Results 1 
7 of
7
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 ..."
Abstract

Cited by 142 (6 self)
 Add to MetaCart
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.
Ambivalent data structures for dynamic 2edgeconnectivity and k smallest spanning trees
 In 32nd Annual Symposium on Foundations of Computer Science FOCS
, 1991
"... ..."
(Show Context)
An Empirical Assessment of Algorithms for Constructing a Minimum Spanning Tree
, 1994
"... We address the question of theoretical vs. practical behavior of algorithms for the minimum spanning tree problem. We review the factors that influence the actual running time of an algorithm, from choice of language, machine, and compiler, through lowlevel implementation choices, to purely algorit ..."
Abstract

Cited by 44 (3 self)
 Add to MetaCart
We address the question of theoretical vs. practical behavior of algorithms for the minimum spanning tree problem. We review the factors that influence the actual running time of an algorithm, from choice of language, machine, and compiler, through lowlevel implementation choices, to purely algorithmic issues. We discuss how to design a careful experimental comparison between various alternatives. Finally, we present the results from a study in which we used: multiple languages, compilers, and machines; all the major variants of the comparisonbased algorithms; and eight varieties of graphs in five families, with sizes of up to 0.5 million vertices (in sparse graphs) or 1.3 million edges (in dense graphs).
Clustering in Massive Data Sets
 Handbook of massive data sets
, 1999
"... We review the time and storage costs of search and clustering algorithms. We exemplify these, based on casestudies in astronomy, information retrieval, visual user interfaces, chemical databases, and other areas. Sections 2 to 6 relate to nearest neighbor searching, an elemental form of clustering, ..."
Abstract

Cited by 17 (0 self)
 Add to MetaCart
We review the time and storage costs of search and clustering algorithms. We exemplify these, based on casestudies in astronomy, information retrieval, visual user interfaces, chemical databases, and other areas. Sections 2 to 6 relate to nearest neighbor searching, an elemental form of clustering, and a basis for clustering algorithms to follow. Sections 7 to 11 review a number of families of clustering algorithm. Sections 12 to 14 relate to visual or image representations of data sets, from which a number of interesting algorithmic developments arise.
Logic Programming With Costs
, 1999
"... We investigate logic programs whose rules are assigned nonnegative real numbers. These numbers are interpreted as the costs of applying rules. There are several ways in which these costs can be interpreted. In the paper, two such interpretations are discussed in detail. They are referred to as nore ..."
Abstract

Cited by 3 (0 self)
 Add to MetaCart
We investigate logic programs whose rules are assigned nonnegative real numbers. These numbers are interpreted as the costs of applying rules. There are several ways in which these costs can be interpreted. In the paper, two such interpretations are discussed in detail. They are referred to as noreusability and reusability interpretations. The former requires that an atom be paid for each time it appears in the body of a rule that fires. In the latter, once an atom is derived (and the cost of its derivation is covered), it can be used for free in the future. We show that under the first interpretation, weighted logic programming has several useful properties. In the finite case, it is computationally tractable and there are polynomial time algorithms for computing lowest costs of deriving atoms. Moreover, several basic concepts of logic programming, including resolution and onestep provability operator, can be generalized to weighted logic programming with the noreusability interpre...
Randomization in Graph Optimization Problems: A Survey
 OPTIMA
, 1998
"... Randomization has become a pervasive technique in combinatorial optimization. We survey our thesis and subsequent work, which uses four common randomization techniques to attack numerous optimization problems on undirected graphs. ..."
Abstract

Cited by 2 (0 self)
 Add to MetaCart
(Show Context)
Randomization has become a pervasive technique in combinatorial optimization. We survey our thesis and subsequent work, which uses four common randomization techniques to attack numerous optimization problems on undirected graphs.
Increasing Digraph ArcConnectivity by Arc Addition, Reversal and Complement
, 2001
"... This paper deals with increasing the arcconnectivity of directed graphs by arc additions, reversals or complements. We study several optimization problems, which dier in their arcconnectivity requirements de ned by the set of sources, the set of targets and the arcconnectivity value. ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
(Show Context)
This paper deals with increasing the arcconnectivity of directed graphs by arc additions, reversals or complements. We study several optimization problems, which dier in their arcconnectivity requirements de ned by the set of sources, the set of targets and the arcconnectivity value.