We consider an optimization problem consisting of an undirected graph, with cost and profit functions defined on all vertices. The goal is to find a connected subset of vertices with maximum total profit, whose total cost does not exceed a given budget. The best result known prior to this work guaranteed a (2,O(log n)) bicriteria approximation, i.e. the solution's profit is at least a fraction of (1/O(log n)) of an optimum solution respecting the budget, while its cost is at most twice the given budget. We improve these results and present a bicriteria tradeoff that, given any ε ∈ (0,1), guarantees a (1 + ε,O((1/ε) log n))-approximation.
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