Parameterized Complexity of Broadcasting in Graphs

TL;DR

This paper investigates the computational complexity of the broadcast problem in graphs, demonstrating fixed-parameter tractability when parameterized by feedback edge-set size, vertex-cover size, or deadline-related parameters.

Contribution

It establishes that the broadcast problem is fixed-parameter tractable with respect to certain graph parameters, providing new insights into its computational complexity.

Findings

NP-hardness of the broadcast problem.

FPT results for parameters like feedback edge-set and vertex-cover.

Fixed-parameter algorithms for deadline-based parameters.

Abstract

The task of the broadcast problem is, given a graph G and a source vertex s, to compute the minimum number of rounds required to disseminate a piece of information from s to all vertices in the graph. It is assumed that, at each round, an informed vertex can transmit the information to at most one of its neighbors. The broadcast problem is known to NP-hard. We show that the problem is FPT when parametrized by the size k of a feedback edge-set, or by the size k of a vertex-cover, or by k=n-t where t is the input deadline for the broadcast protocol to complete.