Parallel Algorithms for Hierarchical Clustering and Applications to Split Decomposition and Parity Graph Recognition

Dahlhaus, Elias

doi:10.1006/jagm.2000.1090

Cited by 90 publications

(83 citation statements)

References 25 publications

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“…The proposed algorithm, called similarity-based agglomerative clustering (SBAC), employs a mixed data measure scheme that pays extra attention to less common matches of feature values [183]. Parallel techniques for HC are discussed in [69] and [217], respectively.…”

Section: )mentioning

confidence: 99%

Survey of Clustering Algorithms

Wunsch

2005

IEEE Trans. Neural Netw.

5,056

2,338

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Abstract-Data analysis plays an indispensable role for understanding various phenomena. Cluster analysis, primitive exploration with little or no prior knowledge, consists of research developed across a wide variety of communities. The diversity, on one hand, equips us with many tools. On the other hand, the profusion of options causes confusion. We survey clustering algorithms for data sets appearing in statistics, computer science, and machine learning, and illustrate their applications in some benchmark data sets, the traveling salesman problem, and bioinformatics, a new field attracting intensive efforts. Several tightly related topics, proximity measure, and cluster validation, are also discussed.Index Terms-Adaptive resonance theory (ART), clustering, clustering algorithm, cluster validation, neural networks, proximity, self-organizing feature map (SOFM).

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Section: )mentioning

confidence: 99%

Survey of Clustering Algorithms

Wunsch

2005

IEEE Trans. Neural Netw.

5,056

2,338

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“…However, the algorithm therein is not that simple and relies on a rather sophisticated algorithm [12]. Moreover their approach is not extended to general modular decomposition.…”

Section: Resultsmentioning

confidence: 99%

Revisiting T. Uno and M. Yagiura’s Algorithm

Xuan

Habib

Paul

2005

Algorithms and Computation

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Abstract.In 2000, T. Uno and M. Yagiura published an algorithm that computes all the K common intervals of two given permutations of length n in O(n + K) time. Our paper first presents a decomposition approach to obtain a compact encoding for common intervals of d permutations. Then, we revisit T. Uno and M. Yagiura's algorithm to yield a linear time algorithm for finding this encoding. Besides, we adapt the algorithm to obtain a linear time modular decomposition of an undirected graph, and thereby propose a formal invariant-based proof for all these algorithms.

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“…We call it the decomposition tree of G associated with A split decomposition D of G is called a canonical split decomposition (or canonical decomposition for short) if each bag of D is either a prime graph, a star, or a complete graph, and D is not the refinement of a decomposition with the same property. The following is due to Cunningham and Edmonds [9], and Dahlhaus [10]. Theorem 2.7 (Cunningham and Edmonds [9]; Dahlhaus [10]).…”

Section: Split Decompositions and Local Complementationsmentioning

confidence: 99%

“…The following is due to Cunningham and Edmonds [9], and Dahlhaus [10]. Theorem 2.7 (Cunningham and Edmonds [9]; Dahlhaus [10]). Every connected graph G has a unique canonical decomposition, up to isomorphism, and it can be computed in time Op|V pGq|`|EpGq|q.…”

Section: Split Decompositions and Local Complementationsmentioning

confidence: 99%

Linear Rank-Width of Distance-Hereditary Graphs I. A Polynomial-Time Algorithm

2016

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Abstract. Linear rank-width is a linearized variation of rank-width, and it is deeply related to matroid path-width. In this paper, we show that the linear rank-width of every n-vertex distance-hereditary graph, equivalently a graph of rank-width at most 1, can be computed in time Opn 2¨l og 2 nq, and a linear layout witnessing the linear rank-width can be computed with the same time complexity. As a corollary, we show that the path-width of every n-element matroid of branch-width at most 2 can be computed in time Opn 2¨l og 2 nq, provided that the matroid is given by its binary representation.To establish this result, we present a characterization of the linear rankwidth of distance-hereditary graphs in terms of their canonical split decompositions. This characterization is similar to the known characterization of the path-width of forests given by Ellis, Sudborough, and Turner [The vertex separation and search number of a graph. Inf. Comput., 113(1): 1994]. However, different from forests, it is non-trivial to relate substructures of the canonical split decomposition of a graph with some substructures of the given graph. We introduce a notion of 'limbs' of canonical split decompositions, which correspond to certain vertex-minors of the original graph, for the right characterization.

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Parallel Algorithms for Hierarchical Clustering and Applications to Split Decomposition and Parity Graph Recognition

Cited by 90 publications

References 25 publications

Survey of Clustering Algorithms

Survey of Clustering Algorithms

Revisiting T. Uno and M. Yagiura’s Algorithm

Linear Rank-Width of Distance-Hereditary Graphs I. A Polynomial-Time Algorithm

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