14 Search Results for "Daniel, Rolf"


Document
Invited Talk
Amortised Analysis of Dynamic Data Structures (Invited Talk)

Authors: Eva Rotenberg

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


Abstract
In dynamic data structures, one is interested in efficiently facilitating queries to a data set, while being able to efficiently perform updates as the data set undergoes changes. Often, relaxing the efficiency measure to the amortised setting allows for simpler algorithms. A well-known example of a data structure with amortised guarantees is the splay tree by Sleator and Tarjan [Daniel D. Sleator and Robert E. Tarjan, 1985]. Similarly, in data structures for dynamic graphs, one is interested in efficiently maintaining some information about the graph, or facilitating queries, as the graph undergoes changes in the form of insertion and deletion of edges. Examples of such information include connectivity, planarity, and approximate sparsity of the graph: is the graph presently connected? Is it planar? Has its arboricity grossly exceeded some specified number α̃? The related queries could be: is a connected to b? Are the edges uv and uw consecutive in the ordering around u in its current planar embedding? Or, report the O(α) out-edges of vertex x. In this talk, we will see Brodal and Fagerberg’s amortised algorithm for orienting sparse graphs (i.e. of arboricity ≤ α), so that each vertex has O(α) out-edges [Gerth Stølting Brodal and Rolf Fagerberg, 1999]. The algorithm itself is extremely simple, and uses an elegant amortised argument in its analysis. Then, we will visit the problem of dynamic planarity testing: is the graph presently planar? Here, we will see an elegant amortised reduction to the seemingly easier problem, where planarity-violating edges may be detected and rejected [Eppstein et al., 1996]. We will see a sketch of how the current state-of-the-art algorithm for efficient planarity testing [Jacob Holm and Eva Rotenberg, 2020] uses ideas similar to those in [Gerth Stølting Brodal and Rolf Fagerberg, 1999] to analyse the behaviour of a greedy algorithm via a possibly inefficient algorithm with provably low recourse [Jacob Holm and Eva Rotenberg, 2020]. If time permits, we will touch upon a recent simple amortised data structure for maintaining information in dynamic forests [Jacob Holm et al., 2023], which builds on ideas from splay trees. The talk concludes with some open questions in the area.

Cite as

Eva Rotenberg. Amortised Analysis of Dynamic Data Structures (Invited Talk). In 40th International Symposium on Theoretical Aspects of Computer Science (STACS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 254, pp. 2:1-2:2, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


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@InProceedings{rotenberg:LIPIcs.STACS.2023.2,
  author =	{Rotenberg, Eva},
  title =	{{Amortised Analysis of Dynamic Data Structures}},
  booktitle =	{40th International Symposium on Theoretical Aspects of Computer Science (STACS 2023)},
  pages =	{2:1--2:2},
  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.2023.2},
  URN =		{urn:nbn:de:0030-drops-176547},
  doi =		{10.4230/LIPIcs.STACS.2023.2},
  annote =	{Keywords: Amortised analysis, splaying, dynamic graphs, planarity testing}
}
Document
Erdös-Pósa Property of Obstructions to Interval Graphs

Authors: Akanksha Agrawal, Daniel Lokshtanov, Pranabendu Misra, Saket Saurabh, and Meirav Zehavi

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


Abstract
The duality between packing and covering problems lies at the heart of fundamental combinatorial proofs, as well as well-known algorithmic methods such as the primal-dual method for approximation and win/win-approach for parameterized analysis. The very essence of this duality is encompassed by a well-known property called the Erdös-Pósa property, which has been extensively studied for over five decades. Informally, we say that a class of graphs F admits the Erdös-Pósa property if there exists f such that for any graph G, either G has vertex-disjoint "copies" of the graphs in F, or there is a set S \subseteq V(G) of f(k) vertices that intersects all copies of the graphs in F. In the context of any graph class G, the most natural question that arises in this regard is as follows - do obstructions to G have the Erdös-Pósa property? Having this view in mind, we focus on the class of interval graphs. Structural properties of interval graphs are intensively studied, also as they lead to the design of polynomial-time algorithms for classic problems that are NP-hard on general graphs. Nevertheless, about one of the most basic properties of such graphs, namely, the Erdös-Pósa property, nothing is known. In this paper, we settle this anomaly: we prove that the family of obstructions to interval graphs - namely, the family of chordless cycles and ATs---admits the Erdös-Pósa property. Our main theorem immediately results in an algorithm to decide whether an input graph G has vertex-disjoint ATs and chordless cycles, or there exists a set of O(k^2 log k) vertices in G that hits all ATs and chordless cycles.

