Heuristic Algorithms for the Min-Max Edge 2-Coloring Problem

Abstract

In multi-channel Wireless Mesh Networks (WMN), each node is able to use multiple non-overlapping frequency channels. Raniwala et al. (MC2R 2004, INFOCOM 2005 propose and study several such architectures in which a computer can have multiple network interface cards. These architectures are modeled as a graph problem named maximum edge q-coloring and studied in several papers by Feng et. al (TAMC 2007), Adamaszek and Popa (ISAAC 2010, JDA 2016). Later on Larjomaa and Popa (IWOCA 2014, JGAA 2015) define and study an alternative variant, named the min-max edge q-coloring. The above mentioned graph problems, namely the maximum edge q-coloring and the min-max edge q-coloring are studied mainly from the theoretical perspective. In this paper, we study the min-max edge 2-coloring problem from a practical perspective. More precisely, we introduce, implement and test four heuristic approximation algorithms for the min-max edge 2-coloring problem. These algorithms are based on a Breadth First Search (BFS)-based heuristic and on local search methods like basic hill climbing, simulated annealing and tabu search techniques, respectively. Although several algorithms for particular graph classes were proposed by Larjomaa and Popa (e.g., trees, planar graphs, cliques, bi-cliques, hypergraphs), we design the first algorithms for general graphs. We study and compare the running data for all algorithms on Unit Disk Graphs, as well as some graphs from the DIMACS vertex coloring benchmark dataset.

Best Path in Mountain Environment based on Parallel Hill Climbing Algorithm

“…Hill climbing is a heuristic search technique for solving certain mathematical optimization problems in the field of artificial intelligence [18]. In this technique, starting with a suboptimal solution is compared to starting from the base of the hill, and improving the solution is compared to walking up the hill; the solution is improved repeatedly until some condition is maximized and becomes optimal, as illustrated in Fig.…”