3 research outputs found

    Heuristic algorithms for the min-max edge 2-coloring problem

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    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 \emph{maximum edge qq-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 \emph{min-max edge qq-coloring}. The above mentioned graph problems, namely the maximum edge qq-coloring and the min-max edge qq-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 22-coloring problem. These algorithms are based on a \emph{Breadth First Search} (BFS)-based heuristic and on \emph{local search} methods like basic \emph{hill climbing}, \emph{simulated annealing} and \emph{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.Comment: This is a post-peer-review, pre-copyedit version of an article published in International Computing and Combinatorics Conference (COCOON'18). The final authenticated version is available online at: http://www.doi.org/10.1007/978-3-319-94776-1_5

    The min-max edge q-coloring problem

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    In this paper we introduce and study a new problem named \emph{min-max edge qq-coloring} which is motivated by applications in wireless mesh networks. The input of the problem consists of an undirected graph and an integer qq. The goal is to color the edges of the graph with as many colors as possible such that: (a) any vertex is incident to at most qq different colors, and (b) the maximum size of a color group (i.e. set of edges identically colored) is minimized. We show the following results: 1. Min-max edge qq-coloring is NP-hard, for any q≥2q \ge 2. 2. A polynomial time exact algorithm for min-max edge qq-coloring on trees. 3. Exact formulas of the optimal solution for cliques and almost tight bounds for bicliques and hypergraphs. 4. A non-trivial lower bound of the optimal solution with respect to the average degree of the graph. 5. An approximation algorithm for planar graphs.Comment: 16 pages, 5 figure
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