warping. In 31st Annual Symposium on Combinatorial Pattern Matching (CPM 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 161, pp. 28:1-28:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{schaar_et_al:LIPIcs.CPM.2020.28,
  author =	{Schaar, Nathan and Froese, Vincent and Niedermeier, Rolf},
  title =	{{Faster Binary Mean Computation Under Dynamic Time Warping}},
  booktitle =	{31st Annual Symposium on Combinatorial Pattern Matching (CPM 2020)},
  pages =	{28:1--28:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-149-8},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{161},
  editor =	{G{\o}rtz, Inge Li and Weimann, Oren},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2020.28},
  URN =		{urn:nbn:de:0030-drops-121538},
  doi =		{10.4230/LIPIcs.CPM.2020.28},
  annote =	{Keywords: consensus string problems, time series averaging, minimum 1-separated sum, sparse strings}
}
Document
DOI: 10.4230/LIPIcs.STACS.2020.27
Computing Maximum Matchings in Temporal Graphs

Authors: George B. Mertzios, Hendrik Molter, Rolf Niedermeier, Viktor Zamaraev, and Philipp Zschoche

Published in: LIPIcs, Volume 154, 37th International Symposium on Theoretical Aspects of Computer Science (STACS 2020)

Abstract
Temporal graphs are graphs whose topology is subject to discrete changes over time. Given a static underlying graph G, a temporal graph is represented by assigning a set of integer time-labels to every edge e of G, indicating the discrete time steps at which e is active. We introduce and study the complexity of a natural temporal extension of the classical graph problem Maximum Matching, taking into account the dynamic nature of temporal graphs. In our problem, Maximum Temporal Matching, we are looking for the largest possible number of time-labeled edges (simply time-edges) (e,t) such that no vertex is matched more than once within any time window of Δ consecutive time slots, where Δ ∈ ℕ is given. The requirement that a vertex cannot be matched twice in any Δ-window models some necessary "recovery" period that needs to pass for an entity (vertex) after being paired up for some activity with another entity. We prove strong computational hardness results for Maximum Temporal Matching, even for elementary cases. To cope with this computational hardness, we mainly focus on fixed-parameter algorithms with respect to natural parameters, as well as on polynomial-time approximation algorithms.
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George B. Mertzios, Hendrik Molter, Rolf Niedermeier, Viktor Zamaraev, and Philipp Zschoche. Computing Maximum Matchings in Temporal Graphs. In 37th International Symposium on Theoretical Aspects of Computer Science (STACS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 154, pp. 27:1-27:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{mertzios_et_al:LIPIcs.STACS.2020.27,
  author =	{Mertzios, George B. and Molter, Hendrik and Niedermeier, Rolf and Zamaraev, Viktor and Zschoche, Philipp},
  title =	{{Computing Maximum Matchings in Temporal Graphs}},
  booktitle =	{37th International Symposium on Theoretical Aspects of Computer Science (STACS 2020)},
  pages =	{27:1--27:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-140-5},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{154},
  editor =	{Paul, Christophe and Bl\"{a}ser, Markus},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2020.27},
  URN =		{urn:nbn:de:0030-drops-118881},
  doi =		{10.4230/LIPIcs.STACS.2020.27},
  annote =	{Keywords: Temporal Graph, Link Stream, Temporal Line Graph, NP-hardness, APX-hardness, Approximation Algorithm, Fixed-parameter Tractability, Independent Set}
}
Document
DOI: 10.4230/DagRep.9.10.134
Algorithms and Complexity in Phylogenetics (Dagstuhl Seminar 19443)

Authors: Magnus Bordewich, Britta Dorn, Simone Linz, and Rolf Niedermeier

Published in: Dagstuhl Reports, Volume 9, Issue 10 (2020)

Abstract
Phylogenetics is the study of ancestral relationships between species. Its central goal is the reconstruction and analysis of phylogenetic trees and networks. Even though research in phylogenetics is motivated by biological questions and applications, it heavily relies on mathematics and computer science. Dagstuhl Seminar 19443 on Algorithms and Complexity in Phylogenetics aimed at bringing together researchers from phylogenetics and theoretical computer science to enable an exchange of expertise, facilitate interactions across both research areas, and establish new collaborations. This report documents the program and outcomes of the seminar. It contains an executive summary, abstracts of talks, short summaries of working groups, and a list of open problems that were posed during the seminar.
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Magnus Bordewich, Britta Dorn, Simone Linz, and Rolf Niedermeier. Algorithms and Complexity in Phylogenetics (Dagstuhl Seminar 19443). In Dagstuhl Reports, Volume 9, Issue 10, pp. 134-151, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@Article{bordewich_et_al:DagRep.9.10.134,
  author =	{Bordewich, Magnus and Dorn, Britta and Linz, Simone and Niedermeier, Rolf},
  title =	{{Algorithms and Complexity in Phylogenetics (Dagstuhl Seminar 19443)}},
  pages =	{134--151},
  journal =	{Dagstuhl Reports},
  ISSN =	{2192-5283},
  year =	{2020},
  volume =	{9},
  number =	{10},
  editor =	{Bordewich, Magnus and Dorn, Britta and Linz, Simone and Niedermeier, Rolf},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/DagRep.9.10.134},
  URN =		{urn:nbn:de:0030-drops-118590},
  doi =		{10.4230/DagRep.9.10.134},
  annote =	{Keywords: Approximation algorithms, Evolution, Parameterized algorithms, Phylogenetic trees and networks}
}
Document
DOI: 10.4230/DagRep.9.9.45
Application-Oriented Computational Social Choice (Dagstuhl Seminar 19381)

Authors: Umberto Grandi, Stefan Napel, Rolf Niedermeier, and Kristen Brent Venable

Published in: Dagstuhl Reports, Volume 9, Issue 9 (2020)

