10 Search Results for "Fischbeck, Philipp"

Document
DOI: 10.4230/LIPIcs.STACS.2026.11
The Diameter of (Threshold) Geometric Inhomogeneous Random Graphs

Authors: Zylan Benjert, Kostas Lakis, Johannes Lengler, and Raghu Raman Ravi

Published in: LIPIcs, Volume 364, 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)

Abstract
We prove that the diameter of threshold (zero temperature) Geometric Inhomogeneous Random Graphs (GIRG) is asymptotically almost surely Θ(log n). This has strong implications for the runtime of many distributed protocols on those graphs, which often have runtimes bounded as a function of the diameter. The GIRG model exhibits many properties empirically found in real-world networks, and the runtime of various practical algorithms has empirically been found to scale in the same way for GIRG and for real-world networks, in particular related to computing distances, diameter, clustering, cliques and chromatic numbers. Thus the GIRG model is a promising candidate for deriving insight about the performance of algorithms in real-world instances. The diameter was previously only known in the one-dimensional case, and the proof relied very heavily on dimension one. Our proof employs a similar Peierls-type argument alongside a novel renormalization scheme. Moreover, instead of using topological arguments (which become complicated in high dimensions) in establishing the connectivity of certain boundaries, we employ some comparatively recent and clearer graph-theoretic machinery. The lower bound is proven via a simple ad-hoc construction.
Cite as

Zylan Benjert, Kostas Lakis, Johannes Lengler, and Raghu Raman Ravi. The Diameter of (Threshold) Geometric Inhomogeneous Random Graphs. In 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 364, pp. 11:1-11:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{benjert_et_al:LIPIcs.STACS.2026.11,
  author =	{Benjert, Zylan and Lakis, Kostas and Lengler, Johannes and Ravi, Raghu Raman},
  title =	{{The Diameter of (Threshold) Geometric Inhomogeneous Random Graphs}},
  booktitle =	{43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)},
  pages =	{11:1--11:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-412-3},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{364},
  editor =	{Mahajan, Meena and Manea, Florin and McIver, Annabelle and Thắng, Nguy\~{ê}n Kim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2026.11},
  URN =		{urn:nbn:de:0030-drops-255009},
  doi =		{10.4230/LIPIcs.STACS.2026.11},
  annote =	{Keywords: GIRG, Diameter, Distributed Algorithms, Complex Networks}
}
Document
DOI: 10.4230/LIPIcs.WADS.2025.32
Fantastic Flips and Where to Find Them: A General Framework for Parameterized Local Search on Partitioning Problems

Authors: Niels Grüttemeier, Nils Morawietz, and Frank Sommer

Published in: LIPIcs, Volume 349, 19th International Symposium on Algorithms and Data Structures (WADS 2025)

Abstract
Parameterized local search combines classic local search heuristics with the paradigm of parameterized algorithmics. While most local search algorithms aim to improve given solutions by performing one single operation on a given solution, the parameterized approach aims to improve a solution by performing k simultaneous operations. Herein, k is a parameter called search radius for which the value can be chosen by a user. One major goal in the field of parameterized local search is to outline the trade-off between the size of k and the running time of the local search step. In this work, we introduce an abstract framework that generalizes natural parameterized local search approaches for a large class of partitioning problems: Given n items that are partitioned into b bins and a target function that evaluates the quality of the current partition, one asks whether it is possible to improve the solution by removing up to k items from their current bins and reassigning them to other bins. Among others, our framework applies for the local search versions of problems like Cluster Editing, Vector Bin Packing, and Nash Social Welfare. Motivated by a real-world application of the problem Vector Bin Packing, we introduce a parameter called number of types τ ≤ n and show that all problems fitting in our framework can be solved in τ^k ⋅ 2^𝒪(k) ⋅ |I|^𝒪(1) time, where |I| denotes the total input size. In case of Cluster Editing, the parameter τ generalizes the well-known parameter neighborhood diversity of the input graph. We complement these algorithms by showing that for all considered problems, an algorithm significantly improving over our algorithm with running time τ^k ⋅ 2^𝒪(k) ⋅ |I|^𝒪(1) would contradict the Exponential Time Hypothesis. Additionally, we show that even on very restricted instances, all considered problems are W[1]-hard when parameterized by the search radius k alone. In case of the local search version of Vector Bin Packing, we provide an even stronger W[1]-hardness result.
Cite as

