A better than “best possible” algorithm to edge color multigraphs
Journal of Algorithms
On the 1.1 edge-coloring of multigraphs
SIAM Journal on Discrete Mathematics
Asymptotics of the chromatic index for multigraphs
Journal of Combinatorial Theory Series B
Improving a family of approximation algorithms to edge color multigraphs
Information Processing Letters
A sublinear bound on the chromatic index of multigraphs
Discrete Mathematics
Approximating Maximum Edge Coloring in Multigraphs
APPROX '02 Proceedings of the 5th International Workshop on Approximation Algorithms for Combinatorial Optimization
Improved results for data migration and open shop scheduling
ACM Transactions on Algorithms (TALG)
Approximating the maximum 2- and 3-edge-colorable subgraph problems
Discrete Applied Mathematics
Graph edge colouring: Tashkinov trees and Goldberg's conjecture
Journal of Combinatorial Theory Series B
On a local protocol for concurrent file transfers
Proceedings of the twenty-third annual ACM symposium on Parallelism in algorithms and architectures
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The edge coloring problem asks for assigning colors from a minimum number of colors to edges of a graph such that no two edges with the same color are incident to the same node. We give polynomial time algorithms for approximate edge coloring of multigraphs, i.e., parallel edges are allowed. The best previous algorithms achieve a fixed constant approximation factor plus a small additive offset. Our algorithms achieve arbitrarily good approximation factors at the cost of slightly larger additive terms. In particular, for any ∈ 0 we achieve a solution quality of (1 + ∈)opt + O(1/∈). The execution times of one algorithm are independent of ∈ and polynomial in the number of nodes and the logarithm of the maximum edge multiplicity.