Biblio

We present and explore a model of stateless and self-stabilizing distributed computation, inspired by real-world applications such as routing on today's Internet. Processors in our model do not have an internal state, but rather interact by repeatedly mapping incoming messages ("labels") to outgoing messages and output values. While seemingly too restrictive to be of interest, stateless computation encompasses both classical game-theoretic notions of strategic interaction and a broad range of practical applications (e.g., Internet protocols, circuits, diffusion of technologies in social networks). Our main technical contribution is a general impossibility result for stateless self-stabilization in our model, showing that even modest asynchrony (with wait times that are linear in the number of processors) can prevent a stateless protocol from reaching a stable global configuration. Furthermore, we present hardness results for verifying stateless self-stabilization. We also address several aspects of the computational power of stateless protocols. Most significantly, we show that short messages (of length that is logarithmic in the number of processors) yield substantial computational power, even on very poorly connected topologies.

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(log2 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 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(y logΔ) 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.