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This paper considers the problem of designing fast, approximate, combinatorial algorithms for multicommodity flows and other fractional packing problems. We provide a different approach to these problems which yields faster and much simpler algorithms. Our approach also allows us to substitute shortest path computations for min-cost flow computations in(More)
In this paper, we analyze local search heuristics for the <italic>k</italic>-median and facility location problems. We define the {\em locality gap\/} of a local search procedure as the maximum ratio of a locally optimum solution (obtained using this procedure) to the global optimum. For <italic>k</italic>-median, we show that local search with swaps has a(More)
Consider the multicommodity flow problem in which the object is to maximize the sum of commodities routed. We prove the following approximate max-flow min-multicut theorem: min multicut O(log k) ~ max flow ~ min multicut, where k is the number of commodities. Our proof is constructive; it enables us to find a multicut within O(log k) of the max flow (and(More)
The group Steiner tree problem is a generalization of the Steiner tree problem where we are given several subsets (groups) of vertices in a weighted graph, and the goal is to find a minimum-weight connected subgraph containing at least one vertex from each group. The problem was introduced by Reich and Widmayer and linds applications in VLSI design. The(More)
We study the maximum integral multicommodity flow problem and the minimum multicut problem restricted to trees. This restriction is quite rich and contains as special cases classical optimization problems such as matching and vertex cover for general graphs. It is shown that both the maximum integral multicommodity flow and the minimum multicut problem are(More)
We propose a general dual-fitting technique for analyzing online scheduling algorithms in the unrelated machines setting where the objective function involves weighted flow-time, and we allow the machines of the on-line algorithm to have (1 + ε)-extra speed than the offline optimum (the so-called speed augmentation model). Typically, such algorithms are(More)