An integer program and new lower bounds for computing the strong rainbow connection numbers of graphs

Abstract

We present an integer programming model to compute the strong rainbow connection number, src(G), of any simple graph G. We introduce several enhancements to the proposed model, including a fast heuristic, and a variable elimination scheme. Moreover, we present a novel lower bound for src(G) which may be of independent research interest. We solve the integer program both directly and using an alternative method based on iterative lower bound improvement, the latter of which we show to be highly effective in practice. To our knowledge, these are the first computational methods for the strong rainbow connection problem. We demonstrate the efficacy of our methods by computing the strong rainbow connection numbers of graphs containing up to 379 vertices.

Document Details

Document Type
Pub Defense Publication
Publication Date
Feb 28, 2021
Source ID
10.1002/net.22031

Entities

People

  • David Mildebrath
  • Illya V. Hicks
  • Logan A. Smith

Organizations

  • National Science Foundation
  • Rice University
  • United States Department of Defense

Tags

Fields of Study

  • Computer science
  • Mathematics

Readers

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