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

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 $q$-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 \emph{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 \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

In this paper we introduce and study a new problem named \emph{min-max edge $q$-coloring} which is motivated by applications in wireless mesh networks. The input of the problem consists of an undirected graph and an integer $q$. 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 $q$ 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 $q$-coloring is NP-hard, for any $q \ge 2$. 2. A polynomial time exact algorithm for min-max edge $q$-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

Topology preservation and control approach for interference aware non-overlapping channel assignment in wireless mesh networks

The Wireless Mesh Networks (WMN) has attracted significant interests due to their fast and inexpensive deployment and the ability to provide flexible and ubiquitous internet access. A key challenge to deploy the WMN is the interference problem between the links. The interference results in three problems of limited throughput, capacity and fairness of the WMN. The topology preservation strategy is used in this research to improve the throughput and address the problems of link failure and partitioning of the WMN. However, the existing channel assignment algorithms, based on the topology preservation strategy, result in high interference. Thus, there is a need to improve the network throughput by using the topology preservation strategy while the network connectivity is maintained. The problems of fairness and network capacity in the dense networks are due to limited available resources in WMN. Hence, efficient exploitation of the available resources increases the concurrent transmission between the links and improves the network performance. Firstly, the thesis proposes a Topology Preservation for Low Interference Channel Assignment (TLCA) algorithm to mitigate the impact of interference based on the topology preservation strategy. Secondly, it proposes the Max-flow based on Topology Control Channel Assignment (MTCA) algorithm to improve the network capacity by removing useless links from the original topology. Thirdly, the proposed Fairness Distribution of the Non-Overlapping Channels (FNOC) algorithm improves the fairness of the WMN through an equitable distribution of the non-overlapping channels between the wireless links. The F-NOC is based on the Differential Evolution optimization algorithm. The numerical and simulation results indicate that the proposed algorithms perform better compared to Connected Low Interference Channel Assignment algorithm (CLICA) in terms of network capacity (19%), fractional network interference (80%) and network throughput (28.6%). In conclusion, the proposed algorithms achieved higher throughput, better network capacity and lower interference compared to previous algorithms

Approximation algorithm for maximum edge coloring

AbstractWe propose a polynomial time approximation algorithm for a novel maximum edge coloring problem which arises from wireless mesh networks [Ashish Raniwala, Tzi-cker Chiueh, Architecture and algorithms for an IEEE 802.11-based multi-channel wireless mesh network, in: INFOCOM 2005, pp. 2223–2234; Ashish Raniwala, Kartik Gopalan, Tzi-cker Chiueh, Centralized channel assignment and routing algorithms for multi-channel wireless mesh networks, Mobile Comput. Commun. Rev. 8 (2) (2004) 50–65]. The problem is to color all the edges in a graph with maximum number of colors under the following q-Constraint: for every vertex in the graph, all the edges incident to it are colored with no more than q (q∈Z,q≥2) colors. We show that the algorithm is a 2-approximation for the case q=2 and a (1+4q−23q2−5q+2)-approximation for the case q>2 respectively. The case q=2 is of great importance in practice. For complete graphs and trees, polynomial time accurate algorithms are found for them when q=2. The approximation algorithm gives a feasible solution to channel assignment in multi-channel wireless mesh networks