Dynamic Tree Routing under the "Matching with Consumption" Model

In this paper we consider dynamic routing on trees under the \matching with consumption" routing model, a natural extension of the matching routing model introduced by Alon, Chung and Gra-ham 1, 2], which allows for the consumption of packets when they reach their destination. We present an asymptotically optimal on-line algorithm that routes k packets to their destination within d(k ? 1) + d dist routing steps where d is the degree of tree T on which the routing takes place and dist is the maximum distance some packet has to travel. We present an oo-line algorithm that solves the same problem within 2(k ? 1) + dist steps. Versions of both the on-line and the oo-line algorithms which avoid live-lock situations are also provided. We establish a close relation between the \matching with consumption" and the hot-potato routing models, and we exploit it in the analysis of our routing algorithms.