Polylog-Competitive Deterministic Local Routing and Scheduling
arxiv(2024)
摘要
This paper addresses point-to-point packet routing in undirected networks,
which is the most important communication primitive in most networks. The main
result proves the existence of routing tables that guarantee a
polylog-competitive completion-time deterministically: in any
undirected network, it is possible to give each node simple stateless
deterministic local forwarding rules, such that, any adversarially chosen set
of packets are delivered as fast as possible, up to polylog factors.
All previous routing strategies crucially required randomization for both
route selection and packet scheduling.
The core technical contribution of this paper is a new local packet
scheduling result of independent interest. This scheduling strategy integrates
well with recent sparse semi-oblivious path selection strategies. Such
strategies deterministically select not one but several candidate paths for
each packet and require a global coordinator to select a single good path from
those candidates for each packet. Another challenge is that, even if a single
path is selected for each packet, no strategy for scheduling packets along
low-congestion paths that is both local and deterministic is known. Our novel
scheduling strategy utilizes the fact that every semi-oblivious routing
strategy uses only a small (polynomial) subset of candidate routes. It
overcomes the issue of global coordination by furthermore being provably robust
to adversarial noise. This avoids the issue of having to choose a single path
per packet because congestion caused by ineffective candidate paths can be
treated as noise.
Our results imply the first deterministic universally-optimal algorithms in
the distributed supported-CONGEST model for many important global distributed
tasks, including computing minimum spanning trees, approximate shortest paths,
and part-wise aggregates.
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