Approximation algorithms for prize collecting forest problems with submodular penalty functions

Authors:
Yogeshwer Sharma;Chaitanya Swamy;David P. Williamson
Affiliations:
Cornell University, Ithaca, NY;University of Waterloo, Waterloo, ON;Cornell University, Ithaca, NY
Venue:
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Year:
2007

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Abstract

In this paper, we study the prize-collecting version of constrained forest problems with an arbitrary 0-1 connectivity requirement function and a submodular penalty function. Our framework generalizes the Prize Collecting Generalized Steiner Tree framework of Hajiaghayi and Jain [HJ06] to incorporate more general connectivity requirements and penalty functions. We generalize their primal-dual algorithm using submodular function minimization to give a 3-approximation algorithm, and devise an LP rounding algorithm with a performance guarantee of 2.54.