Abstract
This report documents the program and the outcomes of Dagstuhl Seminar 19381 ``Application-Oriented Computational Social Choice''. The seminar was organised around four focus topics: group recommender systems, fair allocation, electoral systems, and interactive democracy. For each topic, an invited survey was given by one of the participants. 26 participants presented their research in a regular talk, and two rump sessions allowed other participants to present their ongoing work and open problems in short talks. A special session was dedicated to software demonstrations, and 3 voting experiments were run during the seminar, also thanks to a mobile experimental laboratory that was brought to Dagstuhl. Finally, three afternoons were dedicated to group works.
Cite as

Umberto Grandi, Stefan Napel, Rolf Niedermeier, and Kristen Brent Venable. Application-Oriented Computational Social Choice (Dagstuhl Seminar 19381). In Dagstuhl Reports, Volume 9, Issue 9, pp. 45-65, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@Article{grandi_et_al:DagRep.9.9.45,
  author =	{Grandi, Umberto and Napel, Stefan and Niedermeier, Rolf and Venable, Kristen Brent},
  title =	{{Application-Oriented Computational Social Choice (Dagstuhl Seminar 19381)}},
  pages =	{45--65},
  journal =	{Dagstuhl Reports},
  ISSN =	{2192-5283},
  year =	{2020},
  volume =	{9},
  number =	{9},
  editor =	{Grandi, Umberto and Napel, Stefan and Niedermeier, Rolf and Venable, Kristen Brent},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/DagRep.9.9.45},
  URN =		{urn:nbn:de:0030-drops-118445},
  doi =		{10.4230/DagRep.9.9.45},
  annote =	{Keywords: ai for the social good, collective decision making, multi-agent systems, social choice}
}
Document
DOI: 10.4230/LIPIcs.IPEC.2019.14
Multistage Vertex Cover

Authors: Till Fluschnik, Rolf Niedermeier, Valentin Rohm, and Philipp Zschoche

Published in: LIPIcs, Volume 148, 14th International Symposium on Parameterized and Exact Computation (IPEC 2019)

Abstract
Covering all edges of a graph by a small number of vertices, this is the NP-hard Vertex Cover problem, is among the most fundamental algorithmic tasks. Following a recent trend in studying dynamic and temporal graphs, we initiate the study of Multistage Vertex Cover. Herein, having a series of graphs with same vertex set but over time changing edge sets (known as temporal graph consisting of time layers), the goal is to find for each layer of the temporal graph a small vertex cover and to guarantee that the two vertex cover sets between two subsequent layers differ not too much (specified by a given parameter). We show that, different from classic Vertex Cover and some other dynamic or temporal variants of it, Multistage Vertex Cover is computationally hard even in fairly restricted settings. On the positive side, however, we also spot several fixed-parameter tractability results based on some of the most natural parameterizations.
Cite as

Till Fluschnik, Rolf Niedermeier, Valentin Rohm, and Philipp Zschoche. Multistage Vertex Cover. In 14th International Symposium on Parameterized and Exact Computation (IPEC 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 148, pp. 14:1-14:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{fluschnik_et_al:LIPIcs.IPEC.2019.14,
  author =	{Fluschnik, Till and Niedermeier, Rolf and Rohm, Valentin and Zschoche, Philipp},
  title =	{{Multistage Vertex Cover}},
  booktitle =	{14th International Symposium on Parameterized and Exact Computation (IPEC 2019)},
  pages =	{14:1--14:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-129-0},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{148},
  editor =	{Jansen, Bart M. P. and Telle, Jan Arne},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2019.14},
  URN =		{urn:nbn:de:0030-drops-114753},
  doi =		{10.4230/LIPIcs.IPEC.2019.14},
  annote =	{Keywords: NP-hardness, dynamic graph problems, temporal graphs, time-evolving networks, W\lbrack1\rbrack-hardness, fixed-parameter tractability, kernelization}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2019.44
Parameterized Complexity of Stable Roommates with Ties and Incomplete Lists Through the Lens of Graph Parameters

Authors: Robert Bredereck, Klaus Heeger, Dušan Knop, and Rolf Niedermeier

Published in: LIPIcs, Volume 149, 30th International Symposium on Algorithms and Computation (ISAAC 2019)

Abstract
We continue and extend previous work on the parameterized complexity analysis of the NP-hard Stable Roommates with Ties and Incomplete Lists problem, thereby strengthening earlier results both on the side of parameterized hardness as well as on the side of fixed-parameter tractability. Other than for its famous sister problem Stable Marriage which focuses on a bipartite scenario, Stable Roommates with Incomplete Lists allows for arbitrary acceptability graphs whose edges specify the possible matchings of each two agents (agents are represented by graph vertices). Herein, incomplete lists and ties reflect the fact that in realistic application scenarios the agents cannot bring all other agents into a linear order. Among our main contributions is to show that it is W[1]-hard to compute a maximum-cardinality stable matching for acceptability graphs of bounded treedepth, bounded tree-cut width, and bounded feedback vertex number (these are each time the respective parameters). However, if we "only" ask for perfect stable matchings or the mere existence of a stable matching, then we obtain fixed-parameter tractability with respect to tree-cut width but not with respect to treedepth. On the positive side, we also provide fixed-parameter tractability results for the parameter feedback edge set number.
Cite as

Robert Bredereck, Klaus Heeger, Dušan Knop, and Rolf Niedermeier. Parameterized Complexity of Stable Roommates with Ties and Incomplete Lists Through the Lens of Graph Parameters. In 30th International Symposium on Algorithms and Computation (ISAAC 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 149, pp. 44:1-44:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{bredereck_et_al:LIPIcs.ISAAC.2019.44,
  author =	{Bredereck, Robert and Heeger, Klaus and Knop, Du\v{s}an and Niedermeier, Rolf},
  title =	{{Parameterized Complexity of Stable Roommates with Ties and Incomplete Lists Through the Lens of Graph Parameters}},
  booktitle =	{30th International Symposium on Algorithms and Computation (ISAAC 2019)},
  pages =	{44:1--44:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-130-6},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{149},
  editor =	{Lu, Pinyan and Zhang, Guochuan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2019.44},
  URN =		{urn:nbn:de:0030-drops-115406},
  doi =		{10.4230/LIPIcs.ISAAC.2019.44},
  annote =	{Keywords: Stable matching, acceptability graph, fixed-parameter tractability, W\lbrack1\rbrack-hardness, treewidth, treedepth, tree-cut width, feedback set numbers}
}
Document
Complete Volume
DOI: 10.4230/LIPIcs.STACS.2019
LIPIcs, Volume 126, STACS'19, Complete Volume

