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the Complexity of Graph Exploration Games 50th

The Complexity of Graph Exploration Games

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50th International conference on current trends in theory and practice of computer science, SOFSEM 2025

作者： Fuchs, Janosch Grüne, Christoph Janßen, Tom Department of Computer Science RWTH Aachen University Aachen Germany

ISBN: (纸本)9783031826962

Graph Exploration problems ask a searcher to explore an unknown environment. the environment is modeled as a graph, where the searcher needs to visit each vertex beginning at some vertex. Treasure Hunt problems are a variation of Graph Exploration, in which the searcher needs to find a hidden treasure, which is located at a designated vertex. Usually these problems are modeled as online problems, and any online algorithm performs poorly because it has too little knowledge about the instance to react adequately to the requests of the adversary. thus, the impact of a priori knowledge is of interest. One form of a priori knowledge is an unlabeled map, which is an isomorphic copy of the graph. We analyze Graph Exploration and Treasure Hunt problems with an unlabeled map that is provided to the searcher. For this, we formulate decision variants of both problems by interpreting the online problems as a game between the online algorithm (the searcher) and the adversary. the map, however, is not controllable by the adversary. the question is whether the searcher is able to explore the graph completely or find the treasure for all possible decisions of the adversary. We analyze these games in multiple settings, with and without costs on the edges, on directed and undirected graphs and with different constraints (allowing multiple visits to vertices or edges) on the solution. We prove PSPACE-completeness for most of these games. Additionally, we analyze the complexity of related problems that have additional constraints on the solution. © the Author(s), under exclusive license to Springer Nature Switzerland AG 2025.

关键词： Graph algorithms

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Parameterized Complexity of Feedback Vertex Set with Connectivity Constraints 50th

Parameterized Complexity of Feedback Vertex Set with Conne...

引用

50th International conference on current trends in theory and practice of computer science, SOFSEM 2025

作者： Abhinav, Ankit Jana, Satyabrata Purohit, Nidhi Sahu, Abhishek Saurabh, Saket National Institute of Science Education and Research An OCC of Homi Bhabha National Institute Odisha Bhubaneswar752050 India University of Warwick Coventry United Kingdom National University of Singapore Singapore Singapore The Institute of Mathematical Sciences HBNI Chennai India University of Bergen Bergen Norway

ISBN: (纸本)9783031826696

the Feedback Vertex Set (FVS) problem, together with several of its variants, is arguably one of the most well-studied problems in the field of Parameterized Complexity. Two versions of the problem that have garnered significant interest involve the inclusion of an independence constraint and a connectivity constraint in the solution. this paper introduces generalized versions of both these variants, known as At least-c-FVS and At most-c-FVS, respectively, serving as extensions of Connected FVS and Independent FVS, respectively. the problem At most-c-FVS (resp., At least-c-FVS) is defined as follows: given a graph G and an integer k, the objective is to determine whether there exists a subset S⊆V(G), with |S|≤k, such that the subgraph G-S is a forest and each component of G[S] contains at most c (resp., at least c) vertices. We study these problems in the realm of Parameterized Complexity and obtain the following results: – At most-c-FVS parameterized by k has a kernel of size O(k3+c), and admits an FPT algorithm running in time 2O(k)+clogk2)nO(1). – At least-c-FVS parameterized by k has no kernel of size kf(c) for any computable function f (unless co-NP-NP/poly), but admits an FPT algorithm running in time 2O(k)nO(1). © the Author(s), under exclusive license to Springer Nature Switzerland AG 2025.

关键词： Parameterization

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Multi-agent Search-Type Problems on Polygons: (Extended Abstract) 50th

Multi-agent Search-Type Problems on Polygons: (Extended Abs...

引用

50th International conference on current trends in theory and practice of computer science, SOFSEM 2025

作者： Georgiou, Konstantinos Jones, Caleb Lucier, Jesse Department of Mathematics Toronto Metropolitan University TorontoON Canada

