Efficient Algorithms for Finding a Core of a Tree with a Specified Length

Peng, Shietung; Lo, Win-Tsung

doi:10.1006/jagm.1996.0022

Cited by 38 publications

(26 citation statements)

References 8 publications

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“…As in the papers of Peng and Lo [9] and Becker et al [2], we use Remark 1 in a recursive algorithm that, given a "central" vertex v, finds a (k, l )-core containing v in T v . If it is not the (k, l )-core of the tree T, then the (k, l )-core must lie entirely in one of the subtrees rooted at the adjacent vertices of the "central" vertex.…”

Section: Definition 3 Given a Weighted Tree T A Central Vertex V Ofmentioning

confidence: 98%

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Efficient algorithms for finding the (k, l)‐core of tree networks

et al. 2002

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Given a tree T ‫؍‬ (V, E), with ͦVͦ ‫؍‬ n, we consider the problem of selecting a subtree with at most k leaves and with a diameter of at most l which minimizes the sum of the distances of the vertices from the selected subtree. We call such a subtree the (k, l)-core of T. We provide two algorithms; the first one for unweighted trees has time complexity of O(n 2 ), whereas the second one for weighted trees has time complexity of O(n 2 log n). The idea for both the algorithms is that, by starting from the tree T, we construct new rooted trees where the maximum length of a path is at most l. Then, for each new tree, we can apply a greedy-type procedure to find a subtree containing the root with at most k leaves and which minimizes the sum of the distances.

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Section: Definition 3 Given a Weighted Tree T A Central Vertex V Ofmentioning

confidence: 98%

“…Linear time algorithms for finding a core of a tree were presented in Morgan and Slater [8] and in Becker [1]. A number of authors later extended the problem to finding a core of specified size l on tree networks [2,7,9].…”

Section: Introductionmentioning

confidence: 98%

Efficient algorithms for finding the (k, l)‐core of tree networks

et al. 2002

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“…As shown in Hakimi, Schmeichel, and Labbé (1993), this problem is NP-hard on arbitrary graphs. Thus, most of the papers deal with these problems when the network is a tree and in particular several efficient polynomial time algorithms were provided when the median criterion is considered (Becker, 1990;Becker et al, 2002;Minieka, 1985;Morgan and Slater, 1980;Peng and Lo, 1996). In Lari, Ricca, and Scozzari (2004) it is shown that the location of a path which minimizes the sum of the distances is NP-hard on cactus graphs, while in Richey (1990) a pseudo-polynomial time algorithm is given for series-parallel graphs.…”

Section: Introductionmentioning

confidence: 97%

The location of median paths on grid graphs

et al. 2007

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In this paper we consider the location of a path shaped facility on a grid graph. In the literature this problem was extensively studied on particular classes of graphs as trees or series-parallel graphs. We consider here the problem of finding a path which minimizes the sum of the (shortest) distances from it to the other vertices of the grid, where the path is also subject to an additional constraint that takes the form either of the length of the path or of the cardinality. We study the complexity of these problems and we find two polynomial time algorithms for two special cases, with time complexity of O(n) and O(n tau o) respectively, where n is the number of vertices of the grid and iota is the cardinality of the path to be located. The literature about locating dimensional facilities distinguishes between the location of extensive facilities in continuous spaces and network facility location. We will show that the problems presented here have a close connection with continuous dimensional facility problems, so that the procedures provided can also be useful for solving some open problems of dimensional facilities location in the continuous case

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“…Location problems imposed by a lengthconstraint were studied in [12,13,16,23]. The constraint is to limit the total edge length to the selected facilities.…”

Section: Introductionmentioning

confidence: 99%

“…Due to the variety of facilities and different criteria for optimality, many location problems have been defined and studied [7][8][9][12][13][14][15][16]18,[22][23][24][25]. The facility can be a point, a set of points, a path, a tree, or a forest in the network.…”

Section: Introductionmentioning

confidence: 99%