A general approximation technique for constrained forest problems
SODA '92 Proceedings of the third annual ACM-SIAM symposium on Discrete algorithms
A primal-dual approximation algorithm for generalized Steiner network problems
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
The primal-dual method for approximation algorithms and its application to network design problems
Approximation algorithms for NP-hard problems
A minimum spanning tree algorithm with inverse-Ackermann type complexity
Journal of the ACM (JACM)
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A class of network design problems, including the k -path/ tree/cycle covering problems and some location-routing problems, can be modeled by downwards monotone functions [5]. We consider a class of network design problems, called the p -constrained path/tree/cycle covering problems, obtained by introducing an additional constraint to these problems; i.e., we require that the number of connected components in the optimal solution be at most p for some integer p . The p -constrained path/tree/cycle covering problems cannot be modeled by downwards monotone functions. In this paper, we present a different analysis for the performance guarantee of the algorithm in [5]. As a result of the analysis, we are able to tackle p -constrained path/tree/cycle covering problems, and show the performance bounds of 2 and 4 for p -constrained tree/cycle problems and p -constrained path covering problems respectively.