Cite as

Akanksha Agrawal, Daniel Lokshtanov, Pranabendu Misra, Saket Saurabh, and Meirav Zehavi. Erdös-Pósa Property of Obstructions to Interval Graphs. In 35th Symposium on Theoretical Aspects of Computer Science (STACS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 96, pp. 7:1-7:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)


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@InProceedings{agrawal_et_al:LIPIcs.STACS.2018.7,
  author =	{Agrawal, Akanksha and Lokshtanov, Daniel and Misra, Pranabendu and Saurabh, Saket and Zehavi, Meirav},
  title =	{{Erd\"{o}s-P\'{o}sa Property of Obstructions to Interval Graphs}},
  booktitle =	{35th Symposium on Theoretical Aspects of Computer Science (STACS 2018)},
  pages =	{7:1--7:15},
  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.2018.7},
  URN =		{urn:nbn:de:0030-drops-84815},
  doi =		{10.4230/LIPIcs.STACS.2018.7},
  annote =	{Keywords: Interval Graphs, Obstructions, Erd\"{o}s-P\'{o}sa Property}
}
Document
Finding List Homomorphisms from Bounded-treewidth Graphs to Reflexive Graphs: a Complete Complexity Characterization

Authors: László Egri, Dániel Marx, and Pawel Rzazewski

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


Abstract
In the list homomorphism problem, the input consists of two graphs G and H, together with a list L(v) \subseteq V(H) for every vertex v \in V(G). The task is to find a homomorphism phi:V(G) -> V(H) respecting the lists, that is, we have that phi(v) \in L(v) for every v \in V(H) and if u and v are adjacent in G, then phi(u) and phi(v) are adjacent in H. If H is a fixed graph, then the problem is denoted LHom(H). We consider the reflexive version of the problem, where we assume that every vertex in H has a self-loop. If is known that reflexive LHom(H) is polynomial-time solvable if H is an interval graph and it is NP-complete otherwise [Feder and Hell, JCTB 1998]. We explore the complexity of the problem parameterized by the treewidth tw(G) of the input graph G. If a tree decomposition of G of width tw(G) is given in the input, then the problem can be solved in time |V(H)|^{tw(G)} n^{O(1)} by naive dynamic programming. Our main result completely reveals when and by exactly how much this naive algorithm can be improved. We introduce a simple combinatorial invariant i^*(H), which is based on the existence of decompositions and incomparable sets, and show that this number should appear as the base of the exponent in the best possible running time. Specifically, we prove for every fixed non-interval graph H that * If a tree decomposition of width tw(G) is given in the input, then the problem can be solved in time i^*(H)^{tw(G)} n^{O(1)}. * Assuming the Strong Exponential-Time Hypothesis (SETH), the probem cannot be solved in time (i^*(H)-epsilon)^{tw(G)} n^{O(1)} for any epsilon>0. Thus by matching upper and lower bounds, our result exactly characterizes for every fixed H the complexity of reflexive LHom(H) parameterized by treewidth.

Cite as

László Egri, Dániel Marx, and Pawel Rzazewski. Finding List Homomorphisms from Bounded-treewidth Graphs to Reflexive Graphs: a Complete Complexity Characterization. In 35th Symposium on Theoretical Aspects of Computer Science (STACS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 96, pp. 27:1-27:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)


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@InProceedings{egri_et_al:LIPIcs.STACS.2018.27,
  author =	{Egri, L\'{a}szl\'{o} and Marx, D\'{a}niel and Rzazewski, Pawel},
  title =	{{Finding List Homomorphisms from Bounded-treewidth Graphs to Reflexive Graphs: a Complete Complexity Characterization}},
  booktitle =	{35th Symposium on Theoretical Aspects of Computer Science (STACS 2018)},
  pages =	{27:1--27:15},
  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.2018.27},
  URN =		{urn:nbn:de:0030-drops-84867},
  doi =		{10.4230/LIPIcs.STACS.2018.27},
  annote =	{Keywords: graph homomorphism, list homomorphism, reflexive graph, treewidth}
}
Document
Automata Theory on Sliding Windows

