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Given an edge-weighted connected graph G on n vertices and a positive integer k≤n, a subgraph of G on k vertices is called a k-subgraph in G. We design combinatorial approximation algorithms for finding a connected k-subgraph in G such that its weighted density is at least a factor Ω(max{1/k,k2/n2}) of the maximum weighted density among all k-subgraph in G (which are not necessarily connected), where...
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