Abstract

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

Links

• presentation at PODC 2014

Conference Version

• Mika Göös, Juho Hirvonen, and Jukka Suomela: Linear-in-Δ lower bounds in the LOCAL model · PODC 2014