Improved Combinatorial Algorithms for Wireless Information Flow

TL;DR

This paper presents an improved combinatorial algorithm for determining the unicast capacity in deterministic wireless network models, reducing computational complexity and enhancing efficiency over previous methods.

Contribution

It introduces a more efficient polynomial-time algorithm that fully exploits combinatorial features, applicable to any finite field size, improving upon prior algorithms.

Findings

Reduced algorithmic complexity compared to previous methods

Applicable to any finite field size in wireless network models

Competitive performance in computational experiments

Abstract

The work of Avestimehr et al. '07 has recently proposed a deterministic model for wireless networks and characterized the unicast capacity C of such networks as the minimum rank of the adjacency matrices describing all possible source-destination cuts. Amaudruz & Fragouli first proposed a polynomial-time algorithm for finding the unicast capacity of a linear deterministic wireless network in their 2009 paper. In this work, we improve upon Amaudruz & Fragouli's work and further reduce the computational complexity of the algorithm by fully exploring the useful combinatorial features intrinsic in the problem. Our improvement applies generally with any size of finite fields associated with the channel model. Comparing with other algorithms on solving the same problem, our improved algorithm is very competitive in terms of complexity.