Edge Coloring with Delays

Consider the following communication problem, that leads to a new notion of edge coloring. The communication network is represented by a bipartite multigraph, where the nodes on one side are the transmitters and the nodes on the other side are the receivers. The edges correspond to messages, and every edge e is associated with an integer c(e), corresponding to the time it takes the message to reach its destination. A proper k-edge-coloring with delays is a function f from the edges to {0, 1, ..., k − 1}, such that for every two edges e1 and e2 with the same transmitter, f(e1) = f(e2), and for every two edges e1 and e2 with the same receiver, f(e1) + c(e1) ≡ f(e2) + c(e2) (mod k). Haxell, Wilfong and Winkler [10] conjectured that there always exists a proper edge coloring with delays using k = ∆ + 1 colors, where ∆ is the maximum degree of the graph. We prove that the conjecture asymptotically holds for simple bipartite graphs, using a probabilistic approach, and further show t...

• Type: Conference
• Year: 2004
• Where: APPROX
• Authors: Noga Alon, Vera Asodi
• Keywords: Algorithms, APPROX 2004, Bipartite Multigraph, Communication Problem, Edge Coloring