Abstract (100 words or less): |  | We study the global routing problem in VLSI design and the multicast routing problem in communication networks. First, we develop a model to minimize the total wirelength and total number of vias with respect to the capacity constraints for the global routing problem. Furthmore, we propose the model to minimize the total edge length in communication networks. For both problem we develop asymptotic approximation algorithms with a ratio c(1+epsilon), where c is the best known ratio for the minimum Steiner tree problem. |