# A Practical Approach for Successive Omniscience

## TL;DR

This paper introduces a polynomial-time algorithm for efficiently achieving successive omniscience in a multi-user system, enabling staged information recovery without increasing total communication costs.

## Contribution

It proposes the CompSetSO algorithm to identify user subsets for local omniscience, facilitating a multi-stage approach to global omniscience with lower bound-based conditions.

## Key findings

- The algorithm finds complimentary user subsets in polynomial time.
- It enables multi-stage successive omniscience with minimal additional communication.
- A sufficient condition allows using lower bounds instead of exact minimum sum-rate.

## Abstract

The system that we study in this paper contains a set of users that observe a discrete memoryless multiple source and communicate via noise-free channels with the aim of attaining omniscience, the state that all users recover the entire multiple source. We adopt the concept of successive omniscience (SO), i.e., letting the local omniscience in some user subset be attained before the global omniscience in the entire system, and consider the problem of how to efficiently attain omniscience in a successive manner. Based on the existing results on SO, we propose a CompSetSO algorithm for determining a complimentary set, a user subset in which the local omniscience can be attained first without increasing the sum-rate, the total number of communications, for the global omniscience. We also derive a sufficient condition for a user subset to be complimentary so that running the CompSetSO algorithm only requires a lower bound, instead of the exact value, of the minimum sum-rate for attaining global omniscience. The CompSetSO algorithm returns a complimentary user subset in polynomial time. We show by example how to recursively apply the CompSetSO algorithm so that the global omniscience can be attained by multi-stages of SO.