Authors: Rolf Niedermeier and Christophe Paul

Published in: LIPIcs, Volume 126, 36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019)

Abstract
LIPIcs, Volume 126, STACS'19, Complete Volume
Cite as

36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 126, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@Proceedings{niedermeier_et_al:LIPIcs.STACS.2019,
  title =	{{LIPIcs, Volume 126, STACS'19, Complete Volume}},
  booktitle =	{36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019)},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-100-9},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{126},
  editor =	{Niedermeier, Rolf and Paul, Christophe},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2019},
  URN =		{urn:nbn:de:0030-drops-103324},
  doi =		{10.4230/LIPIcs.STACS.2019},
  annote =	{Keywords: Theory of computation, Models of computation, Mathematics of computing, Combinatorics, Graph theory, Formal language theory, Logic}
}
Document
Front Matter
DOI: 10.4230/LIPIcs.STACS.2019.0
Front Matter, Table of Contents, Preface, Conference Organization

Authors: Rolf Niedermeier and Christophe Paul

Published in: LIPIcs, Volume 126, 36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019)

Abstract
Front Matter, Table of Contents, Preface, Conference Organization
Cite as

36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 126, pp. 0:i-0:xvi, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{niedermeier_et_al:LIPIcs.STACS.2019.0,
  author =	{Niedermeier, Rolf and Paul, Christophe},
  title =	{{Front Matter, Table of Contents, Preface, Conference Organization}},
  booktitle =	{36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019)},
  pages =	{0:i--0:xvi},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-100-9},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{126},
  editor =	{Niedermeier, Rolf and Paul, Christophe},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2019.0},
  URN =		{urn:nbn:de:0030-drops-102392},
  doi =		{10.4230/LIPIcs.STACS.2019.0},
  annote =	{Keywords: Front Matter, Table of Contents, Preface, Conference Organization}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2018.36
An Adaptive Version of Brandes' Algorithm for Betweenness Centrality

Authors: Matthias Bentert, Alexander Dittmann, Leon Kellerhals, André Nichterlein, and Rolf Niedermeier

Published in: LIPIcs, Volume 123, 29th International Symposium on Algorithms and Computation (ISAAC 2018)

Abstract
Betweenness centrality - measuring how many shortest paths pass through a vertex - is one of the most important network analysis concepts for assessing the relative importance of a vertex. The well-known algorithm of Brandes [2001] computes, on an n-vertex and m-edge graph, the betweenness centrality of all vertices in O(nm) worst-case time. In follow-up work, significant empirical speedups were achieved by preprocessing degree-one vertices and by graph partitioning based on cut vertices. We further contribute an algorithmic treatment of degree-two vertices, which turns out to be much richer in mathematical structure than the case of degree-one vertices. Based on these three algorithmic ingredients, we provide a strengthened worst-case running time analysis for betweenness centrality algorithms. More specifically, we prove an adaptive running time bound O(kn), where k < m is the size of a minimum feedback edge set of the input graph.
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Matthias Bentert, Alexander Dittmann, Leon Kellerhals, André Nichterlein, and Rolf Niedermeier. An Adaptive Version of Brandes' Algorithm for Betweenness Centrality. In 29th International Symposium on Algorithms and Computation (ISAAC 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 123, pp. 36:1-36:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{bentert_et_al:LIPIcs.ISAAC.2018.36,
  author =	{Bentert, Matthias and Dittmann, Alexander and Kellerhals, Leon and Nichterlein, Andr\'{e} and Niedermeier, Rolf},
  title =	{{An Adaptive Version of Brandes' Algorithm for Betweenness Centrality}},
  booktitle =	{29th International Symposium on Algorithms and Computation (ISAAC 2018)},
  pages =	{36:1--36:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-094-1},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{123},
  editor =	{Hsu, Wen-Lian and Lee, Der-Tsai and Liao, Chung-Shou},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2018.36},
  URN =		{urn:nbn:de:0030-drops-99846},
  doi =		{10.4230/LIPIcs.ISAAC.2018.36},
  annote =	{Keywords: network science, social network analysis, centrality measures, shortest paths, tree-like graphs, efficient pre- and postprocessing, FPT in P}
}
Document
DOI: 10.4230/LIPIcs.FSTTCS.2018.46
Parameterized Dynamic Cluster Editing

Authors: Junjie Luo, Hendrik Molter, André Nichterlein, and Rolf Niedermeier

Published in: LIPIcs, Volume 122, 38th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2018)

Abstract
We introduce a dynamic version of the NP-hard Cluster Editing problem. The essential point here is to take into account dynamically evolving input graphs: Having a cluster graph (that is, a disjoint union of cliques) that represents a solution for a first input graph, can we cost-efficiently transform it into a "similar" cluster graph that is a solution for a second ("subsequent") input graph? This model is motivated by several application scenarios, including incremental clustering, the search for compromise clusterings, or also local search in graph-based data clustering. We thoroughly study six problem variants (edge editing, edge deletion, edge insertion; each combined with two distance measures between cluster graphs). We obtain both fixed-parameter tractability as well as parameterized hardness results, thus (except for two open questions) providing a fairly complete picture of the parameterized computational complexity landscape under the perhaps two most natural parameterizations: the distance of the new "similar" cluster graph to (i) the second input graph and to (ii) the input cluster graph.
Cite as

