Self-stabilizing pivot interval routing in general networks

Compact routing protocols are used to reduce the routing table size at the cost of the optimality of the computed (shortest) paths. Interval routing (IR) is a compact routing scheme, where nodes are labeled with unique integers from a continuous range, and the outgoing arcs in every node are labeled with a set of intervals forming a partition of the range. Pivot interval routing (PIR) applies IR to an arbitrary weighted network such that the stretch factor (the ratio between the length of a path induced by PIR and the actual distance between the nodes) is at most five and three on the average. A self-stabilizing system has the ability to automatically recover from transient faults in finite time. We present a self-stabilizing PIR (SPIR.). Our algorithm, with no knowledge of the network layout, tolerates node/link addition and/or failure, and builds correct routing tables in O(d√n(1+log n)) time units (d is the network diameter and n is the maximum number of nodes). The stretch factor and the average stretch factor are preserved. Each node builds its own routing table of size O(n¹2/log³2/n+Δlog n) bits (where A is the node degree) with a total number of O(n³2/Iog³2/n+nΔlog(n)) bits for the whole network (Δ is the maximum degree of a node in the network).