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.
A. Popa—This work was supported by the research programme PN 1819 “Advanced IT resources to support digital transformation processes in the economy and society - RESINFO-TD” (2018), project PN 1819-01-01 “New research in complex systems modelling and optimization with applications in industry, business and cloud computing”, funded by the Ministry of Research and Innovation.
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References
Adamaszek, A., Popa, A.: Approximation and hardness results for the maximum edge q-coloring problem. In: Cheong, O., Chwa, K.-Y., Park, K. (eds.) ISAAC 2010. LNCS, vol. 6507, pp. 132–143. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-17514-5_12
Feng, W., Chen, P., Zhang, B.: Approximate maximum edge coloring within factor 2: a further analysis. In: ISORA, pp. 182–189 (2008)
Feng, W., Zhang, L., Qu, W., Wang, H.: Approximation Algorithms for maximum edge coloring problem. In: Cai, J.-Y., Cooper, S.B., Zhu, H. (eds.) TAMC 2007. LNCS, vol. 4484, pp. 646–658. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-72504-6_59
Feng, W., Zhang, L., Wang, H.: Approximation algorithm for maximum edge coloring. Theor. Comput. Sci. 410(11), 1022–1029 (2009)
Kirkpatrick, S., Gelatt, C.D., Vecchi, M.P., et al.: Optimization by simulated annealing. Science 220(4598), 671–680 (1983)
Kyasanur, P., Vaidya, N.H.: Routing and interface assignment in multi-channel multi-interface wireless networks. In: 2005 IEEE Wireless Communications and Networking Conference, vol. 4, pp. 2051–2056. IEEE (2005)
Larjomaa, T.: Improving bandwidth in wireless mesh networks. Master’s thesis, School of Electrical Engineering, Aalto University, February 2013
Larjomaa, T., Popa, A.: The min-max edge q-coloring problem. In: Kratochvíl, J., Miller, M., Froncek, D. (eds.) IWOCA 2014. LNCS, vol. 8986, pp. 226–237. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-19315-1_20
Larjomaa, T., Popa, A.: The min-max edge q-coloring problem. J. Graph Algorithms Appl. 19(1), 507–528 (2015)
Lipton, R., Tarjan, R.: Applications of a planar separator theorem. SIAM J. Comput. 9(3), 615–627 (1980)
Mincu, R.S.: Java implementation of heuristic algorithms for the maximum and min-max 2-coloring problems (2017). https://github.com/radusm/minmax
Muir, A., Garcia-Luma-Aceves, J.J.: A channel access protocol for multihop wireless networks with multiple channels. In: ICC 1998, vol. 3, pp. 1617–1621, June 1998
Raniwala, A., Chiueh, T.: Architecture and algorithms for an IEEE 802.11-based multi-channel wireless mesh network. In: INFOCOM, pp. 2223–2234 (2005)
Raniwala, A., Gopalan, K., Chiueh, T.: Centralized channel assignment and routing algorithms for multi-channel wireless mesh networks. Mobile Comput. Commun. Rev. 8(2), 50–65 (2004)
So, J., Vaidya, N.H.: Multi-channel MAC for ad hoc networks: handling multi-channel hidden terminals using a single transceiver. In: MobiHoc 2004, pp. 222–233. ACM (2004)
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Mincu, R.S., Popa, A. (2018). Heuristic Algorithms for the Min-Max Edge 2-Coloring Problem. In: Wang, L., Zhu, D. (eds) Computing and Combinatorics. COCOON 2018. Lecture Notes in Computer Science(), vol 10976. Springer, Cham. https://doi.org/10.1007/978-3-319-94776-1_55
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