Bicriteria approximation tradeoff for the node-cost budget problem

Authors:
Yuval Rabani;Gabriel Scalosub
Affiliations:
Technion—Israel Institute of Technology, Haifa, Israel;University of Toronto, Toronto, ON, Canada
Venue:
ACM Transactions on Algorithms (TALG)
Year:
2009

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Abstract

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, that is, 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 + &epsis;, O(1/ϵ log n))-approximation.