Approximate local sums and their applications in radio networks

Abstract

Although any problem in a radio network can be solved using broadcast algorithms, some problems can be solved substantially more efficiently by more specialized algorithms. This paper presents two new approximate algorithms for the local sum problem, in which each node computes a (1 ± ∈)-approximation to the sum of the values held by its incoming neighbors (nodes that have outgoing edges to the node). We propose algorithms both with and without collision detection, as well as for the beeping model, with round complexity where n is the number of nodes and the value held by each node is a real number in {0}∪[1,m]. We then show how these algorithms can be used as building blocks to construct applications such as approximate random walk distribution, PageRank, and global sum.