Finding Optimal Strategies of Almost Acyclic Simple Stochatic Games
نویسندگان
چکیده
The optimal value computation for turned-based stochastic games with reachability objectives, also known as simple stochastic games, is one of the few problems in NP∩coNP which are not known to be in P. However, there are some cases where these games can be easily solved, as for instance when the underlying graph is acyclic. In this work, we try to extend this tractability to several classes of games that can be thought as ”almost” acyclic. We give some fixed-parameter tractable or polynomial algorithms in terms of different parameters such as the number of cycles or the size of the minimal feedback vertex set. keywords: algorithmic game theory · stochastic games · FPT algorithms
منابع مشابه
Finding Optimal Strategies of Almost Acyclic Simple Stochastic Games
The optimal value computation for turned-based stochastic games with reachability objectives, also known as simple stochastic games, is one of the few problems in NP ∩ coNP which are not known to be in P. However, there are some cases where these games can be easily solved, as for instance when the underlying graph is acyclic. In this work, we try to extend this tractability to several classes ...
متن کاملSimple Priced Timed Games are not That Simple
Priced timed games are two-player zero-sum games played on priced timed automata (whose locations and transitions are labeled by weights modeling the costs of spending time in a state and executing an action, respectively). The goals of the players are to minimise and maximise the cost to reach a target location, respectively. We consider priced timed games with one clock and arbitrary (positiv...
متن کاملA Classification of Weakly Acyclic Games
Weakly acyclic games form a natural generalization of the class of games that have the finite improvement property (FIP). In such games one stipulates that from any initial joint strategy some finite improvement path exists. We classify weakly acyclic games using the concept of a scheduler introduced in [15]. We also show that finite games that can be solved by the iterated elimination of never...
متن کاملFinding Induced Acyclic Subgraphs in Random Digraphs
Consider the problem of finding a large induced acyclic subgraph of a given simple digraph D = (V,E). The decision version of this problem is NP -complete and its optimization is not likely to be approximable within a ratio of O(n ) for some > 0. We study this problem when D is a random instance. We show that, almost surely, any maximal solution is within an o(ln n) factor from the optimal one....
متن کاملImproved upper bounds for Random-Edge and Random-Jump on abstract cubes
Upper bounds are given for the complexity of two very natural randomized algorithms for finding the sink of an Acyclic Unique Sink Orientation (AUSO) of the ncube. For Random-Edge, we obtain an upper bound of about 1.80n, improving upon the the previous upper bound of about 2n/nlogn obtained by Gärtner and Kaibel. For Random-Jump, we obtain an upper bound of about (3/2)n, improving upon the pre...
متن کامل