Randomized algorithms
Bipartite Edge Coloring in $O(\Delta m)$ Time
SIAM Journal on Computing
Edge Coloring of Bipartite Graphs with Constraints
MFCS '99 Proceedings of the 24th International Symposium on Mathematical Foundations of Computer Science
Constrained Bipartite Edge Coloring with Applications to Wavelength Routing
ICALP '97 Proceedings of the 24th International Colloquium on Automata, Languages and Programming
Approximating Circular Arc Colouring and Bandwidth Allocation in All-Optical Ring Networks
APPROX '98 Proceedings of the International Workshop on Approximation Algorithms for Combinatorial Optimization
Efficient access to optical bandwidth
FOCS '95 Proceedings of the 36th Annual Symposium on Foundations of Computer Science
Randomized rounding and discrete ham-sandwich theorems: provably good algorithms for routing and packing problems (integer programming)
Graphs and Hypergraphs
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We study the following Constrained Bipartite Edge Coloring (CBEC) problem:We are given a bipartite graph G(U, V,E) of maximum degree l with n vertices, in which some of the edges have been legally colored with c colors. We wish to complete the coloring of the edges of G minimizing the total number of colors used. The problem has been proved to be NP-hard even for bipartite graphs of maximum degree three [5]. In previous work Caragiannis et al. [2] consider two special cases of the problem and proved tight bounds on the optimal number of colors by decomposing the bipartite graph into matchings which are colored into pairs using detailed potential and averaging arguments. Their techniques lead to 3/2-aproximation algorithms for both problems. In this paper we present a randomized (1.37 + o(1))-approximation algorithm for the general problem in the case where max {l, c} = 驴(ln n). Our techniques are motivated by recent work of Kumar [11] on the Circular Arc Coloring problem and are essentially different and simpler than those presented in [2].