Efficient algorithms for finding the (<i>k</i>, <i>l</i>)‐core of tree networks

Becker, Ronald I.; Lari, Isabella; Storchi, Giovanni; Scozzari, Andrea

doi:10.1002/net.10051

Cited by 11 publications

(9 citation statements)

References 13 publications

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“…4, some entries of B are listed in Table 1. Consider the computation of B [1,2,4]. We have Y = Proof.…”

Section: Lemma 8 Let I Be a Vertex In T And J ∈ N(i) We Havementioning

confidence: 99%

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Efficient algorithms for a constrained k-tree core problem in a tree network

Wang

Peng

et al. 2006

Journal of Algorithms

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“…4, some entries of B are listed in Table 1. Consider the computation of B [1,2,4]. We have Y = Proof.…”

Section: Lemma 8 Let I Be a Vertex In T And J ∈ N(i) We Havementioning

confidence: 99%

“…When the values of k and l are small compared to n, the O(lkn) time algorithm is preferred. Recently, Becker et al [1] gave an O(n 2 log n)-time algorithm for arbitrary edge lengths and an O(n 2 )-time algorithm for equal edge lengths.…”

Section: Introductionmentioning

confidence: 99%

Efficient algorithms for a constrained k-tree core problem in a tree network

Wang

Peng

et al. 2006

Journal of Algorithms

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“…Jennings [6] presents distributed algorithms for finding center path and core path in asynchronous networks in O( ) time with O(n) messages, where is the diameter of the network. Additional results on center/core paths can be found in [6,[8][9][10][11][23][24][25].…”

Section: Introductionmentioning

confidence: 97%

“…The (k, l)-core tree of T is a subtree T ⊆ T that minimizes the sum of the weighted distances from the nodes of T to the subtree T , with precisely k leaves, and a diameter of at most l. The problem of constructing a (k, l)-core tree is a constrained version of the k-core tree problem [8,11] with an unbounded diameter (l = ∞). Peng et al [8] first presented O(n log n) and O(kn) time algorithms that solve the k-core tree problem.…”

Section: Introductionmentioning

confidence: 99%

“…Later, Shioura and Uno [9] improved the results for the k-core tree problem to O(n) time. Becker et al [11] dealt with the (k, l)-core tree problem and presented an O(n 2 log n) time algorithm for arbitrary edge lengths and an O(n 2 ) time algorithm for equal edge lengths. Recently, Wang et al [10] presented two algorithms for constructing a (k, l)-core tree.…”

Section: Introductionmentioning

confidence: 99%

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The (k,l) Coredian Tree for Ad Hoc Networks

Dvir

Segal

2008

2008 the 28th International Conference on Distributed Computing Systems Workshops

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In this paper, we present new efficient strategy for constructing a wireless tree network containing n nodes of diameter ∆ while satisfying the QoS requirements such as bandwidth and delay. Given a tree network T , a coredian path is a path in T that minimizes the centdian function, a k-coredian tree is a subtree of T with k leaves that minimizes the centdian function, and a (k, l)-coredian tree is a subtree of T with k leaves and diameter l at most that minimizes the centdian function. The (k, l)-coredian tree can serve as a backbone for a network, where intermediate nodes belong to the backbone and the leaves serve as the heads of the clusters covering the rest of the network. We show that a coredian path can be constructed at O(∆) time with O(n) messages and a k-coredian tree can be constructed at O(k∆) time with O(kn) messages. While a (k, l)-coredian tree can be constructed at O(n 2 ) time with O(n 2 ) messages. A simulation is presented for various values of n and k. 1

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The bi‐criteria doubly weighted center‐median path problem on a tree

Puerto

Rodríguez‐Chía

Tamir³

et al. 2006

Networks

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Given a tree network T with n nodes, let PL be the subset of all discrete paths whose length is bounded above by a prespeciﬁed value L. We consider the location of a path-shaped facility P ∈ PL, where customers are represented by the nodes of the tree. We use a bi-criteria model to represent the total transportation cost of the customers to the facility. Each node is associated with a pair of nonnegative weights: the center-weightand the median-weight. In this doubly weighted model, a path P is assigned a pair of values (MAX (P ), SUM (P )),which are, respectively, the maximum center-weighted distance and the sum of the median-weighted distances from P to the nodes of the tree. Viewing PL and the planar set {(MAX (P), SUM (P )) : P ∈ PL} as the decisionspace and the bi-criteria or outcome space respectively,we focus on ﬁnding all the nondominated points of the bi-criteria space. We prove that there are at most 2n non-dominated outcomes, even though the total number of efﬁcient paths can be Ω(n2), and they can all be generated in O(n log n) optimal time. We apply this result to solve the cent-dian model, whose objective is a convex combination of the weighted center and weighted median functions. We also solve the restricted models, where the goal is to minimize one of the two functions MAX or SUM, subject to an upper bound on the other one, both withand without a constraint on the length of the path. All these problems are solved in linear time, once the set of non dominated outcomes has been obtained, which in turn, results in an overall complexity of O(n log n). The latter bounds improve upon the best known results by a factor of O(log n).Ministerio de Ciencia y Tecnologí

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

Cited by 11 publications

References 13 publications

Efficient algorithms for a constrained k-tree core problem in a tree network

Efficient algorithms for a constrained k-tree core problem in a tree network

The (k,l) Coredian Tree for Ad Hoc Networks

The bi‐criteria doubly weighted center‐median path problem on a tree

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