Restricted Flow Games

Classical graph problems are defined with respect to plain graphs, namely vertices connected by possibly weighted edges. On the other hand, model checking studies rich graph structure and semantics, in particular labeled graphs and game graphs, which model involved realistic settings. Extending classical graph problems to graphs with a rich semantics offers an interesting and fresh perspective for classical graph algorithms. In addition, it extends the applicability of graph algorithms to rich settings. In the classical maximum-flow problem, the goal is to find the maximal amount of flow that can be transferred through a network, by directing the flow in each vertex into outgoing edges. The problem has been recently extended to labeled graphs and game graphs. We introduce and study restricted flow games, an extension of the maximum flow-problem to graphs that are both labeled and game graphs. In these games, the edges of the network are labeled by letters over some alphabet, and the vertices are partitioned between two players, the authority and the environment. Each player directs the flow entering her vertices to outgoing edges. The goal of the authority is to maximize the amount of flow that reaches the target along routes that satisfy a given specification – a language over the alphabet of labels. We study several aspects of restricted flow game as well as the complexity of decision problems on them.