Junjie Luo, Hendrik Molter, André Nichterlein, and Rolf Niedermeier. Parameterized Dynamic Cluster Editing. In 38th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 122, pp. 46:1-46:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{luo_et_al:LIPIcs.FSTTCS.2018.46,
  author =	{Luo, Junjie and Molter, Hendrik and Nichterlein, Andr\'{e} and Niedermeier, Rolf},
  title =	{{Parameterized Dynamic Cluster Editing}},
  booktitle =	{38th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2018)},
  pages =	{46:1--46:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-093-4},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{122},
  editor =	{Ganguly, Sumit and Pandya, Paritosh},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2018.46},
  URN =		{urn:nbn:de:0030-drops-99450},
  doi =		{10.4230/LIPIcs.FSTTCS.2018.46},
  annote =	{Keywords: graph-based data clustering, goal-oriented clustering, compromise clustering, NP-hard problems, fixed-parameter tractability, parameterized hardness}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2018.45
The Complexity of Finding Small Separators in Temporal Graphs

Authors: Philipp Zschoche, Till Fluschnik, Hendrik Molter, and Rolf Niedermeier

Published in: LIPIcs, Volume 117, 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)

Abstract
Temporal graphs are graphs with time-stamped edges. We study the problem of finding a small vertex set (the separator) with respect to two designated terminal vertices such that the removal of the set eliminates all temporal paths connecting one terminal to the other. Herein, we consider two models of temporal paths: paths that pass through arbitrarily many edges per time step (non-strict) and paths that pass through at most one edge per time step (strict). Regarding the number of time steps of a temporal graph, we show a complexity dichotomy (NP-hardness versus polynomial-time solvability) for both problem variants. Moreover we prove both problem variants to be NP-complete even on temporal graphs whose underlying graph is planar. We further show that, on temporal graphs with planar underlying graph, if additionally the number of time steps is constant, then the problem variant for strict paths is solvable in quasi-linear time. Finally, we introduce and motivate the notion of a temporal core (vertices whose incident edges change over time). We prove that the non-strict variant is fixed-parameter tractable when parameterized by the size of the temporal core, while the strict variant remains NP-complete, even for constant-size temporal cores.
Cite as

Philipp Zschoche, Till Fluschnik, Hendrik Molter, and Rolf Niedermeier. The Complexity of Finding Small Separators in Temporal Graphs. In 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 117, pp. 45:1-45:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{zschoche_et_al:LIPIcs.MFCS.2018.45,
  author =	{Zschoche, Philipp and Fluschnik, Till and Molter, Hendrik and Niedermeier, Rolf},
  title =	{{The Complexity of Finding Small Separators in Temporal Graphs}},
  booktitle =	{43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)},
  pages =	{45:1--45:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-086-6},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{117},
  editor =	{Potapov, Igor and Spirakis, Paul and Worrell, James},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2018.45},
  URN =		{urn:nbn:de:0030-drops-96277},
  doi =		{10.4230/LIPIcs.MFCS.2018.45},
  annote =	{Keywords: (non-)strict temporal paths, temporal core, single-source shortest paths, node multiway cut, length-bounded cuts, parameterized complexity}
}
Document
DOI: 10.4230/LIPIcs.ESA.2018.53
Data Reduction for Maximum Matching on Real-World Graphs: Theory and Experiments

Authors: Viatcheslav Korenwein, André Nichterlein, Rolf Niedermeier, and Philipp Zschoche

Published in: LIPIcs, Volume 112, 26th Annual European Symposium on Algorithms (ESA 2018)

Abstract
Finding a maximum-cardinality or maximum-weight matching in (edge-weighted) undirected graphs is among the most prominent problems of algorithmic graph theory. For n-vertex and m-edge graphs, the best known algorithms run in O~(m sqrt{n}) time. We build on recent theoretical work focusing on linear-time data reduction rules for finding maximum-cardinality matchings and complement the theoretical results by presenting and analyzing (thereby employing the kernelization methodology of parameterized complexity analysis) linear-time data reduction rules for the positive-integer-weighted case. Moreover, we experimentally demonstrate that these data reduction rules provide significant speedups of the state-of-the art implementation for computing matchings in real-world graphs: the average speedup is 3800% in the unweighted case and "just" 30% in the weighted case.
Cite as

Viatcheslav Korenwein, André Nichterlein, Rolf Niedermeier, and Philipp Zschoche. Data Reduction for Maximum Matching on Real-World Graphs: Theory and Experiments. In 26th Annual European Symposium on Algorithms (ESA 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 112, pp. 53:1-53:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{korenwein_et_al:LIPIcs.ESA.2018.53,
  author =	{Korenwein, Viatcheslav and Nichterlein, Andr\'{e} and Niedermeier, Rolf and Zschoche, Philipp},
  title =	{{Data Reduction for Maximum Matching on Real-World Graphs: Theory and Experiments}},
  booktitle =	{26th Annual European Symposium on Algorithms (ESA 2018)},
  pages =	{53:1--53:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-081-1},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{112},
  editor =	{Azar, Yossi and Bast, Hannah and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2018.53},
  URN =		{urn:nbn:de:0030-drops-95169},
  doi =		{10.4230/LIPIcs.ESA.2018.53},
  annote =	{Keywords: Maximum-cardinality matching, maximum-weight matching, linear-time algorithms, preprocessing, kernelization, parameterized complexity analysis}
}
Document
Complete Volume
DOI: 10.4230/LIPIcs.STACS.2018
LIPIcs, Volume 96, STACS'18, Complete Volume

Authors: Rolf Niedermeier and Brigitte Vallée

Published in: LIPIcs, Volume 96, 35th Symposium on Theoretical Aspects of Computer Science (STACS 2018)

Abstract
LIPIcs, Volume 96, STACS'18, Complete Volume
Cite as

35th Symposium on Theoretical Aspects of Computer Science (STACS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 96, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@Proceedings{niedermeier_et_al:LIPIcs.STACS.2018,
  title =	{{LIPIcs, Volume 96, STACS'18, Complete Volume}},
  booktitle =	{35th Symposium on Theoretical Aspects of Computer Science (STACS 2018)},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-062-0},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{96},
  editor =	{Niedermeier, Rolf and Vall\'{e}e, Brigitte},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2018},
  URN =		{urn:nbn:de:0030-drops-86179},
  doi =		{10.4230/LIPIcs.STACS.2018},
  annote =	{Keywords: Mathematics of computing, Theory of computation}
}
Document
Front Matter
DOI: 10.4230/LIPIcs.STACS.2018.0
Front Matter, Table of Contents, Preface, Conference Organization