Niels Grüttemeier, Nils Morawietz, and Frank Sommer. Fantastic Flips and Where to Find Them: A General Framework for Parameterized Local Search on Partitioning Problems. In 19th International Symposium on Algorithms and Data Structures (WADS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 349, pp. 32:1-32:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{gruttemeier_et_al:LIPIcs.WADS.2025.32,
  author =	{Gr\"{u}ttemeier, Niels and Morawietz, Nils and Sommer, Frank},
  title =	{{Fantastic Flips and Where to Find Them: A General Framework for Parameterized Local Search on Partitioning Problems}},
  booktitle =	{19th International Symposium on Algorithms and Data Structures (WADS 2025)},
  pages =	{32:1--32:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-398-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{349},
  editor =	{Morin, Pat and Oh, Eunjin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WADS.2025.32},
  URN =		{urn:nbn:de:0030-drops-242631},
  doi =		{10.4230/LIPIcs.WADS.2025.32},
  annote =	{Keywords: Flip-Neighborhood, Cluster Editing, Vector Bin Packing, Vertex Cover, NP-hard problem, Max c-Cut}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2025.21
Structure and Independence in Hyperbolic Uniform Disk Graphs

Authors: Thomas Bläsius, Jean-Pierre von der Heydt, Sándor Kisfaludi-Bak, Marcus Wilhelm, and Geert van Wordragen

Published in: LIPIcs, Volume 332, 41st International Symposium on Computational Geometry (SoCG 2025)

Abstract
We consider intersection graphs of disks of radius r in the hyperbolic plane. Unlike the Euclidean setting, these graph classes are different for different values of r, where very small r corresponds to an almost-Euclidean setting and r ∈ Ω(log n) corresponds to a firmly hyperbolic setting. We observe that larger values of r create simpler graph classes, at least in terms of separators and the computational complexity of the Independent Set problem. First, we show that intersection graphs of disks of radius r in the hyperbolic plane can be separated with 𝒪((1+1/r)log n) cliques in a balanced manner. Our second structural insight concerns Delaunay complexes in the hyperbolic plane and may be of independent interest. We show that for any set S of n points with pairwise distance at least 2r in the hyperbolic plane, the corresponding Delaunay complex has outerplanarity 1+𝒪((log n)/r), which implies a similar bound on the balanced separators and treewidth of such Delaunay complexes. Using this outerplanarity (and treewidth) bound we prove that Independent Set can be solved in n^𝒪(1+(log n)/r) time. The algorithm is based on dynamic programming on some unknown sphere cut decomposition that is based on the solution. The resulting algorithm is a far-reaching generalization of a result of Kisfaludi-Bak (SODA 2020), and it is tight under the Exponential Time Hypothesis. In particular, Independent Set is polynomial-time solvable in the firmly hyperbolic setting of r ∈ Ω(log n). Finally, in the case when the disks have ply (depth) at most 𝓁, we give a PTAS for Maximum Independent Set that has only quasi-polynomial dependence on 1/ε and 𝓁. Our PTAS is a further generalization of our exact algorithm.
Cite as

Thomas Bläsius, Jean-Pierre von der Heydt, Sándor Kisfaludi-Bak, Marcus Wilhelm, and Geert van Wordragen. Structure and Independence in Hyperbolic Uniform Disk Graphs. In 41st International Symposium on Computational Geometry (SoCG 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 332, pp. 21:1-21:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{blasius_et_al:LIPIcs.SoCG.2025.21,
  author =	{Bl\"{a}sius, Thomas and von der Heydt, Jean-Pierre and Kisfaludi-Bak, S\'{a}ndor and Wilhelm, Marcus and van Wordragen, Geert},
  title =	{{Structure and Independence in Hyperbolic Uniform Disk Graphs}},
  booktitle =	{41st International Symposium on Computational Geometry (SoCG 2025)},
  pages =	{21:1--21:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-370-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{332},
  editor =	{Aichholzer, Oswin and Wang, Haitao},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2025.21},
  URN =		{urn:nbn:de:0030-drops-231731},
  doi =		{10.4230/LIPIcs.SoCG.2025.21},
  annote =	{Keywords: hyperbolic geometry, unit disk graphs, independent set, treewidth}
}
Document
DOI: 10.4230/LIPIcs.STACS.2025.13
Hyperbolic Random Graphs: Clique Number and Degeneracy with Implications for Colouring

