D. Lozovanu and A. Zelikovsky, "Minimal and bounded tree problems," Tezele Congresului XVIII al Academiei Romano-Americane, Kishniev (1993), pp. 25. 26  Home/Search   Document Not in Database   Summary   Related Articles

....be incorporated into the network. Unlike the MST problem which admits a polynomial time solution [25, 28] the kMST problem is considerably harder to solve. In Theorem 2.1 of Section 2 we prove that the kMST problem is NP complete. This result was independently obtained by Lozovanu and Zelikovsky [26]. The kMST problem remains NP complete even when all the edge weights are drawn from the set f1; 2; 3g (i.e. the graph is complete and every edge takes one of three different weights) It is not hard to show a polynomial time solution for the case of two distinct weights. The problem remains ....

....graphs. We use a dynamic programming technique to show that for any class of decomposable graphs (or treewidth bounded graphs) there is an O(nk 2 ) time algorithm for solving the kMST problem. A polynomial time algorithm for trees was also independently obtained by Lozovanu and Zelikovsky [26]. Though the kMST problem is hard for arbitrary configurations of points in the plane, we show in Subsection 5.2 that there is a polynomial time algorithm for solving the kMST problem for the case of points in the Euclidean plane that lie on the boundary of a convex region. We also provide a ....

D. Lozovanu and A. Zelikovsky, "Minimal and bounded tree problems," Tezele Congresului XVIII al Academiei Romano-Americane, Kishniev (1993), pp. 25. 26

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