Distributed Models and Algorithms for Survivability in Network Routing

We introduce a natural distributed model for analyzing the survivability of distributed networks and network routing schemes based on considering the effects of local constraints on network connectivity. We investigate the computational consequences of two fundamental interpretations of the meaning of local constraints. We consider a fullduplex model in which constraints are applied to edges of a graph representing two-way communication links and a half-duplex model in which constraints are applied to edges representing one-way links. We show that the problem of determining the survivability of a network under the fullduplex model is NP-hard, even in the restricted case of simply defined constraints. We also show that the problem of determining the survivability of network routing under the half-duplex model is highly tractable. We are able to effectively determine fault-tolerant routing schemes that are able to dynamically adapt to withstand any connectivity threats consistent with the constraints of the half-duplex model. The routing scheme is based on a multitree data structure, and we are able to generate optimal multitrees of minimum weighted depth. We also investigate an optimization problem related to achieving survivable network routing using a small sets of retransmission or landmark sites. Although the associated optimization problem is NP-hard, we show that sufficiently dense graphs can achieve survivable routing schemes using a small sets of landmarks. We prove an associated extremal result that is optimal over all graphs with minimum degree .