Abstract
This paper studies two problems of locating two paths in a tree with positive and negative weights. The first problem has objective to minimize the sum of minimum weighted distance from every vertex of the tree to the two paths, while the second is to minimize the sum of the weighted minimum distance from each vertex to the two paths. We develop an \(O(n^{2})\) algorithm based on the optimal properties for the first problem, and also an \(O(n^{3})\) algorithm for the second problem.
This research was partially supported by the National Nature Science Foundation of China (Nos. 11471210, 11171207).
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Zhou, J., Kang, L., Shan, E. (2014). Two Paths Location of a Tree with Positive or Negative Weights. In: Zhang, Z., Wu, L., Xu, W., Du, DZ. (eds) Combinatorial Optimization and Applications. COCOA 2014. Lecture Notes in Computer Science(), vol 8881. Springer, Cham. https://doi.org/10.1007/978-3-319-12691-3_25
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DOI: https://doi.org/10.1007/978-3-319-12691-3_25
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