Related papers: New Deterministic Algorithms for Solving Parity Ga…
Parity games can be used to represent many different kinds of decision problems. In practice, tools that use parity games often rely on a specification in a higher-order logic from which the actual game can be obtained by means of an…
The performance of two pivoting algorithms, due to Lemke and Cottle and Dantzig, is studied on linear complementarity problems (LCPs) that arise from infinite games, such as parity, average-reward, and discounted games. The algorithms have…
This paper investigates the discrete-time asynchronous games in which noncooperative agents seek to minimize their individual cost functions. Building on the assumption of partial asynchronism, i.e., each agent updates at least once within…
We present two new deterministic algorithms for the Feedback Vertex Set problem parameterized by the solution size. We begin with a simple algorithm, which runs in O*((2 + \phi)^k) time, where \phi < 1.619 is the golden ratio. It already…
Nonzero-sum stochastic differential games with impulse controls offer a realistic and far-reaching modelling framework for applications within finance, energy markets, and other areas, but the difficulty in solving such problems has…
We consider concurrent games played by two-players on a finite-state graph, where in every round the players simultaneously choose a move, and the current state along with the joint moves determine the successor state. We study a…
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…
We study online bipartite edge coloring, with nodes on one side of the graph revealed sequentially. The trivial greedy algorithm is $(2-o(1))$-competitive, which is optimal for graphs of low maximum degree, $\Delta=O(\log n)$ [BNMN IPL'92].…
Calude et al. have recently shown that parity games can be solved in quasi-polynomial time, a landmark result that has led to a number of approaches with quasi-polynomial complexity. Jurdinski and Lasic have further improved the precise…
We study the fair k-set selection problem where we aim to select $k$ sets from a given set system such that the (weighted) occurrence times that each element appears in these $k$ selected sets are balanced, i.e., the maximum (weighted)…
The domination problem and its variants represent a classical domain within algorithmic graph theory. Among these variants, the paired-domination problem holds particular prominence due to its real-world implications in security and…
We analyse an algorithm solving stochastic mean-payoff games, combining the ideas of relative value iteration and of Krasnoselskii-Mann damping. We derive parameterized complexity bounds for several classes of games satisfying…
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…
The $k$-cardinality assignment problem asks for finding a maximal (minimal) weight of a matching of cardinality $k$ in a weighted bipartite graph $K_{n,n}$, $k \leq n$. The algorithm of Gassner and Klinz from 2010 for the parametric…
Evolutionary game theory is a powerful mathematical framework to study how intelligent individuals adjust their strategies in collective interactions. It has been widely believed that it is impossible to unilaterally control players'…
We introduce a `concrete complexity' model for studying algorithms for matching in bipartite graphs. The model is based on the "demand query" model used for combinatorial auctions. Most (but not all) known algorithms for bipartite matching…
We study the complexity of computing equilibria in binary public goods games on undirected graphs. In such a game, players correspond to vertices in a graph and face a binary choice of performing an action, or not. Each player's decision…
Node Kayles is a well-known two-player impartial game on graphs: Given an undirected graph, each player alternately chooses a vertex not adjacent to previously chosen vertices, and a player who cannot choose a new vertex loses the game. The…
We consider simple stochastic games $\mathcal G$ with energy-parity objectives, a combination of quantitative rewards with a qualitative parity condition. The Maximizer tries to avoid running out of energy while simultaneously satisfying a…
A naive way to solve the model-checking problem of the mu-calculus uses fixpoint iteration. Traditionally however mu-calculus model-checking is solved by a reduction in linear time to a parity game, which is then solved using one of the…