Path Diminution is Unavoidable in Node-Disjoint Multipath Routing with Single Route Discovery

Abstract

In an ad hoc network, identification of all node-disjoint paths between a given pair of nodes is a challenging task. The phenomena that a protocol is not able to identify all node-disjoint paths that exist between a given pair of nodes is called path diminution. In this paper, we discuss that path diminution is unavoidable when a protocol discovers multiple node-disjoint paths in a single route discovery. We discuss schemes to mitigate path diminution. However, no such scheme is guaranteed to discover all node-disjoint paths that exist between a given pair of nodes. We have proved that one cannot devise an efficient algorithm that is guaranteed to compute all node-disjoint paths between a given pair of nodes in a single route discovery.