Improved Approximation Algorithms for the Max-Edge Coloring Problem

The max edge-coloring problem asks for a proper edge-coloring of an edge-weighted graph minimizing the sum of the weights of the heaviest edge in each color class. In this paper we present a PTAS for trees and an 1.74-approximation algorithm for bipartite graphs; we also adapt the last algorithm to one for general graphs of the same, asymptotically, approximation ratio. Up to now, no approximation algorithm of ratio 2-δ, for any constant δ > 0, was known for general or bipartite graphs, while the complexity of the problem on trees remains an open question.

[1]  Marek Kubale.  Some results concerning the complexity of restricted colorings of graphs , 1992, Discret. Appl. Math..

[2]  Vangelis Th. Paschos,et al.  Approximating the Max Edge-Coloring Problem , 2009, IWOCA.

[3]  Rajiv Raman,et al.  Approximation Algorithms for the Max-coloring Problem , 2005, ICALP.

[4]  Vangelis Th. Paschos,et al.  On the max-weight edge coloring problem , 2010, J. Comb. Optim..

[5]  Dominique de Werra,et al.  Restrictions and Preassignments in Preemptive open Shop Scheduling , 1996, Discret. Appl. Math..

[6]  Chak-Kuen Wong,et al.  Minimizing the Number of Switchings in an SS/TDMA System , 1985, IEEE Trans. Commun..

[7]  Leah Epstein,et al.  On the Max Coloring Problem , 2007, WAOA.

[8]  Gerd Finke,et al.  Batch processing with interval graph compatibilities between tasks , 2005, Discret. Appl. Math..

[9]  Kirill Kogan,et al.  Nonpreemptive Scheduling of Optical Switches , 2007, IEEE Transactions on Communications.

[10]  Richard P. Anstee,et al.  An Algorithmic Proof of Tutte's f-Factor Theorem , 1985, J. Algorithms.

[11]  Rajiv Raman,et al.  Buffer minimization using max-coloring , 2004, SODA '04.

[12]  D. de Werra,et al.  Time slot scheduling of compatible jobs , 2007, J. Sched..

[13]  Vangelis Th. Paschos,et al.  Weighted coloring on planar, bipartite and split graphs: Complexity and approximation , 2009, Discret. Appl. Math..

[14]  Vangelis Th. Paschos,et al.  Weighted Coloring: further complexity and approximability results , 2006, Inf. Process. Lett..

[15]  Ian Holyer,et al.  The NP-Completeness of Edge-Coloring , 1981, SIAM J. Comput..

[16]  Jean-Pierre Bourguignon,et al.  Mathematische Annalen , 1893 .

[17]  D. König.  Über Graphen und ihre Anwendung auf Determinantentheorie und Mengenlehre , 1916 .

[18]  Telikepalli Kavitha,et al.  Max-Coloring Paths: Tight Bounds and Extensions , 2009, ISAAC.

[19]  Hadas Shachnai,et al.  Batch Coloring Flat Graphs and Thin , 2008, SWAT.

[20]  Vangelis Th. Paschos,et al.  Weighted Coloring: Further Complexity and Approximability Results , 2005, ICTCS.