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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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Generalisation under gradient descent via deterministic PAC-Bayes 36

Generalisation under gradient descent via deterministic PAC-...

引用

36th International conference on Algorithmic Learning theory, ALT 2025

作者： Clerico, Eugenio Farghly, Tyler Deligiannidis, George Guedj, Benjamin Doucet, Arnaud Universitat Pompeu Fabra Barcelona Spain Department of Statistics University of Oxford United Kingdom AI Centre Department of Computer Science UCL London United Kingdom Inria London United Kingdom

We establish disintegrated PAC-Bayesian generalisation bounds for models trained with gradient descent methods or continuous gradient flows. Contrary to standard practice in the PAC-Bayesian setting, our result applies to optimisation algorithms that are deterministic, without requiring any de-randomisation step. Our bounds are fully computable, depending on the density of the initial distribution and the Hessian of the training objective over the trajectory. We show that our framework can be applied to a variety of iterative optimisation algorithms, including stochastic gradient descent (SGD), momentum-based schemes, and damped Hamiltonian dynamics. © 2025 E. Clerico, T. Farghly, G. Deligiannidis, B. Guedj & A. Doucet.

关键词： Stochastic systems

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Parameterized Complexity of Feedback Vertex Set with Connectivity Constraints 50th

Parameterized Complexity of Feedback Vertex Set with Conne...

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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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Web science: the Digital-Heritage Case

Web Science: The Digital-Heritage Case

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36th conference on current trends in theory and practice of computer science

作者： Schreiber, Guus Vrije Univ Amsterdam NL-1081 HV Amsterdam Netherlands

Web science studies the interpay between web technology and the human behaviour it induces at the micro, meso and macro level. In this extended abstract we examine Web science research issues by taking a closer look a... 详细信息

ISBN: (纸本)9783642112652

关键词： Behavioral research

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Clock Synchronization: Open Problems in theory and practice

Clock Synchronization: Open Problems in Theory and Practice

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36th conference on current trends in theory and practice of computer science

作者： Lenzen, Christoph Locher, thomas Sommer, Philipp Wattenhofer, Roger ETH Comp Engn & Networks Lab TIK CH-8092 Zurich Switzerland

ISBN: (纸本)9783642112652

Clock synchronization is one of the most basic building blocks for many applications in computer science and engineering. the purpose of clock synchronization is to provide the constituent parts of a distributed system with a common notion of time. While the problem of synchronizing clocks in distributed systems has already received considerable attention from researchers and practitioners alike, we believe that there are many fascinating problems that remain unsolved. In this paper, we give a brief overview of previous work in this area;followed by a discussion of open clock synchronization problems in theory and practice.

关键词： Synchronization

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Homophily of Neighborhood in Graph Relational Classifier

Homophily of Neighborhood in Graph Relational Classifier

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36th conference on current trends in theory and practice of computer science

作者： Vojtek, Peter Bielikova, Maria Slovak Tech Univ Fac Informat & Informat Technol Inst Informat & Software Engn Bratislava 84216 Slovakia

ISBN: (纸本)9783642112652

Quality of collective inference relational graph classifier depends on a. degree of homophily in a classified graph. If we increase homophily in the graph, the classifier would assign class-membership to the instances with reduced error rate. We propose to substitute traditionally used graph neighborhood method (based on direct neighborhood of vertex) with local graph ranking algorithm (activation spreading), which provides wider set of neighboring vertices and their weights. We demonstrate that our approach increases homophily in the graph by inferring optimal homophily distribution of a binary Simple Relational Classifier in an unweighted graph. We validate this ability also experimentally using the Social Network of the Slovak Companies dataset.

关键词： Graph theory

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Lessons in Software Evolution Learned by Listening to Smalltalk

Lessons in Software Evolution Learned by Listening to Smallt...

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36th conference on current trends in theory and practice of computer science

作者： Nierstrasz, Oscar Girba, Tudor Univ Bern Software Composit Grp CH-3012 Bern Switzerland

ISBN: (纸本)9783642112652

the biggest challenge facing software developers today is how to gracefully evolve complex software systems in the face of changing requirements. We clearly need software systems to be more dynamic, compositional and model-centric, but instead we continue to build systems that are static, baroque and inflexible. How can we better build change-enabled systems in the future? To answer this question, we propose to look back to one of the most successful systems to support change, namely Smalltalk. We briefly introduce Smalltalk with a few simple examples, and draw some lessons for software evolution. Smalltalk's simplicity, its reflective design, and its highly dynamic nature all go a long way towards enabling change in Smalltalk applications. We then illustrate how these lessons work in practice by reviewing a number of research projects that support software evolution by exploiting Smalltalk's design. We conclude by summarizing open issues and challenges for change-enabled systems of the future.

关键词： computer software

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