Deterministic CONGEST Algorithm for MDS on Bounded Arboricity Graphs

Abstract

We provide a deterministic CONGEST algorithm to constant factor approximate the minimum dominating set on graphs of bounded arboricity in O(log n) rounds. This improves over the well known randomized algorithm of Lenzen and Wattenhofer [19] by making it a deterministic algorithm.

Distributed Distance-r Covering Problems on Sparse High-Girth Graphs

“…This means the algorithm selects at least r vertices per path, and there is one such path for each X × Y combination. Hence |D| ≥ r • 4 • f (r) 2 . Recall that |M| ≤ 4 f (r), so the algorithm achieves an approximation factor of at least r • f (r) for the constructed graph.…”

“…If we go slightly beyond these graphs, to graphs of bounded arboricity (where every subgraph has a constant edge density), the situation is worse: only an O (log )-approximation in O (log n) rounds was known. There was a O (log n) round O (1)-approximation in such graphs; however, this algorithm is randomized [22], only recently it has been proven that it can be performed determinisitically [2].…”