Authors: Samuel Baguley, Yannic Maus, Janosch Ruff, and George Skretas

Published in: LIPIcs, Volume 327, 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)

Abstract
Hyperbolic random graphs inherit many properties that are present in real-world networks. The hyperbolic geometry imposes a scale-free network with a strong clustering coefficient. Other properties like a giant component, the small world phenomena and others follow. This motivates the design of simple algorithms for hyperbolic random graphs. In this paper we consider threshold hyperbolic random graphs (HRGs). Greedy heuristics are commonly used in practice as they deliver a good approximations to the optimal solution even though their theoretical analysis would suggest otherwise. A typical example for HRGs are degeneracy-based greedy algorithms [Bläsius, Fischbeck; Transactions of Algorithms '24]. In an attempt to bridge this theory-practice gap we characterise the parameter of degeneracy yielding a simple approximation algorithm for colouring HRGs. The approximation ratio of our algorithm ranges from (2/√3) to 4/3 depending on the power-law exponent of the model. We complement our findings for the degeneracy with new insights on the clique number of hyperbolic random graphs. We show that degeneracy and clique number are substantially different and derive an improved upper bound on the clique number. Additionally, we show that the core of HRGs does not constitute the largest clique. Lastly we demonstrate that the degeneracy of the closely related standard model of geometric inhomogeneous random graphs behaves inherently different compared to the one of hyperbolic random graphs.
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Samuel Baguley, Yannic Maus, Janosch Ruff, and George Skretas. Hyperbolic Random Graphs: Clique Number and Degeneracy with Implications for Colouring. In 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 327, pp. 13:1-13:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{baguley_et_al:LIPIcs.STACS.2025.13,
  author =	{Baguley, Samuel and Maus, Yannic and Ruff, Janosch and Skretas, George},
  title =	{{Hyperbolic Random Graphs: Clique Number and Degeneracy with Implications for Colouring}},
  booktitle =	{42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)},
  pages =	{13:1--13:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-365-2},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{327},
  editor =	{Beyersdorff, Olaf and Pilipczuk, Micha{\l} and Pimentel, Elaine and Thắng, Nguy\~{ê}n Kim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2025.13},
  URN =		{urn:nbn:de:0030-drops-228386},
  doi =		{10.4230/LIPIcs.STACS.2025.13},
  annote =	{Keywords: hyperbolic random graphs, scale-free networks, power-law graphs, cliques, degeneracy, vertex colouring, chromatic number}
}
Document
DOI: 10.4230/LIPIcs.ESA.2022.21
On the External Validity of Average-Case Analyses of Graph Algorithms

Authors: Thomas Bläsius and Philipp Fischbeck

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

Abstract
The number one criticism of average-case analysis is that we do not actually know the probability distribution of real-world inputs. Thus, analyzing an algorithm on some random model has no implications for practical performance. At its core, this criticism doubts the existence of external validity, i.e., it assumes that algorithmic behavior on the somewhat simple and clean models does not translate beyond the models to practical performance real-world input. With this paper, we provide a first step towards studying the question of external validity systematically. To this end, we evaluate the performance of six graph algorithms on a collection of 2751 sparse real-world networks depending on two properties; the heterogeneity (variance in the degree distribution) and locality (tendency of edges to connect vertices that are already close). We compare this with the performance on generated networks with varying locality and heterogeneity. We find that the performance in the idealized setting of network models translates surprisingly well to real-world networks. Moreover, heterogeneity and locality appear to be the core properties impacting the performance of many graph algorithms.
Cite as

