Tighter Worst-Case Bounds on Algebraic Gossip

TL;DR

This paper improves worst-case bounds for algebraic gossip algorithms, simplifies proofs, and introduces new routing schemes that are more efficient and eliminate randomness, advancing the understanding of distributed message dissemination.

Contribution

Provides a simpler proof for existing bounds, reduces quadratic terms to linear, and introduces a routing scheme that improves efficiency and removes the need for randomization and coding.

Findings

Reduced the quadratic ΔD term to min{3n, ΔD}

Achieved order-optimal dissemination with a simple routing scheme

Eliminated randomness and coding in the routing process

Abstract

Gossip and in particular network coded algebraic gossip have recently attracted attention as a fast, bandwidth-efficient, reliable and distributed way to broadcast or multicast multiple messages. While the algorithms are simple, involved queuing approaches are used to study their performance. The most recent result in this direction shows that uniform algebraic gossip disseminates k messages in O({\Delta}(D + k + log n)) rounds where D is the diameter, n the size of the network and {\Delta} the maximum degree. In this paper we give a simpler, short and self-contained proof for this worst-case guarantee. Our approach also allows to reduce the quadratic {\Delta}D term to min{3n, {\Delta}D}. We furthermore show that a simple round robin routing scheme also achieves min{3n, {\Delta}D} + {\Delta}k rounds, eliminating both randomization and coding. Lastly, we combine a recent non-uniform gossip algorithm with a simple routing scheme to get a O(D + k + log^{O(1)}) gossip information dissemination algorithm. This is order optimal as long as D and k are not both polylogarithmically small.