Authors: Moses Ganardi, Danny Hucke, Daniel König, Markus Lohrey, and Konstantinos Mamouras

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


Abstract
In a recent paper we analyzed the space complexity of streaming algorithms whose goal is to decide membership of a sliding window to a fixed language. For the class of regular languages we proved a space trichotomy theorem: for every regular language the optimal space bound is either constant, logarithmic or linear. In this paper we continue this line of research: We present natural characterizations for the constant and logarithmic space classes and establish tight relationships to the concept of language growth. We also analyze the space complexity with respect to automata size and prove almost matching lower and upper bounds. Finally, we consider the decision problem whether a language given by a DFA/NFA admits a sliding window algorithm using logarithmic/constant space.

Cite as

Moses Ganardi, Danny Hucke, Daniel König, Markus Lohrey, and Konstantinos Mamouras. Automata Theory on Sliding Windows. In 35th Symposium on Theoretical Aspects of Computer Science (STACS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 96, pp. 31:1-31:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)


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@InProceedings{ganardi_et_al:LIPIcs.STACS.2018.31,
  author =	{Ganardi, Moses and Hucke, Danny and K\"{o}nig, Daniel and Lohrey, Markus and Mamouras, Konstantinos},
  title =	{{Automata Theory on Sliding Windows}},
  booktitle =	{35th Symposium on Theoretical Aspects of Computer Science (STACS 2018)},
  pages =	{31:1--31:14},
  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.2018.31},
  URN =		{urn:nbn:de:0030-drops-84851},
  doi =		{10.4230/LIPIcs.STACS.2018.31},
  annote =	{Keywords: regular languages, sliding window algorithms}
}
Document
Knapsack Problems for Wreath Products

Authors: Moses Ganardi, Daniel König, Markus Lohrey, and Georg Zetzsche

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


Abstract
In recent years, knapsack problems for (in general non-commutative) groups have attracted attention. In this paper, the knapsack problem for wreath products is studied. It turns out that decidability of knapsack is not preserved under wreath product. On the other hand, the class of knapsack-semilinear groups, where solutions sets of knapsack equations are effectively semilinear, is closed under wreath product. As a consequence, we obtain the decidability of knapsack for free solvable groups. Finally, it is shown that for every non-trivial abelian group G, knapsack (as well as the related subset sum problem) for the wreath product G \wr Z is NP-complete.

Cite as

Moses Ganardi, Daniel König, Markus Lohrey, and Georg Zetzsche. Knapsack Problems for Wreath Products. In 35th Symposium on Theoretical Aspects of Computer Science (STACS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 96, pp. 32:1-32:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)


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@InProceedings{ganardi_et_al:LIPIcs.STACS.2018.32,
  author =	{Ganardi, Moses and K\"{o}nig, Daniel and Lohrey, Markus and Zetzsche, Georg},
  title =	{{Knapsack Problems for Wreath Products}},
  booktitle =	{35th Symposium on Theoretical Aspects of Computer Science (STACS 2018)},
  pages =	{32:1--32:13},
  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.2018.32},
  URN =		{urn:nbn:de:0030-drops-85201},
  doi =		{10.4230/LIPIcs.STACS.2018.32},
  annote =	{Keywords: knapsack, wreath products, decision problems in group theory}
}
Document
Colouring Square-Free Graphs without Long Induced Paths

Authors: Serge Gaspers, Shenwei Huang, and Daniel Paulusma

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


Abstract
The Colouring problem is to decide if the vertices of a graph can be coloured with at most k colours for a given integer k such that no two adjacent vertices are coloured alike. The complexity of Colouring is fully understood for graph classes characterized by one forbidden induced subgraph H. Despite a huge body of existing work, there are still major complexity gaps if two induced subgraphs H_1 and H_2 are forbidden. We let H_1 be the s-vertex cycle C_s and H_2 be the t-vertex path P_t. We show that Colouring is polynomial-time solvable for s=4 and t<=6, which unifies several known results for Colouring on (H_1,H_2)-free graphs. Our algorithm is based on a novel decomposition theorem for (C_4,P_6)-free graphs without clique cutsets into homogeneous pairs of sets and a new framework for bounding the clique-width of a graph by the clique-width of its subgraphs induced by homogeneous pairs of sets. To apply this framework, we also need to use divide-and-conquer to bound the clique-width of subgraphs induced by homogeneous pairs of sets. To complement our positive result we also prove that Colouring is NP-complete for s=4 and t>=9, which is the first hardness result on Colouring for (C_4,P_t)-free graphs.

