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This paper considers the communication for omniscience (CO) problem: A set ofusers observe a discrete memoryless multiple source and want to recover theentire multiple source via noise-free broadcast communications. We study theproblem of how to determine an optimal rate vector that attains omnisciencewith the minimum sum-rate, the total number of communications. The resultscover both asymptotic and non-asymptotic models where the transmission ratesare real and integral, respectively. We propose a modified decompositionalgorithm (MDA) and a sum-rate increment algorithm (SIA) for the asymptotic andnon-asymptotic models, respectively, both of which determine the value of theminimum sum-rate and a corresponding optimal rate vector in polynomial time.For the coordinate saturation capacity (CoordSatCap) algorithm, a nestingalgorithm in MDA and SIA, we propose to implement it by a fusion method andshow by experimental results that this fusion method contributes to a reductionin computation complexity. Finally, we show that the separable convexminimization problem over the optimal rate vector set in the asymptotic modelcan be decomposed by the fundamental partition, the optimal partition of theuser set that determines the minimum sum-rate, so that the problem can besolved more efficiently.

Determining Optimal Rates for Communication for Omniscience