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On the Complexity of the Max-Edge-Coloring Problem with Its Variants

  • Conference paper
Combinatorics, Algorithms, Probabilistic and Experimental Methodologies (ESCAPE 2007)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4614))

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Abstract

The max-edge-coloring problem (MECP) is finding an edge colorings {E 1, E 2, E 3, ..., E z } of a weighted graph G = (V, E) to minimize \(\sum^{z}_{i-1} {\rm max} \{w(e_{k})|e_{k} \in E_{i}\}\), where w(e k ) is the weight of e k . In the work, we discuss the complexity issues on the MECP and its variants. Specifically, we design a 2-approximmation algorithm for the max-edge-coloring problem on biplanar graphs, which is bipartite and has a biplanar drawing. Next, we show the splitting chromatic max-edge-coloring problem, a variant of MECP, is NP-complete even when the input graph is restricted to biplanar graphs. Finally, we also show that these two problems have applications in scheduling data redistribution on parallel computer systems.

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Authors and Affiliations

  1. Department of Computer Science and Information Engineering, Chung Hua University, Hsinchu, Taiwan 300, R.O.C

    Chang Wu Yu

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  1. Chang Wu Yu
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Bo Chen Mike Paterson Guochuan Zhang

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Yu, C.W. (2007). On the Complexity of the Max-Edge-Coloring Problem with Its Variants. In: Chen, B., Paterson, M., Zhang, G. (eds) Combinatorics, Algorithms, Probabilistic and Experimental Methodologies. ESCAPE 2007. Lecture Notes in Computer Science, vol 4614. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74450-4_32

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  • DOI: https://doi.org/10.1007/978-3-540-74450-4_32

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-74449-8

  • Online ISBN: 978-3-540-74450-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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