ISBN: (纸本)9783031826696

We present several advancements in search-type problems for fleets of mobile agents operating in two dimensions under the wireless model. Potential hidden target locations are equidistant from a central point, forming either a unit-radius disk (infinite possible locations) or regular polygons (finite possible locations) inscribed in a unit-radius disk. Building and extending on the foundational disk evacuation problem [23], the disk priority evacuation problem with k Servants [21, 27], and the disk w-weighted search problem [49], we make improvements on several fronts. First, we establish new upper and lower bounds for the n-gon priority evacuation problem with 1 Servant for n≤13, and for nk-gons with k=2,3,4 Servants, where n2≤11, n3≤9, and n4≤10, offering tight or nearly tight bounds. the only previous results known were a tight upper bound for k=1 and n=6 in [27] and lower bounds for k=1 and n≤9 in [49]. Second, our work improves the best lower bound known for the disk priority evacuation problem with k=1 Servant from 4.46798 to 4.64666 and for k=2 Servants from 3.6307 of [27] to 3.65332. third, we improve the best lower bounds known for the disk w-weighted group search problem, significantly reducing the gap between the best upper and lower bounds for w values where the gap was largest. these improvements are based on nearly tight upper and lower bounds for the 11-gon and 12-gon w-weighted evacuation problems, while the previous study of [49] was limited only to lower bounds and only to 7-gons. © the Author(s), under exclusive license to Springer Nature Switzerland AG 2025.

关键词： Distributed computer systems

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On the Structural Parameterized Complexity of Defective Coloring 50th

On the Structural Parameterized Complexity of Defective Co...

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50th International conference on current trends in theory and practice of computer science, SOFSEM 2025

作者： Bhyravarapu, Sriram Kumar, Pankaj Saurabh, Saket Institute of Mathematical Science HBNI Chennai India School of Computer Science University of Birmingham Birmingham United Kingdom University of Bergen Bergen Norway

ISBN: (纸本)9783031826696

In this paper, we consider the problem Defective Coloring. Given a graph G and two positive integers k and Δ∗, the objective is to determine whether it is possible to obtain a coloring (not necessarily proper) of the vertices of G using at most k colors such that each vertex in a color class c has at most Δ∗ neighbors in the same color class. Defective Coloring is a generalization of Graph Coloring with Δ∗=0. the optimization variant of this problem, which aims to find the minimum number of colors k, is known to be NP-hard even for split graphs and cographs. Belmonte, Lampis, and Mitsou (SIDMA 2020) showed that Defective Coloring is W[1]-hard when parameterized by tree-width, path-width, tree-depth, or feedback vertex set. the problem is W[1]-hard parameterized by modular-width or clique-width as Defective Coloring is NP-hard on cographs. they asked as an open question whether Defective Coloring is fixed-parameter tractable (FPT) when parameterized by modular-width, clique-width or neighborhood diversity combined with either k or Δ∗. In an effort to address the question concerning modular-width, this study investigates the parameters neighborhood diversity and twin-cover, which are special cases of modular-width. We show that Defective Coloring is FPT when parameterized by twin-cover, distance to disjoint paths, or the combined parameters neighborhood diversity and k. the latter result implies an FPT algorithm for complete-d-partite graphs, a subclass of cographs, parameterized by d. this provides a partial response to an open question raised in the above paper. We present an algorithm for graphs with bounded distance to d-degree and as a corollary we obtain an FPTalgorithm parameterized by distance to disjoint paths. Furthermore, the study also presents a 1-additive approximation algorithm for split graphs. © the Author(s), under exclusive license to Springer Nature Switzerland AG 2025.

关键词： Trees (mathematics)

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Parameterized Complexity of Generalizations of Edge Dominating Set 50th

Parameterized Complexity of Generalizations of Edge Domina...

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50th International conference on current trends in theory and practice of computer science, SOFSEM 2025

作者： Aute, Shubhada Panolan, Fahad Saha, Souvik Saurabh, Saket Upasana, Anannya Department of Computer Science and Engineering IIT Hyderabad Kandi India School of Computer Science University of Leeds Leeds United Kingdom The Institute of Mathematical Sciences HBNI Chennai India University of Bergen Bergen Norway

ISBN: (纸本)9783031826696

the objective of this article is to propose two natural generalizations of covering edges by edges (Edge Dominating Set) and study these problems from the multivariate lens. the first is simply considering Edge Dominating Set on hypergraphs, called Hyperedge Dominating Set. Given a hypergraph H=(U,F), a set F⊆F is called a hyperedge dominating set if all hyperedges intersect with at least one hyperedge e∈F. the objective of the Hyperedge Dominating Set problem is to determine whether a hyperedge dominating set of size at most k exists. We find it quite surprising that such generalization is missing from the literature. the second extension we consider is the t-Path Edge Dominating Set problem. In this problem, the input consists of a graph G and an integer k, and the goal is to find a set P of at most k paths, each of length at most t, such that for every edge in G, at least one of its endpoints belongs to the vertex set V(P) for some P∈P. We show the following results and add to the literature on Edge Dominating Set. Hyperedge Dominating Set is FPT parameterized by k+d, where d is the maximum size of a hyperedge in the input hypergraph.A kernel of size O(kd) can be obtained for the Hyperedge Dominating Set problem, where d is the maximum size of a hyperedge in the input *** problem of finding a Hyperedge Dominating Set is computationally difficult;specifically it is W[2]-hard when parameterized by k. this hardness result holds even when each vertex is contained in at most 2 hyperedges and the intersection between any two hyperedges is at most 1.t-Path Edge Dominating Set is FPT when parameterized by k+t. Additionally, it has a kernel of size O(k3t3). Hyperedge Dominating Set is FPT parameterized by k+d, where d is the maximum size of a hyperedge in the input hypergraph. A kernel of size O(kd) can be obtained for the Hyperedge Dominating Set problem, where d is the maximum size of a hyperedge in the input hypergraph. the problem of finding a Hyperedge Dom