Thomas Bläsius and Philipp Fischbeck. On the External Validity of Average-Case Analyses of Graph Algorithms. In 30th Annual European Symposium on Algorithms (ESA 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 244, pp. 21:1-21:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{blasius_et_al:LIPIcs.ESA.2022.21,
  author =	{Bl\"{a}sius, Thomas and Fischbeck, Philipp},
  title =	{{On the External Validity of Average-Case Analyses of Graph Algorithms}},
  booktitle =	{30th Annual European Symposium on Algorithms (ESA 2022)},
  pages =	{21:1--21:14},
  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.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2022.21},
  URN =		{urn:nbn:de:0030-drops-169590},
  doi =		{10.4230/LIPIcs.ESA.2022.21},
  annote =	{Keywords: Average Case, Network Models, Empirical Evaluation}
}
Document
DOI: 10.4230/LIPIcs.SEA.2022.13
A Branch-And-Bound Algorithm for Cluster Editing

Authors: Thomas Bläsius, Philipp Fischbeck, Lars Gottesbüren, Michael Hamann, Tobias Heuer, Jonas Spinner, Christopher Weyand, and Marcus Wilhelm

Published in: LIPIcs, Volume 233, 20th International Symposium on Experimental Algorithms (SEA 2022)

Abstract
The cluster editing problem asks to transform a given graph into a disjoint union of cliques by inserting and deleting as few edges as possible. We describe and evaluate an exact branch-and-bound algorithm for cluster editing. For this, we introduce new reduction rules and adapt existing ones. Moreover, we generalize a known packing technique to obtain lower bounds and experimentally show that it contributes significantly to the performance of the solver. Our experiments further evaluate the effectiveness of the different reduction rules and examine the effects of structural properties of the input graph on solver performance. Our solver won the exact track of the 2021 PACE challenge.
Cite as

Thomas Bläsius, Philipp Fischbeck, Lars Gottesbüren, Michael Hamann, Tobias Heuer, Jonas Spinner, Christopher Weyand, and Marcus Wilhelm. A Branch-And-Bound Algorithm for Cluster Editing. In 20th International Symposium on Experimental Algorithms (SEA 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 233, pp. 13:1-13:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{blasius_et_al:LIPIcs.SEA.2022.13,
  author =	{Bl\"{a}sius, Thomas and Fischbeck, Philipp and Gottesb\"{u}ren, Lars and Hamann, Michael and Heuer, Tobias and Spinner, Jonas and Weyand, Christopher and Wilhelm, Marcus},
  title =	{{A Branch-And-Bound Algorithm for Cluster Editing}},
  booktitle =	{20th International Symposium on Experimental Algorithms (SEA 2022)},
  pages =	{13:1--13:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-251-8},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{233},
  editor =	{Schulz, Christian and U\c{c}ar, Bora},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2022.13},
  URN =		{urn:nbn:de:0030-drops-165473},
  doi =		{10.4230/LIPIcs.SEA.2022.13},
  annote =	{Keywords: cluster editing}
}
Document
PACE Solver Description
DOI: 10.4230/LIPIcs.IPEC.2021.27
PACE Solver Description: The KaPoCE Exact Cluster Editing Algorithm

Authors: Thomas Bläsius, Philipp Fischbeck, Lars Gottesbüren, Michael Hamann, Tobias Heuer, Jonas Spinner, Christopher Weyand, and Marcus Wilhelm

Published in: LIPIcs, Volume 214, 16th International Symposium on Parameterized and Exact Computation (IPEC 2021)

Abstract
The cluster editing problem is to transform an input graph into a cluster graph by performing a minimum number of edge editing operations. A cluster graph is a graph where each connected component is a clique. An edit operation can be either adding a new edge or removing an existing edge. In this write-up we outline the core techniques used in the exact cluster editing algorithm of the KaPoCE framework (contains also a heuristic solver), submitted to the exact track of the 2021 PACE challenge.
Cite as

