The Bounded Edge Coloring Problem and Offline Crossbar Scheduling

TL;DR

This paper studies a new variant of edge coloring related to crossbar switch scheduling, proving NP-completeness, developing bounds, and evaluating approximation algorithms with promising results.

Contribution

It introduces a novel edge coloring variant for crossbar scheduling, establishes its NP-completeness, and analyzes approximation algorithms both theoretically and experimentally.

Findings

NP-complete problem variant identified

Approximation algorithms with 3/2 worst-case ratio developed

Experimental results show algorithms closely match lower bounds

Abstract

This paper introduces a variant of the classical edge coloring problem in graphs that can be applied to an offline scheduling problem for crossbar switches. We show that the problem is NP-complete, develop three lower bounds bounds on the optimal solution value and evaluate the performance of several approximation algorithms, both analytically and experimentally. We show how to approximate an optimal solution with a worst-case performance ratio of $3/2$ and our experimental results demonstrate that the best algorithms produce results that very closely track a lower bound.