Survivable Networks with Bounded Delay

Abstract

We investigate new classes of graphs which guarantee constant delays even in the case of multiple edge failures. This means the following: as long as two vertices remain connected if some edges have failed, then the distance between these vertices in the faulty graph is at most a constant factor k times the original distance.<br /><br />In a first part, we consider k-self-spanners, the class of graphs where the distance constraint holds even for an unlimited number of edge faults. In particular, we give (non-algorithmic) strict characterizations of the graph classes and show that the problem of minimizing k such that a given graph is a k-self-spanner is co-NP-complete. For small values of k, characterizations in terms of possible topologies of biconnected components are given.<br /><br />In the second case, the number of edge failures is bounded by a constant l. These graphs are called (k,l)-self-spanners. We prove that the problem of maximizing l for a given graph when k>4 is fixed is NP-complete, whereas the dual problem of minimizing k when l is fixed is solvable in polynomial time. We show how graph operations such as Cartesian product and split composition affect the self-spanner properties of the composed graph. We also investigate several popular network topologies with respect to their self-spanner properties.