Thomas Bläsius, Philipp Fischbeck, Lars Gottesbüren, Michael Hamann, Tobias Heuer, Jonas Spinner, Christopher Weyand, and Marcus Wilhelm. PACE Solver Description: The KaPoCE Exact Cluster Editing Algorithm. In 16th International Symposium on Parameterized and Exact Computation (IPEC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 214, pp. 27:1-27:3, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{blasius_et_al:LIPIcs.IPEC.2021.27,
  author =	{Bl\"{a}sius, Thomas and Fischbeck, Philipp and Gottesb\"{u}ren, Lars and Hamann, Michael and Heuer, Tobias and Spinner, Jonas and Weyand, Christopher and Wilhelm, Marcus},
  title =	{{PACE Solver Description: The KaPoCE Exact Cluster Editing Algorithm}},
  booktitle =	{16th International Symposium on Parameterized and Exact Computation (IPEC 2021)},
  pages =	{27:1--27:3},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-216-7},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{214},
  editor =	{Golovach, Petr A. and Zehavi, Meirav},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2021.27},
  URN =		{urn:nbn:de:0030-drops-154109},
  doi =		{10.4230/LIPIcs.IPEC.2021.27},
  annote =	{Keywords: cluster editing}
}
Document
PACE Solver Description
DOI: 10.4230/LIPIcs.IPEC.2021.31
PACE Solver Description: KaPoCE: A Heuristic Cluster Editing Algorithm

Authors: Thomas Bläsius, Philipp Fischbeck, Lars Gottesbüren, Michael Hamann, Tobias Heuer, Jonas Spinner, Christopher Weyand, and Marcus Wilhelm

Published in: LIPIcs, Volume 214, 16th International Symposium on Parameterized and Exact Computation (IPEC 2021)

Abstract
The cluster editing problem is to transform an input graph into a cluster graph by performing a minimum number of edge editing operations. A cluster graph is a graph where each connected component is a clique. An edit operation can be either adding a new edge or removing an existing edge. In this write-up we outline the core techniques used in the heuristic cluster editing algorithm of the Karlsruhe and Potsdam Cluster Editing (KaPoCE) framework, submitted to the heuristic track of the 2021 PACE challenge.
Cite as

Thomas Bläsius, Philipp Fischbeck, Lars Gottesbüren, Michael Hamann, Tobias Heuer, Jonas Spinner, Christopher Weyand, and Marcus Wilhelm. PACE Solver Description: KaPoCE: A Heuristic Cluster Editing Algorithm. In 16th International Symposium on Parameterized and Exact Computation (IPEC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 214, pp. 31:1-31:4, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{blasius_et_al:LIPIcs.IPEC.2021.31,
  author =	{Bl\"{a}sius, Thomas and Fischbeck, Philipp and Gottesb\"{u}ren, Lars and Hamann, Michael and Heuer, Tobias and Spinner, Jonas and Weyand, Christopher and Wilhelm, Marcus},
  title =	{{PACE Solver Description: KaPoCE: A Heuristic Cluster Editing Algorithm}},
  booktitle =	{16th International Symposium on Parameterized and Exact Computation (IPEC 2021)},
  pages =	{31:1--31:4},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-216-7},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{214},
  editor =	{Golovach, Petr A. and Zehavi, Meirav},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2021.31},
  URN =		{urn:nbn:de:0030-drops-154147},
  doi =		{10.4230/LIPIcs.IPEC.2021.31},
  annote =	{Keywords: cluster editing, local search, variable neighborhood search}
}
Document
DOI: 10.4230/OASIcs.ATMOS.2020.10
A Strategic Routing Framework and Algorithms for Computing Alternative Paths

Authors: Thomas Bläsius, Maximilian Böther, Philipp Fischbeck, Tobias Friedrich, Alina Gries, Falk Hüffner, Otto Kißig, Pascal Lenzner, Louise Molitor, Leon Schiller, Armin Wells, and Simon Wietheger

Published in: OASIcs, Volume 85, 20th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2020)

Abstract
Traditional navigation services find the fastest route for a single driver. Though always using the fastest route seems desirable for every individual, selfish behavior can have undesirable effects such as higher energy consumption and avoidable congestion, even leading to higher overall and individual travel times. In contrast, strategic routing aims at optimizing the traffic for all agents regarding a global optimization goal. We introduce a framework to formalize real-world strategic routing scenarios as algorithmic problems and study one of them, which we call Single Alternative Path (SAP), in detail. There, we are given an original route between a single origin-destination pair. The goal is to suggest an alternative route to all agents that optimizes the overall travel time under the assumption that the agents distribute among both routes according to a psychological model, for which we introduce the concept of Pareto-conformity. We show that the SAP problem is NP-complete, even for such models. Nonetheless, assuming Pareto-conformity, we give multiple algorithms for different variants of SAP, using multi-criteria shortest path algorithms as subroutines. Moreover, we prove that several natural models are in fact Pareto-conform. The implementation and evaluation of our algorithms serve as a proof of concept, showing that SAP can be solved in reasonable time even though the algorithms have exponential running time in the worst case.
Cite as

