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Related papers: Parity Games of Bounded Tree-Depth

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Planarity Testing is the problem of determining whether a given graph is planar while planar embedding is the corresponding construction problem. The bounded space complexity of these problems has been determined to be exactly Logspace by…

Computational Complexity · Computer Science 2015-03-17 Samir Datta , Gautam Prakriya

We continue the study of graph classes in which the treewidth can only be large due to the presence of a large clique, and, more specifically, of graph classes with bounded tree-independence number. In [Dallard, Milani\v{c}, and…

Data Structures and Algorithms · Computer Science 2022-09-27 Martin Milanič , Paweł Rzążewski

The additively separable hedonic game (ASHG) is a model of coalition formation games on graphs. In this paper, we intensively and extensively investigate the computational complexity of finding several desirable solutions, such as a Nash…

Computational Complexity · Computer Science 2019-10-23 Tesshu Hanaka , Hironori Kiya , Yasuhide Maei , Hirotaka Ono

Parameterized complexity theory has enabled a refined classification of the difficulty of NP-hard optimization problems on graphs with respect to key structural properties, and so to a better understanding of their true difficulties. More…

Data Structures and Algorithms · Computer Science 2017-10-19 David Coudert , Guillaume Ducoffe , Alexandru Popa

The recently introduced graph parameter tree-cut width plays a similar role with respect to immersions as the graph parameter treewidth plays with respect to minors. In this paper, we provide the first algorithmic applications of tree-cut…

Data Structures and Algorithms · Computer Science 2022-06-03 Robert Ganian , Eun Jung Kim , Stefan Szeider

For a tree decomposition $\mathcal{T}$ of a graph $G$, let $\mu(\mathcal{T})$ denote the maximum size of an induced matching in $G$ with the property that some bag of $\mathcal{T}$ contains at least one endpoint of every edge of the…

The node-averaged complexity of a problem captures the number of rounds nodes of a graph have to spend on average to solve the problem in the LOCAL model. A challenging line of research with regards to this new complexity measure is to…

Distributed, Parallel, and Cluster Computing · Computer Science 2024-05-03 Alkida Balliu , Sebastian Brandt , Fabian Kuhn , Dennis Olivetti , Gustav Schmid

Parameterized algorithms are a way to solve hard problems more efficiently, given that a specific parameter of the input is small. In this paper, we apply this idea to the field of answer set programming (ASP). To this end, we propose two…

Logic in Computer Science · Computer Science 2017-02-10 Johannes Fichte , Markus Hecher , Michael Morak , Stefan Woltran

Parity games have important practical applications in formal verification and synthesis, especially to solve the model-checking problem of the modal mu-calculus. They are also interesting from the theory perspective, because they are widely…

Logic in Computer Science · Computer Science 2018-07-30 Tom van Dijk

Recent advances in bandit tools and techniques for sequential learning are steadily enabling new applications and are promising the resolution of a range of challenging related problems. We study the game tree search problem, where the goal…

Machine Learning · Statistics 2017-11-07 Emilie Kaufmann , Wouter Koolen

We consider combinatorial problems that can be solved in polynomial time for graphs of bounded treewidth but where the order of the polynomial that bounds the running time is expected to depend on the treewidth bound. First we review some…

Data Structures and Algorithms · Computer Science 2015-03-19 Stefan Szeider

We study strategic similarity of game positions in two-player extensive games of perfect information, by looking at the structure of their local game trees, with the aim of improving the performance of game playing agents in detecting…

Artificial Intelligence · Computer Science 2019-02-26 Sabrina Evans , Paolo Turrini

The Satisfactory Partition problem consists in deciding if the set of vertices of a given undirected graph can be partitioned into two nonempty parts such that each vertex has at least as many neighbours in its part as in the other part.…

Data Structures and Algorithms · Computer Science 2020-07-29 Ajinkya Gaikwad , Soumen Maity , Shuvam Kant Tripathi

In the well known planted clique problem, a clique (or alternatively, an independent set) of size $k$ is planted at random in an Erdos-Renyi random $G(n, p)$ graph, and the goal is to design an algorithm that finds the maximum clique (or…

Data Structures and Algorithms · Computer Science 2020-04-29 Uriel Feige , Vadim Grinberg

Transformers have revolutionized the field of machine learning. In particular, they can be used to solve complex algorithmic problems, including graph-based tasks. In such algorithmic tasks a key question is what is the minimal size of a…

Machine Learning · Computer Science 2026-01-29 Gilad Yehudai , Clayton Sanford , Maya Bechler-Speicher , Orr Fischer , Ran Gilad-Bachrach , Amir Globerson

In this paper, we show that the $(3k+4)$-dimensional Weisfeiler--Leman algorithm can identify graphs of treewidth $k$ in $O(\log n)$ rounds. This improves the result of Grohe & Verbitsky (ICALP 2006), who previously established the…

Data Structures and Algorithms · Computer Science 2024-04-26 Michael Levet , Puck Rombach , Nicholas Sieger

Treedepth, a more restrictive graph width parameter than treewidth and pathwidth, plays a major role in the theory of sparse graph classes. We show that there exists a constant $C$ such that for every positive integers $a,b$ and a graph…

Discrete Mathematics · Computer Science 2019-09-19 Wojciech Czerwiński , Wojciech Nadara , Marcin Pilipczuk

While discounted payoff games and classic games that reduce to them, like parity and mean-payoff games, are symmetric, their solutions are not. We have taken a fresh view on the constraints that optimal solutions need to satisfy, and…

Data Structures and Algorithms · Computer Science 2023-10-03 Daniele Dell'Erba , Arthur Dumas , Sven Schewe

In 2020, we initiated a systematic study of graph classes in which the treewidth can only be large due to the presence of a large clique, which we call $(\mathrm{tw},\omega)$-bounded. While $(\mathrm{tw},\omega)$-bounded graph classes are…

Combinatorics · Mathematics 2023-10-18 Clément Dallard , Martin Milanič , Kenny Štorgel

We investigate the parameterized complexity of Binary CSP parameterized by the vertex cover number and the treedepth of the constraint graph, as well as by a selection of related modulator-based parameters. The main findings are as follows:…

Discrete Mathematics · Computer Science 2023-09-22 Hans L. Bodlaender , Carla Groenland , Michał Pilipczuk