Linear-in-$\Delta$ Lower Bounds in the LOCAL Model

Abstract

By prior work, there is a distributed algorithm that finds a maximal fractional matching (maximal edge packing) in $O(\Delta )$ rounds, where $\Delta$ is the maximum degree of the graph. We show that this is optimal: there is no distributed algorithm that finds a maximal fractional matching in $o(\Delta )$ rounds. Our work gives the first linear-in-$\Delta$ lower bound for a natural graph problem in the standard model of distributed computing---prior lower bounds for a wide range of graph problems have been at best logarithmic in $\Delta$.

1 + 21 pages, 10 figures

References in corpus (2)

• Lower Bounds for Local Approximation
• Distributed Maximal Matching: Greedy is Optimal