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 edges in the color classes. In this paper we present a PTAS for trees and a 1.74-approximation algorithm for bipartite graphs; we also adapt the last algorithm to one for general graphs of the same, asymptotically, approximation ratio.

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

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

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

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

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

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

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

[8]  Vangelis Th. Paschos,et al.  Approximating the max-edge-coloring problem , 2010, Theor. Comput. Sci..

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

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

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

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

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

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

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

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