Related papers: An Optimal Value Iteration Algorithm for Parity Ga…
In a landmark paper, Papadimitriou and Roughgarden described a polynomial-time algorithm ("Ellipsoid Against Hope") for computing sample correlated equilibria of concisely-represented games. Recently, Stein, Parrilo and Ozdaglar showed that…
Parity games are two-player infinite-duration games on graphs that play a crucial role in various fields of theoretical computer science. Finding efficient algorithms to solve these games in practice is widely acknowledged as a core problem…
We address the problem of solving parity games with imperfect information on finite graphs of bounded structural complexity. It is a major open problem whether parity games with perfect information can be solved in PTIME. Restricting the…
The minimum height of vertex and edge partition trees are well-studied graph parameters known as, for instance, vertex and edge ranking number. While they are NP-hard to determine in general, linear-time algorithms exist for trees.…
For common notions of correlated equilibrium in extensive-form games, computing an optimal (e.g., welfare-maximizing) equilibrium is NP-hard. Other equilibrium notions -- communication (Forges 1986) and certification (Forges & Koessler…
Universal methods for optimization are designed to achieve theoretically optimal convergence rates without any prior knowledge of the problem's regularity parameters or the accurarcy of the gradient oracle employed by the optimizer. In this…
Attractors in parity games are a technical device for solving "alternating" reachability of given node sets. A well known solver of parity games - Zielonka's algorithm - uses such attractor computations recursively. We here propose new…
To analyze the worst-case running time of branching algorithms, the majority of work in exponential time algorithms focuses on designing complicated branching rules over developing better analysis methods for simple algorithms. In the…
Characterizing the performance of no-regret dynamics in multi-player games is a foundational problem at the interface of online learning and game theory. Recent results have revealed that when all players adopt specific learning algorithms,…
It is well-known that the winning region of a parity game with $n$ nodes and $k$ priorities can be computed as a $k$-nested fixpoint of a suitable function; straightforward computation of this nested fixpoint requires…
We study strategy improvement algorithms for solving parity games. While these algorithms are known to solve parity games using a very small number of iterations, experimental studies have found that a high step complexity causes them to…
We introduce the novel notion of winning cores in parity games and develop a deterministic polynomial-time under-approximation algorithm for solving parity games based on winning core approximation. Underlying this algorithm are a number…
Priced timed games (PTGs) are two-player zero-sum games played on the infinite graph of configurations of priced timed automata where two players take turns to choose transitions in order to optimize cost to reach target states. Bouyer et…
We study polynomial-time approximation algorithms for (edge/vertex) Sparsest Cut and Small Set Expansion in terms of $k$, the number of edges or vertices cut in the optimal solution. Our main results are $\mathcal{O}(\text{polylog}\,…
There are many classical problems in P whose time complexities have not been improved over the past decades. Recent studies of "Hardness in P" have revealed that, for several of such problems, the current fastest algorithm is the best…
Two kinds of approximation algorithms exist for the k-BALANCED PARTITIONING problem: those that are fast but compute unsatisfying approximation ratios, and those that guarantee high quality ratios but are slow. In this paper we prove that…
We give a direct polynomial-time reduction from parity games played over the configuration graphs of collapsible pushdown systems to safety games played over the same class of graphs. That a polynomial-time reduction would exist was known…
Self-play via online learning is one of the premier ways to solve large-scale two-player zero-sum games, both in theory and practice. Particularly popular algorithms include optimistic multiplicative weights update (OMWU) and optimistic…
Dull, weak and nested solitaire games are important classes of parity games, capturing, among others, alternation-free mu-calculus and ECTL* model checking problems. These classes can be solved in polynomial time using dedicated algorithms.…
We define memory-efficient certificates for $\mu$-calculus model checking problems based on the well-known correspondence of the $\mu$-calculus model checking with winning certain parity games. Winning strategies can independently checked,…