Tight Bounds for MIS in Multichannel Radio Networks

TL;DR

This paper improves the efficiency of algorithms for computing maximal independent sets in multichannel radio networks, achieving asymptotic optimality and generalizing to broader graph classes.

Contribution

It removes the polyloglog factor in the runtime of MIS algorithms and extends the analysis to graphs with arbitrary local independence bounds.

Findings

Achieved asymptotically optimal MIS algorithm in multichannel radio networks.

Generalized the class of graphs for which MIS algorithms are effective.

Provided a new analysis that broadens applicability to various graph structures.

Abstract

Daum et al. [PODC'13] presented an algorithm that computes a maximal independent set (MIS) within $O(\log^2 n/F+\log n \mathrm{polyloglog} n)$ rounds in an $n$-node multichannel radio network with $F$ communication channels. The paper uses a multichannel variant of the standard graph-based radio network model without collision detection and it assumes that the network graph is a polynomially bounded independence graph (BIG), a natural combinatorial generalization of well-known geographic families. The upper bound of that paper is known to be optimal up to a polyloglog factor. In this paper, we adapt algorithm and analysis to improve the result in two ways. Mainly, we get rid of the polyloglog factor in the runtime and we thus obtain an asymptotically optimal multichannel radio network MIS algorithm. In addition, our new analysis allows to generalize the class of graphs from those with polynomially bounded local independence to graphs where the local independence is bounded by an arbitrary function of the neighborhood radius.