Hardness And Approximation Of The Survivable Multi-Level Fat Tree Problem

With the explosive deployment of "triple play" (voice, video and data services) over the same access network, guaranteeing a certain-level of survivability for the access network is becoming critical for service providers. The problem of economically provisioning survivable access networks has given rise to a new class of network design problems, including the so-called SURVIVABLE MULTI-LEVEL FAT TREE problem (SMFT).We show that two special cases Of SMFT are polynormal-time solvable, and present two approximation algorithms for the general case. The first is a combinatorial algorithm with approximation ratio min{[L/2] + 1,2 log(2) n} where L is the longest Steiner path length between two terminals, and n is the number of nodes. The second is a primal-dual (2 Delta(s) + 2)-approximation algorithm where A. is the maximum Steiner degree of terminals in the access network. We then show that approximating SMFT to within a certain constant c > 1 is NP-hard, even when all edge-weights of G are 1, L <= 10, and Delta(s) <= 3. Finally, we experimentally show that the approximation algorithms perform extremely well on random instances of the problem.