Reachability in choice networks

In this paper, we investigate the problem of determining s - t reachability in choice networks. In the traditional s - t reachability problem, we are given a weighted network tuple G = < V, E, c, s, t >, with the goal of checking if there exists a path from s to t in G. In an optional choice network, we are given a choice set S subset of E x E, in addition to the network tuple G. In the s - t reachability problem in choice networks (OCRD), the goal is to find whether there exists a path from vertex s to vertex t, with the caveat that at most one edge from each edge-pair (x, y) is an element of S is used in the path. OCRD finds applications in a number of domains, including routing in wireless networks and sensor placement. We analyze the computational complexities of the OCRD problem and its variants from a number of algorithmic perspectives. We show that the problem is NP-complete in directed acyclic graphs with bounded pathwidth. Additionally, we show that its optimization version is NPO PB-complete. Additionally, we show that the problem is fixed-parameter tractable in the cardinality of the choice set S. In particular, we show that the problem can be solved in time O*(1.42|S|). We also consider weighted versions of the OCRD problem and detail their computational complexities; in particular, the optimization version of the W OCRD problem is NPO-complete. While similar results have been obtained for related problems, our results improve on those results by providing stronger results or by providing results for more limited graph types.(c) 2023 Elsevier B.V. All rights reserved.