Algorithms and complexity analysis for some network design problems

This dissertation addresses three optimization problems arising from the areas of switching and access network design. The main contributions are the new analytical techniques for analyzing switching networks, the formulation of a new class of weighted graph coloring problems and along with some preliminary results on these problems, and an approximation algorithm to a new access network design problem. In particular, the three problems can briefly be described as follows. The first problem concerns the analysis of non-blocking switching networks. We observe that in many cases we can formulate a linear program to bound the number of "blocking" configurations to a new request. Then, by exploiting the structure of the primal linear program, or by specifying a family of dual-feasible solutions, we quickly derive a sufficient condition for the switching network to be non-blocking. We use this technique to analyze several Clos-type and Banyan-type switching networks. Both unicast and multicast results are discussed. The second problem is a weighted edge-coloring problem, which generalizes both edge-coloring and bin-packing in the natural way. We will focus on the dynamic version of this problem in this dissertation where weighted edges can arrive and depart. Finally, we consider a problem called Survivable Multi-Level Fat Tree (SMFT) which is a new variation of network design problems arising from access network design. This variation has an additional "fat-tree" constraint which renders existing solution to similar network design problem not useful. We present two approximation algorithms for this problem, one is combinatorial, the other is primal-dual, along with experimental results. We believe that the problems formulated and addressed in this dissertation, and the proposed techniques used for solving them will be applicable beyond the scope of the problems discussed here.