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Computing the winning set for B{\"u}chi objectives in alternating games on graphs is a central problem in computer aided verification with a large number of applications. The long standing best known upper bound for solving the problem is…
The goal of the thesis is to leverage fast graph algorithms and modern algorithmic techniques for problems in model checking and synthesis on graphs, MDPs, and game graphs. The results include symbolic algorithms, a well-known class of…
We study 2-player zero-sum concurrent (i.e., simultaneous move) stochastic B\"uchi games and Transience games on countable graphs. Two players, Max and Min, seek respectively to maximize and minimize the probability of satisfying the game…
The classical algorithm for solving B\"uchi games requires time $O(n\cdot m)$ for game graphs with $n$ states and $m$ edges. For game graphs with constant outdegree, the best known algorithm has running time $O(n^2/\log n)$. We present two…
Graph games provide the foundation for modeling and synthesis of reactive processes. Such games are played over graphs where the vertices are controlled by two adversarial players. We consider graph games where the objective of the first…
We study two-player concurrent stochastic games on finite graphs, with B\"uchi and co-B\"uchi objectives. The goal of the first player is to maximize the probability of satisfying the given objective. Following Martin's determinacy theorem…
The UNIQUE GAMES problem is a central problem in algorithms and complexity theory. Given an instance of UNIQUE GAMES, the STRONG UNIQUE GAMES problem asks to find the largest subset of vertices, such that the UNIQUE GAMES instance induced…
In recent years, there has been a growing interest in games on graphs within the research community, fueled by their relevance in applications such as economics, politics, and epidemiology. This paper aims to comprehensively detail the…
We consider fixpoint algorithms for two-player games on graphs with $\omega$-regular winning conditions, where the environment is constrained by a strong transition fairness assumption. Strong transition fairness is a widely occurring…
Graph games with {\omega}-regular winning conditions provide a mathematical framework to analyze a wide range of problems in the analysis of reactive systems and programs (such as the synthesis of reactive systems, program repair, and the…
The computation of the winning set for parity objectives and for Streett objectives in graphs as well as in game graphs are central problems in computer-aided verification, with application to the verification of closed systems with strong…
We introduce the notion of universal graphs as a tool for constructing algorithms solving games of infinite duration such as parity games and mean payoff games. In the first part we develop the theory of universal graphs, with two goals:…
Classic reachability games on graphs are zero-sum games, where the goal of one player, Eve, is to visit a vertex from a given target set, and that of other player, Adam, is to prevent this. Generalised reachability games, studied by…
The graph matching optimization problem is an essential component for many tasks in computer vision, such as bringing two deformable objects in correspondence. Naturally, a wide range of applicable algorithms have been proposed in the last…
We give an algorithm that decides whether the bipartite crossing number of a given graph is at most $k$. The running time of the algorithm is upper bounded by $2^{O(k)} + n^{O(1)}$, where $n$ is the number of vertices of the input graph,…
Parity games are an expressive framework to consider realizability questions for omega-regular languages. However, it is open whether they can be solved in polynomial time, making them unamenable for practical usage. To overcome this…
A dynamic graph algorithm is a data structure that answers queries about a property of the current graph while supporting graph modifications such as edge insertions and deletions. Prior work has shown strong conditional lower bounds for…
Combinatorial optimization algorithms for graph problems are usually designed afresh for each new problem with careful attention by an expert to the problem structure. In this work, we develop a new framework to solve any combinatorial…
The window mechanism, introduced by Chatterjee et al. for mean-payoff and total-payoff objectives in two-player turn-based games on graphs, refines long-term objectives with time bounds. This mechanism has proven useful in a variety of…
Parity games are games that are played on directed graphs whose vertices are labeled by natural numbers, called priorities. The players push a token along the edges of the digraph. The winner is determined by the parity of the greatest…