Estimating Minimum Sum-rate for Cooperative Data Exchange

TL;DR

This paper introduces a new method to estimate the minimum sum-rate in cooperative data exchange systems, reducing computational complexity and providing tighter bounds than previous approaches.

Contribution

It presents a novel deterministic algorithm to approximate a lower bound on the minimum sum-rate, improving efficiency and accuracy in CDE problem solutions.

Findings

The proposed lower bound is significantly tighter than existing bounds.

The deterministic algorithm reduces the need for repetitive complex computations.

Experiments confirm improved efficiency and accuracy in estimating the minimum sum-rate.

Abstract

This paper considers how to accurately estimate the minimum sum-rate so as to reduce the complexity of solving cooperative data exchange (CDE) problems. The CDE system contains a number of geographically close clients who send packets to help the others recover an entire packet set. The minimum sum-rate is the minimum value of total number of transmissions that achieves universal recovery (the situation when all the clients recover the whole packet set). Based on a necessary and sufficient condition for a supermodular base polyhedron to be nonempty, we show that the minimum sum-rate for a CDE system can be determined by a maximization over all possible partitions of the client set. Due to the high complexity of solving this maximization problem, we propose a deterministic algorithm to approximate a lower bound on the minimum sum-rate. We show by experiments that this lower bound is much tighter than those lower bounds derived in the existing literature. We also show that the deterministic algorithm prevents from repetitively running the existing algorithms for solving CDE problems so that the overall complexity can be reduced accordingly.