Compact Routing Messages in Self-Healing Trees

TL;DR

This paper introduces the first self-healing compact routing schemes that maintain efficient routing and resilience in dynamic networks with node failures, using minimal memory and quick recovery times.

Contribution

It presents two novel algorithms, CompactFT and CompactFTZ, enabling self-healing and compact routing with low memory and fast recovery in adversarial failure models.

Findings

CompactFT recovers from node deletions in O(1) time with minimal message overhead.

CompactFTZ guarantees message delivery despite node failures, with bounded latency.

Both schemes operate with low memory, O(log^2 n) and O(log n) respectively.

Abstract

Existing compact routing schemes, e.g., Thorup and Zwick [SPAA 2001] and Chechik [PODC 2013], often have no means to tolerate failures, once the system has been setup and started. This paper presents, to our knowledge, the first self-healing compact routing scheme. Besides, our schemes are developed for low memory nodes, i.e., nodes need only $O(\log^2 n)$ memory, and are thus, compact schemes. We introduce two algorithms of independent interest: The first is CompactFT, a novel compact version (using only $O(\log n)$ local memory) of the self-healing algorithm Forgiving Tree of Hayes et al. [PODC 2008]. The second algorithm (CompactFTZ) combines CompactFT with Thorup-Zwick's tree-based compact routing scheme [SPAA 2001] to produce a fully compact self-healing routing scheme. In the self-healing model, the adversary deletes nodes one at a time with the affected nodes self-healing locally by adding few edges. CompactFT recovers from each attack in only $O(1)$ time and $\Delta$ messages, with only +3 degree increase and $O(log \Delta)$ graph diameter increase, over any sequence of deletions ($\Delta$ 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 $O(y \log \Delta)$ 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 removed from the network.