Lower Bounds for Structuring Unreliable Radio Networks

TL;DR

This paper establishes fundamental lower bounds for randomized algorithms solving MIS and CDS problems in unreliable radio networks, highlighting the importance of network topology constraints and prior knowledge for efficiency.

Contribution

It proves that certain network assumptions are necessary for efficient solutions, confirming the optimality of existing algorithms under these conditions.

Findings

Geographic constraints are necessary for efficient solutions.

Prior knowledge of reliable neighbors is crucial for algorithm efficiency.

Existing algorithms are optimal given the dual graph model assumptions.

Abstract

In this paper, we study lower bounds for randomized solutions to the maximal independent set (MIS) and connected dominating set (CDS) problems in the dual graph model of radio networks---a generalization of the standard graph-based model that now includes unreliable links controlled by an adversary. We begin by proving that a natural geographic constraint on the network topology is required to solve these problems efficiently (i.e., in time polylogarthmic in the network size). We then prove the importance of the assumption that nodes are provided advance knowledge of their reliable neighbors (i.e, neighbors connected by reliable links). Combined, these results answer an open question by proving that the efficient MIS and CDS algorithms from [Censor-Hillel, PODC 2011] are optimal with respect to their dual graph model assumptions. They also provide insight into what properties of an unreliable network enable efficient local computation.