关键词： Parameterization

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Optimizing winning strategies in regular infinite games 1

引用

34th conference on current trends in theory and practice of computer science

作者： thomas, Wolfgang Rhein Westfal TH Aachen D-52056 Aachen Germany

ISBN: (数字)9783540775669

ISBN: (纸本)9783540775652

We consider infinite two-player games played on finite graphs where the winning condition (say for the first player) is given by a regular omega-language. We address issues of optimization in the construction of winning strategies in such games. Two criteria for optimization are discussed: memory size of finite automata that execute winning strategies, and - for games with liveness requests as winning conditions - "waiting times" for the satisfaction of requests. (For the first aspect we report on work of Holtmann and Loding, for the second on work of Horn., Wallmeier, and the author.)

关键词： Game theory

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Parallel immune system for graph coloring 1

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34th conference on current trends in theory and practice of computer science

作者： Dabrowski, Jacek Gdansk Univ Technol PL-80952 Gdansk Poland

ISBN: (数字)9783540775669

ISBN: (纸本)9783540775652

this paper presents a parallel artificial immune system designed for graph coloring. the algorithm is based on the clonal selection principle. Each processor operates on its own pool of antibodies and a migration mechanism is used to allow processors to exchange information. Experimental results show that migration improves the performance of the algorithm. the experiments were performed using a high performance cluster on a set of well-established graph instances available on the Web.

关键词： Graph theory

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On reachability games of ordinal length 1

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34th conference on current trends in theory and practice of computer science

作者： Cristau, Julien Horn, Florian Univ Paris 07 LIAFA F-75251 Paris 05 France

ISBN: (数字)9783540775669

ISBN: (纸本)9783540775652

Games are a classical model in the synthesis of controllers in the open setting. In particular, games of infinite length can represent systems which are not expected to reach a correct state, but rather to handle a continuous stream of events. Yet, even longer sequences of events have to be considered when infinite sequences of events can occur in finite time - Zeno behaviours. In this paper, we extend two-player games to this setting by considering plays of ordinal length. Our two main results are determinacy of reachability games of length less than w(w) on finite arenas, and the PSPACE-completeness of deciding the winner in such a game.

关键词： Interactive computer graphics

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Periodic and infinite traces in matrix semigroups 1

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34th conference on current trends in theory and practice of computer science

作者： Bell, Paul Potapov, Igor Turku Univ Dept Math Turku Finland Univ Liverpool Dept Comp Sci Liverpool L69 3BX Merseyside England

ISBN: (数字)9783540775669

ISBN: (纸本)9783540775652

In this paper we provide several new results concerning word and matrix semigroup problems using counter automaton models. As a main result, we prove a new version of Post's correspondence problem to be undecidable and show its application to matrix semigroup problems, such as Any Diagonal Matrix Problem and Recurrent Matrix Problem. We also use infinite periodic traces in counter automaton models to show the undecidability of a new variation of the Infinite Post Correspondence Problem and Vector Ambiguity Problem for matrix semigroups.

关键词： Set theory

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An automata theoretic approach to rational tree relations 1

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34th conference on current trends in theory and practice of computer science

作者： Radmacher, Frank G. Rhein Westfal TH Aachen Lehrstuhl Informat 7 Aachen Germany

ISBN: (数字)9783540775669

ISBN: (纸本)9783540775652

We investigate rational relations over trees. Our starting point is the definition of rational tree relations via rational expressions by Raoult (Bull. Belg. Math. Sec. 1997). We develop a new class of automata, called asynchronous tree automata, which recognize exactly these relations. the automata theoretic approach is convenient for the solution of algorithmic problems (like the emptiness problem). the second contribution of this paper is a new subclass of the rational tree relations, called separate-rational tree relations, defined via a natural restriction on asynchronous tree automata. these relations are closed under composition, preserve regular tree languages, and generate precisely the regular sets in the unary case (all these properties fail for the general model), and they are still more powerful than, for instance, the automatic tree relations.

关键词： Automata theory

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