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Neighbourhood Searches for the Bounded Diameter . . .
, 2006
"... We consider the Bounded Diameter Minimum Spanning Tree problem and describe four neighbourhood searches for it. They are used as local improvement strategies within a variable neighbourhood search (VNS), an evolutionary algorithm (EA) utilising a new encoding of solutions, and an ant colony optimisa ..."
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Cited by 7 (0 self)
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We consider the Bounded Diameter Minimum Spanning Tree problem and describe four neighbourhood searches for it. They are used as local improvement strategies within a variable neighbourhood search (VNS), an evolutionary algorithm (EA) utilising a new encoding of solutions, and an ant colony
COUNTING HYPERBOLIC MANIFOLDS WITH BOUNDED DIAMETER
, 2006
"... Abstract. Let ρn(V) be the number of complete hyperbolic manifolds of dimension n with volume less than V. Burger, Gelander, Lubotzky, and Moses[2] showed that when n ≥ 4 there exist a, b> 0 depending on the dimension such that aV log V ≤ log ρn(V) ≤ bV log V, for V ≫ 0. In this note, we use the ..."
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Cited by 1 (0 self)
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their methods to bound the number of hyperbolic manifolds with diameter less than d and show that the number grows doubleexponentially. Additionally, this bound holds in dimension 3. 1.
Constructing Connected Dominating Sets with Bounded Diameters
 in Wireless Networks”, in Proc. International Conference on Wireless Algorithms, Systems and Applications (WASA
, 2007
"... In wireless networks, due to the lack of fixed infrastructure or centralized management, a Connected Dominating Set (CDS) of the graph representing the network is an optimum candidate to serve as the virtual backbone of a wireless network. However, constructing a minimum CDS is NPhard. Furthermore, ..."
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Cited by 7 (5 self)
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, almost all of the existing CDS construction algorithms neglect the diameter of a CDS, which is an important factor. In this paper, we investigate the problem of constructing a CDS with a bounded diameter in wireless networks and propose a heuristic algorithm, Connected Dominating Sets with Bounded
Neighborhood Search for the Bounded Diameter Minimum Spaning Tree
"... Many optimization problems including the network design problem of finding the bounded diameter minimum spanning tree are computationally intractable. Therefore, a practical approach for solving such problems is to employ heuristic algorithms that can find solution close to the optimal one within a ..."
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Many optimization problems including the network design problem of finding the bounded diameter minimum spanning tree are computationally intractable. Therefore, a practical approach for solving such problems is to employ heuristic algorithms that can find solution close to the optimal one within a
The Performance of Phylogenetic Methods on Trees of Bounded Diameter
"... We study the convergence rate of neighbor joining and several new phylogenetic reconstruction methods on families of trees of bounded diameter. Our study presents theoretically obtained convergence rates, as well as an empirical study based upon simulation of evolution down random birth death tree ..."
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We study the convergence rate of neighbor joining and several new phylogenetic reconstruction methods on families of trees of bounded diameter. Our study presents theoretically obtained convergence rates, as well as an empirical study based upon simulation of evolution down random birth death
Compactness for manifolds and integral currents with bounded diameter and volume
, 2008
"... Gromov’s compactness theorem for metric spaces asserts that every uniformly compact sequence of metric spaces has a subsequence which converges in the GromovHausdorff sense to a compact metric space. In this article we show that if one replaces the Hausdorff distance appearing in Gromov’s theorem ..."
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Cited by 17 (4 self)
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theorem by the filling volume or flat distance then every sequence of oriented kdimensional Riemannian manifolds with a uniform bound on diameter and volume has a subsequence which converges in this new distance to a countably H krectifiable metric space. Our theorem moreover applies to integral
Addendum: Minimum weight spanning trees with bounded diameter
 Australasian Journal of Combinatorics
, 1993
"... Let G be a simple graph with nonnegative edge weights. Determining a minimum weight spanning tree is a fundamental problem that arises in network design and as a subproblem in many combinatorial optimization problems such as vehicle routing. In some applications, it is necessary to restrict the dia ..."
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Cited by 7 (0 self)
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the diameter of the spanning tree and thus one is interested in the problem: Find, in a given weighted graph G, a minimum weight spanning tree of diameter at most D. This problem is known to be NPcomplete for D 2:: 4. In this paper we present a mixed integer linear programming formulation and discuss some
Greedy Heuristics and an Evolutionary Algorithm for the BoundedDiameter Minimum Spanning Tree Problem
 Proceedings of the 2003 ACM Symposium on Applied Computing
, 2003
"... bound D, the boundeddiameter minimum spanning tree problem seeks a spanning tree on G of lowest weight in which no path between two vertices contains more than D edges. This problem is NPhard for 4 1, where n is the number of vertices in G. An existing greedy heuristic for the problem, called ..."
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Cited by 37 (13 self)
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bound D, the boundeddiameter minimum spanning tree problem seeks a spanning tree on G of lowest weight in which no path between two vertices contains more than D edges. This problem is NPhard for 4 1, where n is the number of vertices in G. An existing greedy heuristic for the problem
Variable neighborhood search for the bounded diameter minimum spanning tree problem
 Proceedings of the 18th Mini Euro Conference on Variable Neighborhood Search
, 2005
"... The bounded diameter minimum spanning tree problem is an NPhard combinatorial optimization problem with applications in various fields like communication network design. We propose a general variable neighborhood search approach for it, utilizing four different types of neighborhoods. They were d ..."
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Cited by 18 (9 self)
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The bounded diameter minimum spanning tree problem is an NPhard combinatorial optimization problem with applications in various fields like communication network design. We propose a general variable neighborhood search approach for it, utilizing four different types of neighborhoods. They were
BoundedDiameter MST Instances with Hybridization of MultiObjective EA
"... The Bounded Diameter (a.k.a Diameter Constraint) Minimum Spanning Tree (BDMST/DCMST) is a wellknown combinatorial optimization problem. In this paper, we recast a few wellknown heuristics, which are evolved for BDMST problem to a BiObjective Minimum Spanning Tree (BOMST) problem and then obtain P ..."
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The Bounded Diameter (a.k.a Diameter Constraint) Minimum Spanning Tree (BDMST/DCMST) is a wellknown combinatorial optimization problem. In this paper, we recast a few wellknown heuristics, which are evolved for BDMST problem to a BiObjective Minimum Spanning Tree (BOMST) problem and then obtain
Results 1  10
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1,780