Cite as

Serge Gaspers, Shenwei Huang, and Daniel Paulusma. Colouring Square-Free Graphs without Long Induced Paths. In 35th Symposium on Theoretical Aspects of Computer Science (STACS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 96, pp. 35:1-35:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)


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@InProceedings{gaspers_et_al:LIPIcs.STACS.2018.35,
  author =	{Gaspers, Serge and Huang, Shenwei and Paulusma, Daniel},
  title =	{{Colouring Square-Free Graphs without Long Induced Paths}},
  booktitle =	{35th Symposium on Theoretical Aspects of Computer Science (STACS 2018)},
  pages =	{35:1--35:15},
  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.2018.35},
  URN =		{urn:nbn:de:0030-drops-84922},
  doi =		{10.4230/LIPIcs.STACS.2018.35},
  annote =	{Keywords: graph colouring, hereditary graph class, clique-width, cycle, path}
}
Document
Surjective H-Colouring over Reflexive Digraphs

Authors: Benoit Larose, Barnaby Martin, and Daniel Paulusma

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


Abstract
The Surjective H-Colouring problem is to test if a given graph allows a vertex-surjective homomorphism to a fixed graph H. The complexity of this problem has been well studied for undirected (partially) reflexive graphs. We introduce endo-triviality, the property of a structure that all of its endomorphisms that do not have range of size 1 are automorphisms, as a means to obtain complexity-theoretic classifications of Surjective H-Colouring in the case of reflexive digraphs. Chen [2014] proved, in the setting of constraint satisfaction problems, that Surjective H-Colouring is NP-complete if H has the property that all of its polymorphisms are essentially unary. We give the first concrete application of his result by showing that every endo-trivial reflexive digraph H has this property. We then use the concept of endo-triviality to prove, as our main result, a dichotomy for Surjective H-Colouring when H is a reflexive tournament: if H is transitive, then Surjective H-Colouring is in NL, otherwise it is NP-complete. By combining this result with some known and new results we obtain a complexity classification for Surjective H-Colouring when H is a partially reflexive digraph of size at most 3.

Cite as

Benoit Larose, Barnaby Martin, and Daniel Paulusma. Surjective H-Colouring over Reflexive Digraphs. In 35th Symposium on Theoretical Aspects of Computer Science (STACS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 96, pp. 49:1-49:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)


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@InProceedings{larose_et_al:LIPIcs.STACS.2018.49,
  author =	{Larose, Benoit and Martin, Barnaby and Paulusma, Daniel},
  title =	{{Surjective H-Colouring over Reflexive Digraphs}},
  booktitle =	{35th Symposium on Theoretical Aspects of Computer Science (STACS 2018)},
  pages =	{49:1--49:14},
  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.2018.49},
  URN =		{urn:nbn:de:0030-drops-84882},
  doi =		{10.4230/LIPIcs.STACS.2018.49},
  annote =	{Keywords: Surjective H-Coloring, Computational Complexity, Algorithmic Graph Theory, Universal Algebra, Constraint Satisfaction}
}
Document
Routing with Congestion in Acyclic Digraphs

Authors: Saeed Akhoondian Amiri, Stephan Kreutzer, Dániel Marx, and Roman Rabinovich

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


Abstract
We study the version of the k-disjoint paths problem where k demand pairs (s_1,t_1), ..., (s_k,t_k) are specified in the input and the paths in the solution are allowed to intersect, but such that no vertex is on more than c paths. We show that on directed acyclic graphs the problem is solvable in time n^{O(d)} if we allow congestion k-d for k paths. Furthermore, we show that, under a suitable complexity theoretic assumption, the problem cannot be solved in time f(k)n^{o(d*log(d))} for any computable function f.

