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Let <italic>G</italic>=(<italic>V,E</italic>) be an <italic>n</italic>-vertex connected graph with positive edge weights. A subgraph <italic>G</italic>&#8242; = (<italic>V,E</italic>&#8242;) is a <italic>t-spanner</italic> of <italic>G</italic> if for all <italic>u, v &#949; V</italic>,the weighted distance between <italic>u</italic> and <italic>v</italic>(More)
Given a collection of weighted sets, each containing at most k elements drawn from a finite base set, the k-set packing problem is to find a maximum weight sub-collection of disjoint sets. A greedy algorithm for this problem approximates it to within a factor of k, and natural local search has been shown to approximate it to within a factor of roughly k-1.(More)
Local search with k-change neighborhoods is perhaps the oldest and most widely used heuristic method for the traveling salesman problem, yet almost no theoretical performance guarantees for it were previously known. This paper develops several results, some worst-case and some probabilistic, on the performance of 2-and k-opt local search for the TSP, with(More)