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- W3131610618 abstract "In this paper, we study the prize-collecting k-Steiner tree problem (PC k-ST), which is an interesting generalization of both the k-Steiner tree problem (k-ST) and the prize-collecting Steiner tree problem (PCST). In the PC k-ST, we are given an undirected connected graph (G =(V, E)), a subset (R subseteq V) called terminals, a root vertex (r in V) and an integer k. Every edge has a non-negative edge cost and every vertex has a non-negative penalty cost. We wish to find an r-rooted tree F that spans at least k vertices in R so as to minimize the total edge costs of F as well as the penalty costs of the vertices not in F. As our main contribution, we propose two approximation algorithms for the PC k-ST with ratios of 5.9672 and 5. The first algorithm is based on an observation of the solutions for the k-ST and the PCST, and the second one is based on the technique of primal-dual." @default.
- W3131610618 created "2021-03-01" @default.
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- W3131610618 date "2021-01-01" @default.
- W3131610618 modified "2023-09-26" @default.
- W3131610618 title "The Prize-Collecting k-Steiner Tree Problem" @default.
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- W3131610618 doi "https://doi.org/10.1007/978-3-030-69244-5_33" @default.
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