Broadcasting Spanning Forests on a Multiple-Access Channel

TL;DR

This paper studies distributed algorithms for finding minimum-weight spanning forests in a network where processors broadcast over a multiple-access channel, analyzing optimality and lower bounds for deterministic and randomized solutions.

Contribution

It introduces and analyzes algorithms for distributed spanning forest construction over a multiple-access channel, comparing deterministic and randomized approaches and establishing lower bounds.

Findings

Optimal algorithms are identified for certain classes of solutions.

Lower bounds justify the optimality of some algorithms.

Performance depends on whether algorithms are adaptive or oblivious.

Abstract

The problem of finding a spanning forest of a graph in a distributed-processing environment is studied. If an input graph is weighted, then the goal is to find a minimum-weight spanning forest. The processors communicate by broadcasting. The output consists of the edges that make a spanning forest and have been broadcast on the network. Input edges are distributed among the processors, with each edge held by one processor. The underlying broadcast network is implemented as a multiple-access channel. If exactly one processor attempts to perform a broadcast, then the broadcast is successful. A message broadcast successfully is delivered to all the processors in one step. If more than one processors broadcast simultaneously, then the messages interfere with each other and no processor can receive any of them. Optimality of algorithmic solutions is investigated, by way of comparing deterministic with randomized algorithms, and adaptive with oblivious ones. Lower bounds are proved that either justify the optimality of specific algorithms or show that the optimal performance depends on a class of algorithms.