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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...

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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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Probabilistic Acceptors for Languages over Infinite Words

Probabilistic Acceptors for Languages over Infinite Words

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35th conference on current trends in theory and practice of computer science

作者： Baier, Christel Bertrand, Nathalie Groesser, Marcus Tech Univ Dresden Fac Comp Sci Dresden Germany INRIA Rennes Bretagne Atlantique Rennes France

ISBN: (纸本)9783540958901

Probabilistic omega-automata are variants of nondeterministic automata for infinite words where all choices are resolved by probabilistic distributions. Acceptance of an infinite input word requires that the probability for the accepting runs is positive. In this paper, we provide a summary of the fundamental properties of probabilistic omega-automata concerning expressiveness, efficiency, compositionality and decision problems.

关键词： Automata theory

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On Stateless Deterministic Restarting Automata

On Stateless Deterministic Restarting Automata

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35th conference on current trends in theory and practice of computer science

作者： Kutrib, Martin Messerschmidt, Hartmut Otto, Friedrich Univ Giessen Inst Informat Arndtstr 2 D-35392 Giessen Germany Intelligent Syst Technol Zentrum Informat D-28359 Bremen Germany Univ Kassel Fachbereich Elektrotechn Informat D-34109 Kassel Germany

ISBN: (纸本)9783540958901

the transitions of a stateless automaton do not depend on internal states but. solely on the symbols currently scanned by its heads accessing the input. or memory. We investigate stateless deterministic restarting automata that, after executing a rewrite step, Continue to read their tape before. performing a restart. Even the weakest class thus obtained contains the regular languages properly. the relations between different classes of stateless automata as well as between stateless automata and the corresponding types of automata with states are investigated, and it is shown that the language classes defined by the various types of deterministic stateless restarting automata without Auxiliary symbols are anti-AFLs that are not even closed under reversal.

关键词： Automata theory

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the Shortcut Problem - Complexity and Approximation

The Shortcut Problem - Complexity and Approximation

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35th conference on current trends in theory and practice of computer science

作者： Bauer, Reinhard D'Angelo, Gianlorenzo Delling, Daniel Wagner, Dorothea Univ Karlsruhe TH Fac Informat Stockholm Sweden Univ Aquila Elect & Informat Engn Dept I-67100 Laquila Italy

ISBN: (纸本)9783540958901

During the last years, speed-up techniques for DIJKSTRA's algorithm have been developed that make the computation of shortest paths a matter of microseconds even oil huge road networks. the most sophisticated methods enhance the graph by inserting shortcuts, i.e. additional edges, that represent shortest paths in the graph. Until now, all existing shortcut-insertion strategies are heuristics and no theoretical results on the topic are known. In this work, we formalize the problem of adding shortcuts as a graph augmentation problem, study the algorithmic complexity of the problem, give approximation algorithms and show how to stochastically evaluate a given shortcut assignment on graphs that are too big to evaluate it exactly.

关键词： Approximation algorithms

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SOFSEM 2009: theory and practice of computer science 2009

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丛书名： Lecture Notes in computer science

2009年

作者： Mogens Nielsen Antonin Kucera Peter Bro Miltersen Catuscia Palamidessi Petr Tuma Frank Valencia

ISBN: (数字)9783540958918

ISBN: (纸本)9783540958901

this book constitutes the refereed proceedings of the 35th conference on current trends in theory and practice of computer science, SOFSEM 2009, held in pindleruv Mln, Czech Republic, in January 2009. the 49 revised full papers, presented together with 9 invited contributions, were carefully reviewed and selected from 132 submissions. SOFSEM 2009 was organized around the following four tracks: Foundations of computer science; theory and practice of Software Services; Game theoretic Aspects of E-commerce; and Techniques and Tools for Formal Verification.

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theoretical computer science 1st ed. 2017

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丛书名： Communications in computer and Information science

2017年

作者： Dingzhu Du Lian Li En Zhu Kun He

ISBN: (数字)9789811068935

ISBN: (纸本)9789811068928

this book constitutes the thoroughly refereed proceedings of the National conference of theoretical computer science, NCTCS 2017, held in Wuhan, Hubei, China, in October 2017. the 25 full papers presented were carefully reviewed and selected from 84 submissions. they present relevant trends of current research in the area of algorithms and complexity, software theory and method, data science and machine learning theory.

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