Randomized path coloring on binary trees

Motivated by the problem of WDM routing in all–optical networks, we study the following NP–hard problem. We are given a directed binary tree T and a set R of directed paths on T. We wish to assign colors to paths in R, in such a way that no two paths that share a directed arc of T are assigned the same color and that the total number of colors used is minimized. Our results are expressed in terms of the depth of the tree and the maximum load l of R, i.e., the maximum number of paths that go through a directed arc of T. So far, only deterministic greedy algorithms have been presented for the problem. The best known algorithm colors any set R of maximum load l using at most 5l/3 colors. Alternatively, we say that this algorithm has performance ratio 5/3. It is also known that no deterministic greedy algorithm can achieve a performance ratio better than 5/3. In this paper we define the class of greedy algorithms that use randomization. We study their limitations and prove that, with ...

• Type: Conference
• Year: 2000
• Where: APPROX
• Authors: Vincenzo Auletta, Ioannis Caragiannis, Christos Kaklamanis, Pino Persiano
• Keywords: Algorithms, APPROX 2000, Deterministic Greedy Algorithm, Directed Arc, Greedy Algorithms