Authors: Rolf Niedermeier and Brigitte Vallée

Published in: LIPIcs, Volume 96, 35th Symposium on Theoretical Aspects of Computer Science (STACS 2018)

Abstract
Front Matter, Table of Contents, Preface, Conference Organization
Cite as

35th Symposium on Theoretical Aspects of Computer Science (STACS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 96, pp. 0:i-0:xvi, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{niedermeier_et_al:LIPIcs.STACS.2018.0,
  author =	{Niedermeier, Rolf and Vall\'{e}e, Brigitte},
  title =	{{Front Matter, Table of Contents, Preface, Conference Organization}},
  booktitle =	{35th Symposium on Theoretical Aspects of Computer Science (STACS 2018)},
  pages =	{0:i--0:xvi},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-062-0},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{96},
  editor =	{Niedermeier, Rolf and Vall\'{e}e, Brigitte},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2018.0},
  URN =		{urn:nbn:de:0030-drops-84807},
  doi =		{10.4230/LIPIcs.STACS.2018.0},
  annote =	{Keywords: Front Matter, Table of Contents, Preface, Conference Organization}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2017.46
The Power of Linear-Time Data Reduction for Maximum Matching

Authors: George B. Mertzios, André Nichterlein, and Rolf Niedermeier

Published in: LIPIcs, Volume 83, 42nd International Symposium on Mathematical Foundations of Computer Science (MFCS 2017)

Abstract
Finding maximum-cardinality matchings in undirected graphs is arguably one of the most central graph primitives. For m-edge and n-vertex graphs, it is well-known to be solvable in O(m\sqrt{n}) time; however, for several applications this running time is still too slow. We investigate how linear-time (and almost linear-time) data reduction (used as preprocessing) can alleviate the situation. More specifically, we focus on linear-time kernelization. We start a deeper and systematic study both for general graphs and for bipartite graphs. Our data reduction algorithms easily comply (in form of preprocessing) with every solution strategy (exact, approximate, heuristic), thus making them attractive in various settings.
Cite as

George B. Mertzios, André Nichterlein, and Rolf Niedermeier. The Power of Linear-Time Data Reduction for Maximum Matching. In 42nd International Symposium on Mathematical Foundations of Computer Science (MFCS 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 83, pp. 46:1-46:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{mertzios_et_al:LIPIcs.MFCS.2017.46,
  author =	{Mertzios, George B. and Nichterlein, Andr\'{e} and Niedermeier, Rolf},
  title =	{{The Power of Linear-Time Data Reduction for Maximum Matching}},
  booktitle =	{42nd International Symposium on Mathematical Foundations of Computer Science (MFCS 2017)},
  pages =	{46:1--46:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-046-0},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{83},
  editor =	{Larsen, Kim G. and Bodlaender, Hans L. and Raskin, Jean-Francois},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2017.46},
  URN =		{urn:nbn:de:0030-drops-81166},
  doi =		{10.4230/LIPIcs.MFCS.2017.46},
  annote =	{Keywords: Maximum-cardinality matching, bipartite graphs, linear-time algorithms, kernelization, parameterized complexity analysis, FPT in P}
}
Document
DOI: 10.4230/LIPIcs.IPEC.2016.10
A Parameterized Algorithmics Framework for Degree Sequence Completion Problems in Directed Graphs

Authors: Robert Bredereck, Vincent Froese, Marcel Koseler, Marcelo Garlet Millani, André Nichterlein, and Rolf Niedermeier

Published in: LIPIcs, Volume 63, 11th International Symposium on Parameterized and Exact Computation (IPEC 2016)

Abstract
There has been intensive work on the parameterized complexity of the typically NP-hard task to edit undirected graphs into graphs fulfilling certain given vertex degree constraints. In this work, we lift the investigations to the case of directed graphs; herein, we focus on arc insertions. To this end, our general two-stage framework consists of efficiently solving a problem-specific number problem transferring its solution to a solution for the graph problem by applying flow computations. In this way, we obtain fixed-parameter tractability and polynomial kernelizability results, with the central parameter being the maximum vertex in- or outdegree of the output digraph. Although there are certain similarities with the much better studied undirected case, the flow computation used in the directed case seems not to work for the undirected case while f-factor computations as used in the undirected case seem not to work for the directed case.
Cite as

Robert Bredereck, Vincent Froese, Marcel Koseler, Marcelo Garlet Millani, André Nichterlein, and Rolf Niedermeier. A Parameterized Algorithmics Framework for Degree Sequence Completion Problems in Directed Graphs. In 11th International Symposium on Parameterized and Exact Computation (IPEC 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 63, pp. 10:1-10:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{bredereck_et_al:LIPIcs.IPEC.2016.10,
  author =	{Bredereck, Robert and Froese, Vincent and Koseler, Marcel and Millani, Marcelo Garlet and Nichterlein, Andr\'{e} and Niedermeier, Rolf},
  title =	{{A Parameterized Algorithmics Framework for Degree Sequence Completion Problems in Directed Graphs}},
  booktitle =	{11th International Symposium on Parameterized and Exact Computation (IPEC 2016)},
  pages =	{10:1--10:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-023-1},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{63},
  editor =	{Guo, Jiong and Hermelin, Danny},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2016.10},
  URN =		{urn:nbn:de:0030-drops-69353},
  doi =		{10.4230/LIPIcs.IPEC.2016.10},
  annote =	{Keywords: NP-hard graph problem, graph realizability, graph modification, arc insertion, fixed-parameter tractability, kernelization}
}
Document
Complete Volume
DOI: 10.4230/LIPIcs.MFCS.2016
LIPIcs, Volume 58, MFCS'16, Complete Volume

Authors: Piotr Faliszewski, Anca Muscholl, and Rolf Niedermeier

Published in: LIPIcs, Volume 58, 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)

