Revisiting the complexity of and/or graph solution

An and/or graph is an acyclic, edge-weighted directed graph containing a single source vertex such that every vertex v has a label f(v)∈{and,or}. A solution subgraph H of an and/or-graph must contain the source and obey the following rule: if an and-vertex (resp. or-vertex) is included in H then all (resp. one) of its out-edges must also be included in H. X-y graphs are defined as a generalization of and/or graphs: every vertex vi of an x-y graph has a label xi-yi, in such a way that if a vertex vi is included in a solution subgraph H of an x-y graph then xi of its yi out-edges must also be included in H. In this work, we analyze complexity aspects (both from the classical and the parameterized point of view) of finding solution subgraphs of minimum weight for and/or and x-y graphs.

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