Cite as

Saeed Akhoondian Amiri, Stephan Kreutzer, Dániel Marx, and Roman Rabinovich. Routing with Congestion in Acyclic Digraphs. In 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 58, pp. 7:1-7:11, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)


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@InProceedings{amiri_et_al:LIPIcs.MFCS.2016.7,
  author =	{Amiri, Saeed Akhoondian and Kreutzer, Stephan and Marx, D\'{a}niel and Rabinovich, Roman},
  title =	{{Routing with Congestion in Acyclic Digraphs}},
  booktitle =	{41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)},
  pages =	{7:1--7:11},
  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.2016.7},
  URN =		{urn:nbn:de:0030-drops-64244},
  doi =		{10.4230/LIPIcs.MFCS.2016.7},
  annote =	{Keywords: algorithms, disjoint paths, congestion, acyclic digraphs, XP, W\lbrack1\rbrack-hard}
}
Document
On the Complexity of Probabilistic Trials for Hidden Satisfiability Problems

Authors: Itai Arad, Adam Bouland, Daniel Grier, Miklos Santha, Aarthi Sundaram, and Shengyu Zhang

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


Abstract
What is the minimum amount of information and time needed to solve 2SAT? When the instance is known, it can be solved in polynomial time, but is this also possible without knowing the instance? Bei, Chen and Zhang (STOC'13) considered a model where the input is accessed by proposing possible assignments to a special oracle. This oracle, on encountering some constraint unsatisfied by the proposal, returns only the constraint index. It turns out that, in this model, even 1SAT cannot be solved in polynomial time unless P=NP. Hence, we consider a model in which the input is accessed by proposing probability distributions over assignments to the variables. The oracle then returns the index of the constraint that is most likely to be violated by this distribution. We show that the information obtained this way is sufficient to solve 1SAT in polynomial time, even when the clauses can be repeated. For 2SAT, as long as there are no repeated clauses, in polynomial time we can even learn an equivalent formula for the hidden instance and hence also solve it. Furthermore, we extend these results to the quantum regime. We show that in this setting 1QSAT can be solved in polynomial time up to constant precision, and 2QSAT can be learnt in polynomial time up to inverse polynomial precision.

Cite as

Itai Arad, Adam Bouland, Daniel Grier, Miklos Santha, Aarthi Sundaram, and Shengyu Zhang. On the Complexity of Probabilistic Trials for Hidden Satisfiability Problems. In 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 58, pp. 12:1-12:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)


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@InProceedings{arad_et_al:LIPIcs.MFCS.2016.12,
  author =	{Arad, Itai and Bouland, Adam and Grier, Daniel and Santha, Miklos and Sundaram, Aarthi and Zhang, Shengyu},
  title =	{{On the Complexity of Probabilistic Trials for Hidden Satisfiability Problems}},
  booktitle =	{41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)},
  pages =	{12:1--12:14},
  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.2016.12},
  URN =		{urn:nbn:de:0030-drops-64284},
  doi =		{10.4230/LIPIcs.MFCS.2016.12},
  annote =	{Keywords: computational complexity, satisfiability problems, trial and error, quantum computing, learning theory}
}
Document
Using Contracted Solution Graphs for Solving Reconfiguration Problems

Authors: Paul Bonsma and Daniël Paulusma

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


Abstract
We introduce a dynamic programming method for solving reconfiguration problems, based on contracted solution graphs, which are obtained from solution graphs by performing an appropriate series of edge contractions that decrease the graph size without losing any critical information needed to solve the reconfiguration problem under consideration. As an example, we consider a well-studied problem: given two k-colorings alpha and beta of a graph G, can alpha be modified into beta by recoloring one vertex of G at a time, while maintaining a k-coloring throughout? By applying our method in combination with a thorough exploitation of the graph structure we obtain a polynomial-time algorithm for (k-2)-connected chordal graphs.

