Bicriteria Approximation Tradeoff for the Node-Cost Budget Problem

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(logn)) bicriteria approximation, i.e. the solution’s profit is at least a fraction of $\frac{1}{O(\log n)}$ 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 $(1+\varepsilon,O(\frac{1}{\varepsilon}\log n))$-approximation.