Abstract
LIPIcs, Volume 58, MFCS'16, Complete Volume
Cite as

41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 58, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@Proceedings{faliszewski_et_al:LIPIcs.MFCS.2016,
  title =	{{LIPIcs, Volume 58, MFCS'16, Complete Volume}},
  booktitle =	{41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-016-3},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{58},
  editor =	{Faliszewski, Piotr and Muscholl, Anca and Niedermeier, Rolf},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2016},
  URN =		{urn:nbn:de:0030-drops-65861},
  doi =		{10.4230/LIPIcs.MFCS.2016},
  annote =	{Keywords: Theory of Computation}
}
Document
DOI: 10.4230/LIPIcs.ICALP.2016.25
Fractals for Kernelization Lower Bounds, With an Application to Length-Bounded Cut Problems

Authors: Till Fluschnik, Danny Hermelin, André Nichterlein, and Rolf Niedermeier

Published in: LIPIcs, Volume 55, 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)

Abstract
Bodlaender et al.'s [Bodlaender/Jansen/Kratsch,2014] cross-composition technique is a popular method for excluding polynomial-size problem kernels for NP-hard parameterized problems. We present a new technique exploiting triangle-based fractal structures for extending the range of applicability of cross-compositions. Our technique makes it possible to prove new no-polynomial-kernel results for a number of problems dealing with length-bounded cuts. Roughly speaking, our new technique combines the advantages of serial and parallel composition. In particular, answering an open question of Golovach and Thilikos [Golovach/Thilikos,2011], we show that, unless NP subseteq coNP/poly, the NP-hard Length-Bounded Edge-Cut problem (delete at most k edges such that the resulting graph has no s-t path of length shorter than l) parameterized by the combination of k and l has no polynomial-size problem kernel. Our framework applies to planar as well as directed variants of the basic problems and also applies to both edge and vertex deletion problems.
Cite as

Till Fluschnik, Danny Hermelin, André Nichterlein, and Rolf Niedermeier. Fractals for Kernelization Lower Bounds, With an Application to Length-Bounded Cut Problems. In 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 55, pp. 25:1-25:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{fluschnik_et_al:LIPIcs.ICALP.2016.25,
  author =	{Fluschnik, Till and Hermelin, Danny and Nichterlein, Andr\'{e} and Niedermeier, Rolf},
  title =	{{Fractals for Kernelization Lower Bounds, With an Application to Length-Bounded Cut Problems}},
  booktitle =	{43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)},
  pages =	{25:1--25:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-013-2},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{55},
  editor =	{Chatzigiannakis, Ioannis and Mitzenmacher, Michael and Rabani, Yuval and Sangiorgi, Davide},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2016.25},
  URN =		{urn:nbn:de:0030-drops-63049},
  doi =		{10.4230/LIPIcs.ICALP.2016.25},
  annote =	{Keywords: Parameterized complexity, polynomial-time data reduction, cross-compositions, lower bounds, graph modification problems, interdiction problems}
}
Document
Front Matter
DOI: 10.4230/LIPIcs.MFCS.2016.0
Front Matter, Foreword, Conference Organization, External Reviewers, Table of Contents

Authors: Piotr Faliszewski, Anca Muscholl, and Rolf Niedermeier

Published in: LIPIcs, Volume 58, 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)

Abstract
Front Matter, Foreword, Conference Organization, External Reviewers, Table of Contents
Cite as

41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 58, pp. 0:i-0:xvi, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{faliszewski_et_al:LIPIcs.MFCS.2016.0,
  author =	{Faliszewski, Piotr and Muscholl, Anca and Niedermeier, Rolf},
  title =	{{Front Matter, Foreword, Conference Organization, External Reviewers, Table of Contents}},
  booktitle =	{41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)},
  pages =	{0:i--0:xvi},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-016-3},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{58},
  editor =	{Faliszewski, Piotr and Muscholl, Anca and Niedermeier, Rolf},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2016.0},
  URN =		{urn:nbn:de:0030-drops-64225},
  doi =		{10.4230/LIPIcs.MFCS.2016.0},
  annote =	{Keywords: front matter, foreword, conference organization, external reviewers, table of contents}
}
Document
DOI: 10.4230/LIPIcs.FSTTCS.2015.448
The Parameterized Complexity of the Minimum Shared Edges Problem

Authors: Till Fluschnik, Stefan Kratsch, Rolf Niedermeier, and Manuel Sorge

Published in: LIPIcs, Volume 45, 35th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2015)

Abstract
We study the NP-complete Minimum Shared Edges (MSE) problem. Given an undirected graph, a source and a sink vertex, and two integers p and k, the question is whether there are p paths in the graph connecting the source with the sink and sharing at most k edges. Herein, an edge is shared if it appears in at least two paths. We show that MSE is W[1]-hard when parameterized by the treewidth of the input graph and the number k of shared edges combined. We show that MSE is fixed-parameter tractable with respect to p, but does not admit a polynomial-size kernel (unless NP is a subset of coNP/poly). In the proof of the fixed-parameter tractability of MSE parameterized by p, we employ the treewidth reduction technique due to Marx, O'Sullivan, and Razgon [ACM TALG 2013].
Cite as

Till Fluschnik, Stefan Kratsch, Rolf Niedermeier, and Manuel Sorge. The Parameterized Complexity of the Minimum Shared Edges Problem. In 35th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 45, pp. 448-462, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)

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@InProceedings{fluschnik_et_al:LIPIcs.FSTTCS.2015.448,
  author =	{Fluschnik, Till and Kratsch, Stefan and Niedermeier, Rolf and Sorge, Manuel},
  title =	{{The Parameterized Complexity of the Minimum Shared Edges Problem}},
  booktitle =	{35th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2015)},
  pages =	{448--462},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-97-2},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{45},
  editor =	{Harsha, Prahladh and Ramalingam, G.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2015.448},
  URN =		{urn:nbn:de:0030-drops-56323},
  doi =		{10.4230/LIPIcs.FSTTCS.2015.448},
  annote =	{Keywords: Parameterized complexity, kernelization, treewidth, treewidth reduction}
}
Document
DOI: 10.4230/LIPIcs.IPEC.2015.102
Polynomial Fixed-parameter Algorithms: A Case Study for Longest Path on Interval Graphs