Thomas Bläsius, Maximilian Böther, Philipp Fischbeck, Tobias Friedrich, Alina Gries, Falk Hüffner, Otto Kißig, Pascal Lenzner, Louise Molitor, Leon Schiller, Armin Wells, and Simon Wietheger. A Strategic Routing Framework and Algorithms for Computing Alternative Paths. In 20th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2020). Open Access Series in Informatics (OASIcs), Volume 85, pp. 10:1-10:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{blasius_et_al:OASIcs.ATMOS.2020.10,
  author =	{Bl\"{a}sius, Thomas and B\"{o}ther, Maximilian and Fischbeck, Philipp and Friedrich, Tobias and Gries, Alina and H\"{u}ffner, Falk and Ki{\ss}ig, Otto and Lenzner, Pascal and Molitor, Louise and Schiller, Leon and Wells, Armin and Wietheger, Simon},
  title =	{{A Strategic Routing Framework and Algorithms for Computing Alternative Paths}},
  booktitle =	{20th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2020)},
  pages =	{10:1--10:14},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-170-2},
  ISSN =	{2190-6807},
  year =	{2020},
  volume =	{85},
  editor =	{Huisman, Dennis and Zaroliagis, Christos D.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2020.10},
  URN =		{urn:nbn:de:0030-drops-131469},
  doi =		{10.4230/OASIcs.ATMOS.2020.10},
  annote =	{Keywords: Routing, Strategic Routing, Selfish Routing, Route Planning, Network Flow, Algorithm Design}
}
Document
DOI: 10.4230/LIPIcs.STACS.2020.25
Solving Vertex Cover in Polynomial Time on Hyperbolic Random Graphs

Authors: Thomas Bläsius, Philipp Fischbeck, Tobias Friedrich, and Maximilian Katzmann

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

Abstract
The VertexCover problem is proven to be computationally hard in different ways: It is NP-complete to find an optimal solution and even NP-hard to find an approximation with reasonable factors. In contrast, recent experiments suggest that on many real-world networks the run time to solve VertexCover is way smaller than even the best known FPT-approaches can explain. Similarly, greedy algorithms deliver very good approximations to the optimal solution in practice. We link these observations to two properties that are observed in many real-world networks, namely a heterogeneous degree distribution and high clustering. To formalize these properties and explain the observed behavior, we analyze how a branch-and-reduce algorithm performs on hyperbolic random graphs, which have become increasingly popular for modeling real-world networks. In fact, we are able to show that the VertexCover problem on hyperbolic random graphs can be solved in polynomial time, with high probability. The proof relies on interesting structural properties of hyperbolic random graphs. Since these predictions of the model are interesting in their own right, we conducted experiments on real-world networks showing that these properties are also observed in practice. When utilizing the same structural properties in an adaptive greedy algorithm, further experiments suggest that, on real instances, this leads to better approximations than the standard greedy approach within reasonable time.
Cite as

Thomas Bläsius, Philipp Fischbeck, Tobias Friedrich, and Maximilian Katzmann. Solving Vertex Cover in Polynomial Time on Hyperbolic Random Graphs. In 37th International Symposium on Theoretical Aspects of Computer Science (STACS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 154, pp. 25:1-25:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{blasius_et_al:LIPIcs.STACS.2020.25,
  author =	{Bl\"{a}sius, Thomas and Fischbeck, Philipp and Friedrich, Tobias and Katzmann, Maximilian},
  title =	{{Solving Vertex Cover in Polynomial Time on Hyperbolic Random Graphs}},
  booktitle =	{37th International Symposium on Theoretical Aspects of Computer Science (STACS 2020)},
  pages =	{25:1--25:14},
  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.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2020.25},
  URN =		{urn:nbn:de:0030-drops-118865},
  doi =		{10.4230/LIPIcs.STACS.2020.25},
  annote =	{Keywords: vertex cover, random graphs, hyperbolic geometry, efficient algorithm}
}
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