Compact routing messages in self-healing trees

© 2016.Existing compact routing schemes, e.g., Thorup and Zwick and Chechik 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(log2n) 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. that uses only . O(logn) bits local memory. The second algorithm (CompactFTZ) combines CompactFT with Thorup-Zwick's tree-based compact routing scheme 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(logδ) 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(ylogδ) 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(logn) bits memory for local fields (such as routing tables) and . O(log2n) bits for the routing labels, thus requiring . O(log2n) bits overall.