Authors: Archontia C. Giannopoulou, George B. Mertzios, and Rolf Niedermeier

Published in: LIPIcs, Volume 43, 10th International Symposium on Parameterized and Exact Computation (IPEC 2015)

Abstract
We study the design of fixed-parameter algorithms for problems already known to be solvable in polynomial time. The main motivation is to get more efficient algorithms for problems with unattractive polynomial running times. Here, we focus on a fundamental graph problem: Longest Path; it is NP-hard in general but known to be solvable in O(n^4) time on n-vertex interval graphs. We show how to solve Longest Path on Interval Graphs, parameterized by vertex deletion number k to proper interval graphs, in O(k^9n) time. Notably, Longest Path is trivially solvable in linear time on proper interval graphs, and the parameter value k can be approximated up to a factor of 4 in linear time. From a more general perspective, we believe that using parameterized complexity analysis for polynomial-time solvable problems offers a very fertile ground for future studies for all sorts of algorithmic problems. It may enable a refined understanding of efficiency aspects for polynomial-time solvable problems, similarly to what classical parameterized complexity analysis does for NP-hard problems.
Cite as

Archontia C. Giannopoulou, George B. Mertzios, and Rolf Niedermeier. Polynomial Fixed-parameter Algorithms: A Case Study for Longest Path on Interval Graphs. In 10th International Symposium on Parameterized and Exact Computation (IPEC 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 43, pp. 102-113, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)

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@InProceedings{giannopoulou_et_al:LIPIcs.IPEC.2015.102,
  author =	{Giannopoulou, Archontia C. and Mertzios, George B. and Niedermeier, Rolf},
  title =	{{Polynomial Fixed-parameter Algorithms: A Case Study for Longest Path on Interval Graphs}},
  booktitle =	{10th International Symposium on Parameterized and Exact Computation (IPEC 2015)},
  pages =	{102--113},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-92-7},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{43},
  editor =	{Husfeldt, Thore and Kanj, Iyad},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2015.102},
  URN =		{urn:nbn:de:0030-drops-55750},
  doi =		{10.4230/LIPIcs.IPEC.2015.102},
  annote =	{Keywords: fixed-parameter algorithm, preprocessing, data reduction, polynomial-time algorithm, longest path problem, interval graphs, proper interval vertex del}
}
Document
DOI: 10.4230/LIPIcs.STACS.2010.2495
Reflections on Multivariate Algorithmics and Problem Parameterization

Authors: Rolf Niedermeier

Published in: LIPIcs, Volume 5, 27th International Symposium on Theoretical Aspects of Computer Science (2010)

Abstract
Research on parameterized algorithmics for NP-hard problems has steadily grown over the last years. We survey and discuss how parameterized complexity analysis naturally develops into the field of multivariate algorithmics. Correspondingly, we describe how to perform a systematic investigation and exploitation of the ``parameter space'' of computationally hard problems.
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Rolf Niedermeier. Reflections on Multivariate Algorithmics and Problem Parameterization. In 27th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 5, pp. 17-32, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2010)

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@InProceedings{niedermeier:LIPIcs.STACS.2010.2495,
  author =	{Niedermeier, Rolf},
  title =	{{Reflections on Multivariate Algorithmics and Problem Parameterization}},
  booktitle =	{27th International Symposium on Theoretical Aspects of Computer Science},
  pages =	{17--32},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-16-3},
  ISSN =	{1868-8969},
  year =	{2010},
  volume =	{5},
  editor =	{Marion, Jean-Yves and Schwentick, Thomas},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2010.2495},
  URN =		{urn:nbn:de:0030-drops-24952},
  doi =		{10.4230/LIPIcs.STACS.2010.2495},
  annote =	{Keywords: Multivariate algorithmics, problem parameterization}
}
Document
DOI: 10.4230/DagSemProc.09171.1
09171 Abstracts Collection – Adaptive, Output Sensitive, Online and Parameterized Algorithms

Authors: Jérémy Barbay, Rolf Klein, Alejandro López-Ortiz, and Rolf Niedermeier

Published in: Dagstuhl Seminar Proceedings, Volume 9171, Adaptive, Output Sensitive, Online and Parameterized Algorithms (2009)

Abstract
From 19.01. to 24.04.2009, the Dagstuhl Seminar 09171 ``Adaptive, Output Sensitive, Online and Parameterized Algorithms '' was held in Schloss Dagstuhl~--~Leibniz Center for Informatics. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available.
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Jérémy Barbay, Rolf Klein, Alejandro López-Ortiz, and Rolf Niedermeier. 09171 Abstracts Collection – Adaptive, Output Sensitive, Online and Parameterized Algorithms. In Adaptive, Output Sensitive, Online and Parameterized Algorithms. Dagstuhl Seminar Proceedings, Volume 9171, pp. 1-11, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)

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@InProceedings{barbay_et_al:DagSemProc.09171.1,
  author =	{Barbay, J\'{e}r\'{e}my and Klein, Rolf and L\'{o}pez-Ortiz, Alejandro and Niedermeier, Rolf},
  title =	{{09171 Abstracts Collection  – Adaptive, Output Sensitive, Online and Parameterized Algorithms}},
  booktitle =	{Adaptive, Output Sensitive, Online and Parameterized Algorithms},
  pages =	{1--11},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2009},
  volume =	{9171},
  editor =	{J\'{e}r\'{e}my Barbay and Rolf Klein and Alejandro Ortiz-L\'{o}pez and Rolf Niedermeier},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/DagSemProc.09171.1},
  URN =		{urn:nbn:de:0030-drops-21228},
  doi =		{10.4230/DagSemProc.09171.1},
  annote =	{Keywords: Adaptive analysis, instance optimal algoritms, fixed parameter tractable, output sensitive algorithms}
}
Document
DOI: 10.4230/DagSemProc.09171.2
09171 Executive Summary – Adaptive, Output Sensitive, Online and Parameterized Algorithms

