We study algorithms for the simple equal ow problem on generalized networks. Network ows problems are concerned with optimization of the ow of... Show moreWe study algorithms for the simple equal ow problem on generalized networks. Network ows problems are concerned with optimization of the ow of commodities over a network, a directed graph. In a network, the amount of ow that leaves a node equals the ow that arrives at the destination node. However, generalized networks have arc multipliers which change the rate of ow on each arc. A classical network ow problem is the min cost ow problem which asks for minimum cost required for the ow of a commodity that satis es individual commodity requirements of each node in a network. The simple equal ow problem considers the min cost ow problem with an additional non-network constraint that requires certain arcs to have equal ow. Ahuja et al. [2] developed a combinatorial parametric algorithm, binary search algorithm, and capacity scaling algorithm for the simple equal ow problem. In this thesis, we extend the rst two algorithms to generalized networks. To do so, we must rst reformulate the simple equal ow problem on generalized networks to parameterize the equal ow arcs. The resulting linear program creates a piecewise linear convex curve as a function of the parameter. Then, we exploit the simplex algorithm derived combinatorial basis of generalized networks to determine the distance between breakpoints of the piecewise parametric linear convex curve of optimal solutions, which helps to determine the appropriate termination condition for the algorithms. This allows us to formulate the modi ed combinatorial parametric algorithm and the modi ed binary search algorithm, and their running times. M.S. in Applied Mathematics, July 2011 Show less
