Fast Routing Table Construction Using Small Messages
Christoph Lenzen, Boaz Patt-Shamir

TL;DR
This paper introduces a fast distributed algorithm for approximate shortest path routing that uses small messages and nearly matches theoretical lower bounds, significantly improving efficiency in large networks.
Contribution
It presents the first distributed algorithm for weighted shortest paths with small messages and sublinear time complexity, using node labels and probabilistic guarantees.
Findings
Runs in weak-O(n^(1/2 + eps) + HD) rounds with high probability
Achieves stretch of O(eps^(-1) log eps^(-1)) for approximate shortest paths
Provides fast algorithms for related problems like Steiner Forest and diameter approximation
Abstract
We describe a distributed randomized algorithm computing approximate distances and routes that approximate shortest paths. Let n denote the number of nodes in the graph, and let HD denote the hop diameter of the graph, i.e., the diameter of the graph when all edges are considered to have unit weight. Given 0 < eps <= 1/2, our algorithm runs in weak-O(n^(1/2 + eps) + HD) communication rounds using messages of O(log n) bits and guarantees a stretch of O(eps^(-1) log eps^(-1)) with high probability. This is the first distributed algorithm approximating weighted shortest paths that uses small messages and runs in weak-o(n) time (in graphs where HD in weak-o(n)). The time complexity nearly matches the lower bounds of weak-Omega(sqrt(n) + HD) in the small-messages model that hold for stateless routing (where routing decisions do not depend on the traversed path) as well as approximation of…
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