A Faster Algorithm for Asymptotic Communication for Omniscience

TL;DR

This paper introduces a faster, more efficient algorithm (MDA) for solving the asymptotic communication for omniscience problem, capable of handling real or fractional rates, and improves upon existing methods in complexity.

Contribution

The paper presents a modified decomposition algorithm (MDA) and a fusion-based implementation of CoordSatCapFus, reducing complexity and extending solutions to non-asymptotic cases with integral rates.

Findings

MDA algorithm is less complex than existing algorithms.

The fusion method accelerates solving the Dilworth truncation problem.

Non-asymptotic CO problem can be solved with an additional CoordSatCapFus call.

Abstract

We propose a modified decomposition algorithm (MDA) to solve the asymptotic communication for omniscience (CO) problem where the communication rates could be real or fractional. By starting with a lower estimation of the minimum sum-rate, the MDA algorithm iteratively updates the estimation by the optimizer of a Dilworth truncation problem until the minimum is reached with a corresponding optimal rate vector. We also propose a fusion method implementation of the coordinate-wise saturation capacity algorithm (CoordSatCapFus) for solving the Dilworth truncation problem, where the minimization is done over a fused user set with a cardinality smaller than the original one. We show that the MDA algorithm is less complex than the existing ones. In addition, we show that the non-asymptotic CO problem, where the communication rates are integral, can be solved by one more call of the CoordSatCapfus algorithm. By choosing a proper linear ordering of the user indices in the MDA algorithm, the optimal rate vector is also the one with the minimum weighted sum-rate.