Cite as

Paul Bonsma and Daniël Paulusma. Using Contracted Solution Graphs for Solving Reconfiguration Problems. In 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 58, pp. 20:1-20:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)


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@InProceedings{bonsma_et_al:LIPIcs.MFCS.2016.20,
  author =	{Bonsma, Paul and Paulusma, Dani\"{e}l},
  title =	{{Using Contracted Solution Graphs for Solving Reconfiguration Problems}},
  booktitle =	{41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)},
  pages =	{20:1--20:15},
  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.2016.20},
  URN =		{urn:nbn:de:0030-drops-64351},
  doi =		{10.4230/LIPIcs.MFCS.2016.20},
  annote =	{Keywords: reconfiguration, contraction, dynamic programming, graph coloring}
}
Document
Competitive Packet Routing with Priority Lists

Authors: Tobias Harks, Britta Peis, Daniel Schmand, and Laura Vargas Koch

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


Abstract
In competitive packet routing games, packets are routed selfishly through a network and scheduling policies at edges determine which packages are forwarded first if there is not enough capacity on an edge to forward all packages at once. We analyze the impact of priority lists on the worst-case quality of pure Nash equilibria. A priority list is an ordered list of players that may or may not depend on the edge. Whenever the number of packets entering an edge exceeds the inflow capacity, packets are processed in list order. We derive several new bounds on the price of anarchy and stability for global and local priority policies. We also consider the question of the complexity of computing an optimal priority list. It turns out that even for very restricted cases, i.e., for routing on a tree, the computation of an optimal priority list is APX-hard.

Cite as

Tobias Harks, Britta Peis, Daniel Schmand, and Laura Vargas Koch. Competitive Packet Routing with Priority Lists. In 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 58, pp. 49:1-49:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)


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@InProceedings{harks_et_al:LIPIcs.MFCS.2016.49,
  author =	{Harks, Tobias and Peis, Britta and Schmand, Daniel and Vargas Koch, Laura},
  title =	{{Competitive Packet Routing with Priority Lists}},
  booktitle =	{41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)},
  pages =	{49:1--49:14},
  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.2016.49},
  URN =		{urn:nbn:de:0030-drops-64622},
  doi =		{10.4230/LIPIcs.MFCS.2016.49},
  annote =	{Keywords: packet routing, Nash equilibrium, price of anarchy, priority policy, complexity}
}
Document
Dinucleotide distance histograms for fast detection of rRNA in metatranscriptomic sequences

Authors: Heiner Klingenberg, Robin Martinjak, Frank Oliver Glöckner, Rolf Daniel, Thomas Lingner, and Peter Meinicke

Published in: OASIcs, Volume 34, German Conference on Bioinformatics 2013


Abstract
With the advent of metatranscriptomics it has now become possible to study the dynamics of microbial communities. The analysis of environmental RNA-Seq data implies several challenges for the development of efficient tools in bioinformatics. One of the first steps in the computational analysis of metatranscriptomic sequencing reads requires the separation of rRNA and mRNA fragments to ensure that only protein coding sequences are actually used in a subsequent functional analysis. In the context of the rRNA filtering task it is desirable to have a broad spectrum of different methods in order to find a suitable trade-off between speed and accuracy for a particular dataset. We introduce a machine learning approach for the detection of rRNA in metatranscriptomic sequencing reads that is based on support vector machines in combination with dinucleotide distance histograms for feature representation. The results show that our SVM-based approach is at least one order of magnitude faster than any of the existing tools with only a slight degradation of the detection performance when compared to state-of-the-art alignment-based methods.

Cite as

Heiner Klingenberg, Robin Martinjak, Frank Oliver Glöckner, Rolf Daniel, Thomas Lingner, and Peter Meinicke. Dinucleotide distance histograms for fast detection of rRNA in metatranscriptomic sequences. In German Conference on Bioinformatics 2013. Open Access Series in Informatics (OASIcs), Volume 34, pp. 80-89, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2013)


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@InProceedings{klingenberg_et_al:OASIcs.GCB.2013.80,
  author =	{Klingenberg, Heiner and Martinjak, Robin and Gl\"{o}ckner, Frank Oliver and Daniel, Rolf and Lingner, Thomas and Meinicke, Peter},
  title =	{{Dinucleotide distance histograms for fast detection of rRNA in metatranscriptomic sequences}},
  booktitle =	{German Conference on Bioinformatics 2013},
  pages =	{80--89},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-939897-59-0},
  ISSN =	{2190-6807},
  year =	{2013},
  volume =	{34},
  editor =	{Bei{\ss}barth, Tim and Kollmar, Martin and Leha, Andreas and Morgenstern, Burkhard and Schultz, Anne-Kathrin and Waack, Stephan and Wingender, Edgar},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/OASIcs.GCB.2013.80},
  URN =		{urn:nbn:de:0030-drops-42324},
  doi =		{10.4230/OASIcs.GCB.2013.80},
  annote =	{Keywords: Metatranscriptomics, metagenomics, rRNA detection, distance histograms}
}
Document
Formal Verification of Abstract SystemC Models

