A graph-theoretical clustering method based on two rounds of minimum spanning trees

Zhong, Chongquan; Miao, Duoqian; Wang, Ruizhi

doi:10.1016/j.patcog.2009.07.010

Cited by 106 publications

(39 citation statements)

References 27 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…The classical MST has been played a significant role and become a powerful tool for performing clustering analysis [11]. Several clustering algorithms based minimum spanning tree can be found in the literature [11][12][13][14].…”

Section: Introductionmentioning

confidence: 99%

An exact algorithm fork-cardinality degree constrained clustered minimum spanning tree problem

Kumar

Purusotham

2017

IOP Conf. Ser.: Mater. Sci. Eng.

View full text Add to dashboard Cite

Abstract. The k-cardinality degree constrained clustered minimum spanning tree problem (k-DCCMST) aims to determine a k-node (out of n nodes) spanning tree of minimum weight defined on a complete weighted undirected graph, where the node set is partitioned into set of clusters such that except the root node, the degree of other nodes in the resultant spanning tree does not exceed the predefined degree limit. The k-DCCMST model has significant applications in the context of designing of networks and is then formulated as a zero-one integer linear program. To solve this problem optimally, an exact Lexi-search algorithm (LSA) is developed. The developed LSA is subjected in Matlab, tested on some benchmark as well as randomly generated test instances and computational results are reported. Numerical experimental results demonstrate the efficiency of proposed LSA on dense graphs.

show abstract

Section: Introductionmentioning

confidence: 99%

An exact algorithm fork-cardinality degree constrained clustered minimum spanning tree problem

Kumar

Purusotham

2017

IOP Conf. Ser.: Mater. Sci. Eng.

View full text Add to dashboard Cite

show abstract

“…Examples include recommendation algorithms that run on large social networks [39], clustering algorithms on gene expression data [47], spam detection on the web graph [45], and many others. As graphs grow to sizes that far exceed the memory of a single machine, applications need to perform their computations on distributed systems.…”

Section: Introductionmentioning

confidence: 99%

Optimizing graph algorithms on pregel-like systems

Salihoğlu

Widom

2014

Proc. VLDB Endow.

View full text Add to dashboard Cite

We study the problem of implementing graph algorithms efficiently on Pregel-like systems, which can be surprisingly challenging. Standard graph algorithms in this setting can incur unnecessary inefficiencies such as slow convergence or high communication or computation cost, typically due to structural properties of the input graphs such as large diameters or skew in component sizes. We describe several optimization techniques to address these inefficiencies. Our most general technique is based on the idea of performing some serial computation on a tiny fraction of the input graph, complementing Pregel's vertex-centric parallelism. We base our study on thorough implementations of several fundamental graph algorithms, some of which have, to the best of our knowledge, not been implemented on Pregel-like systems before. The algorithms and optimizations we describe are fully implemented in our open-source Pregel implementation. We present detailed experiments showing that our optimization techniques improve runtime significantly on a variety of very large graph datasets.

show abstract

“…A minimum spanning tree (MST) of an edge-weighted graph is a spanning tree with the minimum sum of edge weights among all spanning trees. Many practical problem can be modeled by using MST, and it has been widely applied in many fields such as wireless sensor networks [1], [2], cluster analysis [3]- [5] and data storage [6].…”

Section: Introductionmentioning

confidence: 99%

Reliability Evaluation of the Minimum Spanning Tree on Uncertain Graph

Tang¹,

Liu²,

Wen³

2015

JCP

View full text Add to dashboard Cite

Abstract:Minimum spanning tree is a minimum-cost spanning tree connecting the whole network, but it couldn't be directly obtained on uncertain graph. In this paper, we define the reliability as the existence probability of all minimum spanning trees and present an algorithm for evaluating reliability of the minimum spanning tree on uncertain graph. The time complexity of the algorithm is O(Nmn), where n, m and N stand for the number of vertices, edges and minimum spanning trees, respectively. Because this algorithm spends more time finding minimum spanning tree, we propose an improved algorithm whose time complexity is O(Nm). The improved algorithm uses disjoint set data structure so that the average time complexity on finding a new minimum spanning tree is O(m/n). The two algorithms are analyzed in detail and the experiment results agree with theoretical analysis.

show abstract

A graph-theoretical clustering method based on two rounds of minimum spanning trees

Cited by 106 publications

References 27 publications

An exact algorithm fork-cardinality degree constrained clustered minimum spanning tree problem

An exact algorithm fork-cardinality degree constrained clustered minimum spanning tree problem

Optimizing graph algorithms on pregel-like systems

Reliability Evaluation of the Minimum Spanning Tree on Uncertain Graph

Contact Info

Product

Resources

About