Optimal Reverse Carpooling Over Wireless Networks - A Distributed Optimization Approach

TL;DR

This paper develops a distributed optimization method for reverse carpooling in wireless networks, minimizing broadcasts needed for unicast demands by leveraging network coding and dual decomposition.

Contribution

It introduces a polynomial-sized linear programming formulation and a decentralized algorithm using dual decomposition for optimal routing with network coding.

Findings

The algorithm achieves optimal routing schemes.

It operates with local neighbor communication.

The primal sub-problem reduces to shortest path computations.

Abstract

We focus on a particular form of network coding, reverse carpooling, in a wireless network where the potentially coded transmitted messages are to be decoded immediately upon reception. The network is fixed and known, and the system performance is measured in terms of the number of wireless broadcasts required to meet multiple unicast demands. Motivated by the structure of the coding scheme, we formulate the problem as a linear program by introducing a flow variable for each triple of connected nodes. This allows us to have a formulation polynomial in the number of nodes. Using dual decomposition and projected subgradient method, we present a decentralized algorithm to obtain optimal routing schemes in presence of coding opportunities. We show that the primal sub-problem can be expressed as a shortest path problem on an \emph{edge-graph}, and the proposed algorithm requires each node to exchange information only with its neighbors.