Abstract
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.
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Bhattacharya, B., Hu, Y., Shi, Q. (2009). Approximation Algorithms for a Network Design Problem. In: Ngo, H.Q. (eds) Computing and Combinatorics. COCOON 2009. Lecture Notes in Computer Science, vol 5609. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02882-3_23
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DOI: https://doi.org/10.1007/978-3-642-02882-3_23
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