Theoretically, the running times of these algorithms are much less than that of linear-programming-based algorithms. We combine and modify the theoretical ideas in these approximation algorithms to yield a fast, practical implementation solving the minimum-cost multicommodity flow problem. From ReaSoN. Jump to: navigation , search. Personal tools Log in.
A combinatorial approximation algorithm for concurrent flow problem and its application. Suh-Wen Chiou. After several decades of sustained research and testing, linear programming has evolved into a remarkably reliable, accurate and useful tool for handling industrial optimization problems.
Yet, large problems arising from several concrete applications routinely defeat the very best linear programming Abstract - Cited by 4 self - Add to MetaCart After several decades of sustained research and testing, linear programming has evolved into a remarkably reliable, accurate and useful tool for handling industrial optimization problems.
Yet, large problems arising from several concrete applications routinely defeat the very best linear programming codes, running on the fastest computing hardware. Moreover, this is a trend that may well continue and intensify, as problem sizes escalate and the need for fast algorithms becomes more stringent. An alternative approach would be to explicitly, and rigorously, trade o accuracy for speed. One motivating factor is that in many practical applications, quickly obtaining a partially accurate solution is much preferable to obtaining a very accurate solution very slowly.
A secondary and independent consideration is that the input data in many practical applications has limited accuracy to begin with. During the last ten years, a new body ofresearch has emerged, which seeks to develop provably good approximation algorithms for classes of linear programming problems. This work both has roots in fundamental areas of mathematical programming and is also framed in the context ofthe modern theory ofalgorithms.
The result ofthis work has been a family ofalgorithms with solid theoretical foundations and with growing experimental success. In this manuscript we will study these algorithms, starting with some ofthe very earliest examples, and through the latest theoretical and computational developments.
We study a version of the capacity expansion problem CEP that arises in telecommunication network design. Given a capacitated network and a traffic demand matrix, the objective in the CEP is to add capacity to the edges, in batches of various modularities, and route traffic, so that the overall co Abstract - Cited by 76 8 self - Add to MetaCart We study a version of the capacity expansion problem CEP that arises in telecommunication network design.
Given a capacitated network and a traffic demand matrix, the objective in the CEP is to add capacity to the edges, in batches of various modularities, and route traffic, so that the overall cost is minimized.
We study the polyhedral structure of a mixed-integer formulation of the problem and develop a cutting-plane algorithm using facet defining inequalities. The algorithm produces an extended formulation providing both a very good lower bound and a starting point for branch and bound. The overall algorithm appears effective when applied to problem instances using real-life data. Citation Context The algorithm is based onthe polyhedralstudyintheaccompanying paper [16].
We describe the underlying problem,the model and the main ingredients in our algorithm: initial formulation,feasibility test, separation for strong cutting planes and primal heuristics. We will follow a similar idea to the way to when we were finding the shortest path between two particular vertices. The first type of constraint makes sure that we never say that a vertex is further away than it would be if we just took the edge corresponding to that constraint.
This is because the only thing holding back the variables is the information about relaxing along the edges, which is what determines shortest paths. Write out explicitly the linear program corresponding to finding the maximum flow in Figure Instead of indexing it by a pair of vertices, we will index it by an edge.
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