Authors: Daniel Grosse, Hoang M. Le, and Rolf Drechsler

Published in: Dagstuhl Seminar Proceedings, Volume 9461, Algorithms and Applications for Next Generation SAT Solvers (2010)


Abstract
In this paper we present a formal verification approach for abstract SystemC models. The approach allows checking expressive properties and lifts induction known from bounded model checking to a higher level, to cope with the large state space of abstract SystemC programs. The technique is tightly integrated with our SystemC to C transformation and generation of monitoring logic to form a complete and efficient method. Properties specifying both hardware and software aspects, e.g. pre- and post-conditions as well as temporal relations of transactions and events, can be specified. As shown by experiments modern proof techniques allow verifying important non-trivial behavior. Moreover, our inductive technique gives significant speed-ups in comparison to simple methods.

Cite as

Daniel Grosse, Hoang M. Le, and Rolf Drechsler. Formal Verification of Abstract SystemC Models. In Algorithms and Applications for Next Generation SAT Solvers. Dagstuhl Seminar Proceedings, Volume 9461, pp. 1-2, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2010)


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@InProceedings{grosse_et_al:DagSemProc.09461.2,
  author =	{Grosse, Daniel and Le, Hoang M. and Drechsler, Rolf},
  title =	{{Formal Verification of Abstract SystemC Models}},
  booktitle =	{Algorithms and Applications for Next Generation SAT Solvers},
  pages =	{1--2},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2010},
  volume =	{9461},
  editor =	{Bernd Becker and Valeria Bertacoo and Rolf Drechsler and Masahiro Fujita},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/DagSemProc.09461.2},
  URN =		{urn:nbn:de:0030-drops-25102},
  doi =		{10.4230/DagSemProc.09461.2},
  annote =	{Keywords: SystemC, TLM, BMC, SAT, SMT}
}
Document
SAT-based Automatic Test Pattern Generation

Authors: Rolf Drechsler, Stephan Eggersglüß, Görschwin Fey, and Daniel Tille

Published in: Dagstuhl Seminar Proceedings, Volume 8351, Evolutionary Test Generation (2009)


Abstract
Due to the rapidly growing size of integrated circuits, there is a need for new algorithms for Automatic Test Pattern Generation (ATPG). While classical algorithms reach their limit, there have been recent advances in algorithms to solve Boolean Satisfiability (SAT). Because Boolean SAT solvers are working on Conjunctive Normal Forms (CNF), the problem has to be transformed. During transformation, relevant information about the problem might get lost and therefore is not available in the solving process. In the following we briefly motivate the problem and provide the latest developments in the field. The technique was implemented and experimental results are presented. The approach was combined with the ATPG framework of NXP Semiconductors. Significant improvements in overall performance and robustness are demonstrated.

Cite as

Rolf Drechsler, Stephan Eggersglüß, Görschwin Fey, and Daniel Tille. SAT-based Automatic Test Pattern Generation. In Evolutionary Test Generation. Dagstuhl Seminar Proceedings, Volume 8351, pp. 1-2, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)


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@InProceedings{drechsler_et_al:DagSemProc.08351.6,
  author =	{Drechsler, Rolf and Eggersgl\"{u}{\ss}, Stephan and Fey, G\"{o}rschwin and Tille, Daniel},
  title =	{{SAT-based Automatic Test Pattern Generation}},
  booktitle =	{Evolutionary Test Generation},
  pages =	{1--2},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2009},
  volume =	{8351},
  editor =	{Holger Schlingloff and Tanja E. J. Vos and Joachim Wegener},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/DagSemProc.08351.6},
  URN =		{urn:nbn:de:0030-drops-20152},
  doi =		{10.4230/DagSemProc.08351.6},
  annote =	{Keywords: Circuit, ATPG, SAT, Boolean Satisfiability}
}
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