Compact routing messages in self-healing trees

Abstract

Existing compact routing schemes, e.g., Thorup and Zwick [4] and Chechik [6] often have no means to tolerate failures, once the system has been set up and started. This paper presents, to our knowledge, the first self-healing compact routing scheme. Besides, our schemes are developed for low memory nodes and are compact schemes, meaning they require only O(log2⁡n) bits memory.We introduce two algorithms of independent interest: The first is CompactFT, a novel compact version of the self-healing algorithm Forgiving Tree of Hayes et al. [7] that uses only O(log⁡n) bits local memory. The second algorithm (CompactFTZ) combines CompactFT with Thorup–Zwick's tree-based compact routing scheme [4] to produce a compact self-healing routing scheme. In the self-healing model, the adversary deletes nodes one at a time and the affected nodes self-heal locally by adding few edges. We introduce the bounded-memory self-healing model, where the memory each node need to use for the self-healing algorithm is bounded. CompactFT recovers from each attack in only O(1) time and Δ messages, with only +3 degree increase and O(log⁡Δ) graph diameter increase, over any sequence of deletions (Δ is the initial maximum degree).Additionally, CompactFTZ guarantees delivery of a packet sent from sender s as long as the receiver t has not been deleted, with only an additional O(ylog⁡Δ) latency, where y is the number of nodes that have been deleted on the path between s and t. If t has been deleted, s gets informed and the packet is removed from the network. CompactFTZ uses only O(log⁡n) bits memory for local fields (such as routing tables) and O(log2⁡n) bits for the routing labels, thus requiring O(log2⁡n) bits overall.