Authors: Jérémy Barbay, Rolf Klein, Alejandro López-Ortiz, and Rolf Niedermeier

Published in: Dagstuhl Seminar Proceedings, Volume 9171, Adaptive, Output Sensitive, Online and Parameterized Algorithms (2009)

Abstract
Traditionally the analysis of algorithms measures the complexity of a problem or algorithm in terms of the worst-case behavior over all inputs of a given size. However, in certain cases an improved algorithm can be obtained by considering a finer partition of the input space. As this idea has been independently rediscovered in many areas, the workshop gathered participants from different fields in order to explore the impact and the limits of this technique, in the hope to spring new collaboration and to seed the unification of the technique.
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Jérémy Barbay, Rolf Klein, Alejandro López-Ortiz, and Rolf Niedermeier. 09171 Executive Summary – Adaptive, Output Sensitive, Online and Parameterized Algorithms. In Adaptive, Output Sensitive, Online and Parameterized Algorithms. Dagstuhl Seminar Proceedings, Volume 9171, p. 1, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)

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@InProceedings{barbay_et_al:DagSemProc.09171.2,
  author =	{Barbay, J\'{e}r\'{e}my and Klein, Rolf and L\'{o}pez-Ortiz, Alejandro and Niedermeier, Rolf},
  title =	{{09171 Executive Summary – Adaptive, Output Sensitive, Online and Parameterized Algorithms}},
  booktitle =	{Adaptive, Output Sensitive, Online and Parameterized Algorithms},
  pages =	{1--1},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2009},
  volume =	{9171},
  editor =	{J\'{e}r\'{e}my Barbay and Rolf Klein and Alejandro Ortiz-L\'{o}pez and Rolf Niedermeier},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/DagSemProc.09171.2},
  URN =		{urn:nbn:de:0030-drops-21207},
  doi =		{10.4230/DagSemProc.09171.2},
  annote =	{Keywords: Adaptive analysis, instance optimal algorithms, fixed parameter tractable, output sensitive algorithms}
}
Document
DOI: 10.4230/LIPIcs.STACS.2009.1820
A Generalization of Nemhauser and Trotter's Local Optimization Theorem

Authors: Michael R. Fellows, Jiong Guo, Hannes Moser, and Rolf Niedermeier

Published in: LIPIcs, Volume 3, 26th International Symposium on Theoretical Aspects of Computer Science (2009)

Abstract
The Nemhauser-Trotter local optimization theorem applies to the NP-hard \textsc{Vertex Cover} problem and has applications in approximation as well as parameterized algorithmics. We present a framework that generalizes Nemhauser and Trotter's result to vertex deletion and graph packing problems, introducing novel algorithmic strategies based on purely combinatorial arguments (not referring to linear programming as the Nemhauser-Trotter result originally did). We exhibit our framework using a generalization of \textsc{Vertex Cover}, called \textrm{\sc Bounded-Degree Deletion}, that has promise to become an important tool in the analysis of gene and other biological networks. For some fixed~$d\geq 0$, \textrm{\sc Bounded-Degree Deletion} asks to delete as few vertices as possible from a graph in order to transform it into a graph with maximum vertex degree at most~$d$. \textsc{Vertex Cover} is the special case of $d=0$. Our generalization of the Nemhauser-Trotter theorem implies that \textrm{\sc Bounded-Degree Deletion} has a problem kernel with a linear number of vertices for every constant~$d$. We also outline an application of our extremal combinatorial approach to the problem of packing stars with a bounded number of leaves. Finally, charting the border between (parameterized) tractability and intractability for \textrm{\sc Bounded-Degree Deletion}, we provide a W[2]-hardness result for \textrm{\sc Bounded-Degree Deletion} in case of unbounded $d$-values.
Cite as

Michael R. Fellows, Jiong Guo, Hannes Moser, and Rolf Niedermeier. A Generalization of Nemhauser and Trotter's Local Optimization Theorem. In 26th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 3, pp. 409-420, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)

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@InProceedings{fellows_et_al:LIPIcs.STACS.2009.1820,
  author =	{Fellows, Michael R. and Guo, Jiong and Moser, Hannes and Niedermeier, Rolf},
  title =	{{A Generalization of Nemhauser and Trotter's Local Optimization Theorem}},
  booktitle =	{26th International Symposium on Theoretical Aspects of Computer Science},
  pages =	{409--420},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-09-5},
  ISSN =	{1868-8969},
  year =	{2009},
  volume =	{3},
  editor =	{Albers, Susanne and Marion, Jean-Yves},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2009.1820},
  URN =		{urn:nbn:de:0030-drops-18200},
  doi =		{10.4230/LIPIcs.STACS.2009.1820},
  annote =	{Keywords: Algorithms, Computational complexity, NP-hard problems, W\lbrack2\rbrack-completeness, Graph problems, Combinatorial optimization, Fixed-parameter tractability, K}
}
Document
DOI: 10.4230/DagSemRep.316
Parameterized Complexity (Dagstuhl Seminar 01311)

Authors: Rodney G. Downey, Michael R. Fellows, Rolf Niedermeier, and Peter Rossmanith

Published in: Dagstuhl Seminar Reports. Dagstuhl Seminar Reports, Volume 1 (2021)

Abstract
Cite as

Rodney G. Downey, Michael R. Fellows, Rolf Niedermeier, and Peter Rossmanith. Parameterized Complexity (Dagstuhl Seminar 01311). Dagstuhl Seminar Report 316, pp. 1-28, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2002)

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@TechReport{downey_et_al:DagSemRep.316,
  author =	{Downey, Rodney G. and Fellows, Michael R. and Niedermeier, Rolf and Rossmanith, Peter},
  title =	{{Parameterized Complexity (Dagstuhl Seminar 01311)}},
  pages =	{1--28},
  ISSN =	{1619-0203},
  year =	{2002},
  type = 	{Dagstuhl Seminar Report},
  number =	{316},
  institution =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/DagSemRep.316},
  URN =		{urn:nbn:de:0030-drops-152009},
  doi =		{10.4230/DagSemRep.316},
}
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