Results 1  10
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22
A Randomized LinearTime Algorithm to Find Minimum Spanning Trees
, 1994
"... We present a randomized lineartime algorithm to find a minimum spanning tree in a connected graph with edge weights. The algorithm uses random sampling in combination with a recently discovered lineartime algorithm for verifying a minimum spanning tree. Our computational model is a unitcost ra ..."
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Cited by 142 (6 self)
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We present a randomized lineartime algorithm to find a minimum spanning tree in a connected graph with edge weights. The algorithm uses random sampling in combination with a recently discovered lineartime algorithm for verifying a minimum spanning tree. Our computational model is a unitcost randomaccess machine with the restriction that the only operations allowed on edge weights are binary comparisons.
An optimal minimum spanning tree algorithm
 J. ACM
, 2000
"... Abstract. We establish that the algorithmic complexity of the minimum spanning tree problem is equal to its decisiontree complexity. Specifically, we present a deterministic algorithm to find a minimum spanning tree of a graph with n vertices and m edges that runs in time O(T ∗ (m, n)) where T ∗ is ..."
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Cited by 60 (12 self)
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Abstract. We establish that the algorithmic complexity of the minimum spanning tree problem is equal to its decisiontree complexity. Specifically, we present a deterministic algorithm to find a minimum spanning tree of a graph with n vertices and m edges that runs in time O(T ∗ (m, n)) where T ∗ is the minimum number of edgeweight comparisons needed to determine the solution. The algorithm is quite simple and can be implemented on a pointer machine. Although our time bound is optimal, the exact function describing it is not known at present. The current best bounds known for T ∗ are T ∗ (m, n) = �(m) and T ∗ (m, n) = O(m · α(m, n)), where α is a certain natural inverse of Ackermann’s function. Even under the assumption that T ∗ is superlinear, we show that if the input graph is selected from Gn,m, our algorithm runs in linear time with high probability, regardless of n, m, or the permutation of edge weights. The analysis uses a new martingale for Gn,m similar to the edgeexposure martingale for Gn,p.
Increasing the Weight of Minimum Spanning Trees
, 1996
"... The problems of computing the maximum increase in the weight of the minimum spanning trees of a graph caused by the removal of a given number of edges, or by finite increases in the weights of the edges, are investigated. For the case of edge removals, the problem is shown to be NPhard and an \Omeg ..."
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Cited by 28 (1 self)
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The problems of computing the maximum increase in the weight of the minimum spanning trees of a graph caused by the removal of a given number of edges, or by finite increases in the weights of the edges, are investigated. For the case of edge removals, the problem is shown to be NPhard and an \Omega\Gamma/ = log k)approximation algorithm is presented for it, where k is the number of edges to be removed. The second problem is studied assuming that the increase in the weight of an edge has an associated cost proportional to the magnitude of the change. An O(n 3 m 2 log(n 2 =m)) time algorithm is presented to solve it. 1 Introduction Consider a communication network in which information is broadcast over a minimum spanning tree. There are applications for which it is important to determine the maximum degradation in the performance of the broadcasting protocol that can be expected as a result of traffic fluctuations and link failures [25]. Also, there are several combinatorial op...
Cost Monotonicity, Consistency And Minimum Cost Spanning Tree Games
 GAMES AND ECONOMIC BEHAVIOR
, 2002
"... We propose a new cost allocation rule for minimum cost spanning tree games. The new rule is a core selection and also satisfies cost monotonicity. We also give characterization theorems for the new rule as well as the muchstudied Bird allocation. We show that the principal difference between these ..."
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Cited by 19 (0 self)
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We propose a new cost allocation rule for minimum cost spanning tree games. The new rule is a core selection and also satisfies cost monotonicity. We also give characterization theorems for the new rule as well as the muchstudied Bird allocation. We show that the principal difference between these two rules is in terms of their consistency properties.
On the History of Combinatorial Optimization (till 1960)
"... As a coherent mathematical discipline, combinatorial optimization is relatively young. When studying the history of the field, one observes a number of independent lines of research, separately considering problems like optimum assignment, shortest spanning tree, transportation, and the traveling ..."
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Cited by 14 (0 self)
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As a coherent mathematical discipline, combinatorial optimization is relatively young. When studying the history of the field, one observes a number of independent lines of research, separately considering problems like optimum assignment, shortest spanning tree, transportation, and the traveling salesman problem. Only in the 1950's, when the unifying tool of linear and integer programming became available and the area of operations research got intensive attention, these problems were put into one framework, and relations between them were laid. Indeed, linear programming forms the hinge in the history of combinatorial optimization. Its initial conception by Kantorovich and Koopmans was motivated by combinatorial applications, in particular in transportation and transshipment. After the formulation of linear programming as generic problem, and the development in 1947 by Dantzig of the simplex method as a tool, one has tried to attack about all combinatorial opti
The Diameter of the Minimum Spanning Tree of a Complete Graph
"... } be independent identically distributed weights for the edges of Kn. If Xi � = Xj for i � = j, then ..."
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Cited by 6 (1 self)
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} be independent identically distributed weights for the edges of Kn. If Xi � = Xj for i � = j, then
Combinatorial Optimization: A Survey
, 1993
"... This paper is a chapter of the forthcoming Handbook of Combinatorics, to be published by NorthHolland. It surveys the basic techniques and methods in combinatorial optimization. We organize our material according to the fundamental algorithmic techniques and illustrate them on problems to which the ..."
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Cited by 4 (0 self)
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This paper is a chapter of the forthcoming Handbook of Combinatorics, to be published by NorthHolland. It surveys the basic techniques and methods in combinatorial optimization. We organize our material according to the fundamental algorithmic techniques and illustrate them on problems to which these methods have been applied successfully. Special attention is given to approximation algorithms and fast (primal and dual) heuristics.
Dynamic degree constrained network design: a genetic algorithm approach
 Proceedings GECCO99. Genetic and Evolutionary Computation Conference. Eighth International Conference on Genetic Algorithms (ICGA99) and the Fourth Annual Genetic Programming Conference (GP99
, 1999
"... The design and development ofnetwork infrastructure to support missioncritical operations has become a critical and complicated issue. In this study we explore the use of genetic algorithms (GA) for the design of a degree constrained minimal spanning tree (DCMST) problem with varied degrees on each ..."
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Cited by 3 (0 self)
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The design and development ofnetwork infrastructure to support missioncritical operations has become a critical and complicated issue. In this study we explore the use of genetic algorithms (GA) for the design of a degree constrained minimal spanning tree (DCMST) problem with varied degrees on each node. The performance of GA was compared with two popular heuristics. The results indicate that GA provide better solution quality compared to heuristics, but is worse than heuristics in terms of computation time. 1
Initialization free graph based clustering
 Laboratoire I3S, CNRS, Universitè de NiceSophia Antipolis
, 2009
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