Compact Routing Schemes for Dynamic Trees in the Fixed Port Model

Abstract

This paper considers the routing problem in dynamic trees under the fixed-port model, in which an adversary chooses the port numbers assigned to each node. We present two routing schemes for dynamic trees that maintain labels of asymptotically optimal size using extremely low average message complexity (per node). Specifically, we first present a dynamic routing scheme that supports additions of both leaves and internal nodes, maintains asymptotically optimal labels and incurs only O(log² n/log²logn) average message complexity. This routing scheme is then extended to supports also deletions of nodes of degree at most 2. The extended scheme incurs O(log² n) average message complexity and still maintains asymptotically optimal labels.

We would like to point out that the best known routing scheme for dynamic trees that maintains asymptotically optimal labels in the fixed port model has very high average message complexity, namely, O(n ^ε). Moreover, that scheme supports additions and removals of leaf nodes only.