Georgia Institute of Technology College of Sciences

Weighted Bipartite Edge Coloring problem is a generalization of two classical optimization problems: Bipartite Edge Coloring and Bin Packing. Given an edge-weighted bipartite multi-graph G, the goal is to color all edges with minimum colors such that the sum of the edges incident to any vertex of any color is at most one. Chung and Ross conjectured that given an instance of the weighted bipartite edge coloring problem, there is a proper weighted coloring using at most 2n-1 colors where n denotes the maximum over all the vertices of the number of unit-sized bins needed to pack the weights of edges incident at the vertex. In this talk I will present an algorithm that gives a proper weighted coloring using $20n/9$ colors and improved results for some special cases. I will also present an alternative proof of Konig's edge coloring theorem using skew-supermodular functions. The talk will have all three components of ACO: Approximation Algorithms, Graph Theory and Supermodular Optimization.