On the complexity of the max-edge-coloring problem with its variants

  • Authors:
  • Chang Wu Yu

  • Affiliations:
  • Department of Computer Science and Information Engineering, Chung Hua University, Hsinchu, Taiwan, R. O.C

  • Venue:
  • ESCAPE'07 Proceedings of the First international conference on Combinatorics, Algorithms, Probabilistic and Experimental Methodologies
  • Year:
  • 2007

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Abstract

The max-edge-coloring problem (MECP) is finding an edge colorings {E1, E2, E3, .., Ez} of a weighted graph G=(V, E) to minimize Σi=1z max {w(ek)|ek ∈Ei}, where w(ek) is the weight of ek. 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.