A note on the prize collecting traveling salesman problem
Mathematical Programming: Series A and B
Survivable networks, linear programming relaxations and the parsimonious property
Mathematical Programming: Series A and B
When Trees Collide: An Approximation Algorithm for theGeneralized Steiner Problem on Networks
SIAM Journal on Computing
A General Approximation Technique for Constrained Forest Problems
SIAM Journal on Computing
The prize collecting Steiner tree problem: theory and practice
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
Sharing the cost of multicast transmissions
Journal of Computer and System Sciences - Special issue on Internet algorithms
Network design for information networks
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
The prize-collecting generalized steiner tree problem via a new approach of primal-dual schema
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Approximation algorithms for prize collecting forest problems with submodular penalty functions
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
IPCO '07 Proceedings of the 12th international conference on Integer Programming and Combinatorial Optimization
A new ILP formulation for 2-root-connected prize-collecting Steiner networks
ESA'07 Proceedings of the 15th annual European conference on Algorithms
Prize-Collecting steiner network problems
IPCO'10 Proceedings of the 14th international conference on Integer Programming and Combinatorial Optimization
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In this paper, we introduce the study of prize-collecting network design problems having general connectivity requirements. Prior work considered only 0-1 or very limited connectivity requirements. We introduce general connectivity requirements in the prize-collecting generalized Steiner tree framework of Hajiaghayi and Jain [9], and consider penalty functions linear in the violation of the connectivity requirements. Using Jain’s iterated rounding algorithm [11] as a black box, and ideas from Goemans [7] and Levi, Lodi, Sviridenko [14], we give a 2.54-factor approximation algorithm for the problem. We also generalize the 0-1 requirements of PCF problem introduced by Sharma, Swamy, and Williamson [15] to include general connectivity requirements. Here we assume that the monotone submodular penalty function of Sharma et al. is generalized to a multiset function that can be decomposed into functions in the same form as that of Sharma et al. Using ideas from Goemans and Berstimas [6], we give an (αlogK)-approximation algorithm for the resulting problem, where K is the maximum connectivity requirement, and α= 2.54.