Listing all the minimum spanning trees in an undirected graph

Yamada, Takeo; Kataoka, Seiji; Watanabe, Kohtaro

doi:10.1080/00207160903329699

Cited by 14 publications

(5 citation statements)

References 12 publications

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“…In addition to investigating the open questions, we plan to incorporate our algorithm in the framework of Abseher et al [1] for supervised learning of effective tree decompositions. all maximal spanning trees, which can be solved in polynomial delay [41]. □…”

Section: Discussionmentioning

confidence: 99%

“…Jordan [24] shows that a tree over the maximal cliques of a chordal graph H is a clique tree if and only if it is a maximal spanning tree, where the weight of an edge between two maximal cliques is the cardinality of their intersection. As the number of maximal cliques of a chordal graph is linear in the number of nodes (Theorem 2.2), this enumeration problem is reduced to enumerating all maximal spanning trees, which can be solved in polynomial delay [41]. □…”

Section: = κ(G H (G))mentioning

confidence: 99%

See 1 more Smart Citation

Ranked Enumeration of Minimal Triangulations

Ravid

Medini

Kimelfeld

2019

Proceedings of the 38th ACM SIGMOD-SIGACT-SIGAI Symposium on Principles of Database Systems

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A tree decomposition of a graph facilitates computations by grouping vertices into bags that are interconnected in an acyclic structure; hence their importance in a plethora of problems such as query evaluation over databases and inference over probabilistic graphical models. The relative benefit from different tree decompositions is measured by diverse (sometime complex) cost functions that vary from one application to another. For generic cost functions like width and fill-in, an optimal tree decomposition can be efficiently computed in some cases, notably when the number of minimal separators is bounded by a polynomial (due to Bouchitte and Todinca); we refer to this assumption as "poly-MS. " To cover the variety of cost functions in need, it has recently been proposed to devise algorithms for enumerating many decomposition candidates for applications to choose from using specialized, or even machinelearned, cost functions.We explore the ability to produce a large collection of "high quality" tree decompositions. We present the first algorithm for ranked enumeration of the proper (non-redundant) tree decompositions, or equivalently minimal triangulations, under a wide class of cost functions that substantially generalizes the above generic ones. On the theoretical side, we establish the guarantee of polynomial delay if poly-MS is assumed, or if we are interested in tree decompositions of a width bounded by a constant. We describe an experimental evaluation on graphs of various domains (including join queries, Bayesian networks, treewidth benchmarks and random), and explore both the applicability of the poly-MS assumption and the performance of our algorithm relative to the state of the art.

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Section: Discussionmentioning

confidence: 99%

Section: = κ(G H (G))mentioning

confidence: 99%

Ranked Enumeration of Minimal Triangulations

Ravid

Medini

Kimelfeld

2019

Proceedings of the 38th ACM SIGMOD-SIGACT-SIGAI Symposium on Principles of Database Systems

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“…The MST is a fully connected subgraph minimal in the sum of edge weights 11 (here-distances) and is shown in Figure 5. The algorithm by Yamada et al (2010) 12 was used. The concept of MST in the context of an abstract dissimilarity space could be employed, as was done by Baron & Ménard (2020), to extract sequences from the data, which could later be compared with physical parameters.…”

Section: Visualization Of the Metric Spacementioning

confidence: 99%

Characterization of Supernovae Based on the Spectral–Temporal Energy Distribution: Two Possible SN Ib Subtypes

Ofek

Gal‐Yam

2022

ApJ

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A quantitative data-driven comparison among supernovae (SNe) based on their spectral time series combined with multiband photometry is presented. We use an unsupervised random forest algorithm as a metric on a set of 82 well-documented SNe representing all the main spectroscopic types, in order to embed these in an abstract metric space reflecting shared correlations between the objects. We visualize the resulting metric space in 3D, revealing strong agreement with the current spectroscopic classification scheme. The embedding splits Type Ib supernovae into two groups, with one subgroup exhibiting broader, less prominent, higher-velocity lines than the other, possibly suggesting a new SN Ib subclass is required. The method could be to classify newly discovered SNe according to their distance from known event groups, or ultimately to devise a new, spectral–temporal classification scheme. Such an embedding could also depend on hidden parameters that may perhaps be physically interpretable.

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“…Spanning tree adalah sebuah tree yang terbentuk dari turunan sebuah graf terhubung (acyclic) dimana semua simpulnya saling terhubung [5], [6], seluruh simpulnya terhubung dalam jaringan tree [4], dan tidak membentuk sirkuit (cyclic) [1]. Minimum spanning tree adalah sebuah spanning tree berbobot minimum [7].…”

Section: Minimumunclassified

Pendekatan Matriks Ketetanggaan Berbobot untuk Solusi Minimum Spanning Tree (MST)

Akhirina

Afrizal

2020

STRING

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Minimum Spanning Tree (MST) atau sering juga disebut Minimum Weighting Spanning Tree (MWST) adalah sebuah algoritma pencarian jalur atau sisi (edge) yang menghubungkan semua simpul (vertex) didalam graf saling terhubung dan tidak membentuk sirkuit dengan bobot minimum. Algoritma klasik yang digunakan untuk menyelesaikan masalah MST adalah algoritma prim dan kruskal. Permasalahan pohon merentang minimum merupakan permasalahan yang berkaitan dengan optimalisasi dalam menemukan sisi (edge) berbobot minimum yang dapat menghubungkan semua simpul (Vertex). (MST) ini banyak digunakan dalam keilmuan komputer seperti menentukan akses point, membangun jaringan network dan banyak lagi. Tujuan penelitian ini adalah menemukan solusi baru yang dapat memberikan alternative solusi MST selain algoritma klasik seperti prim dan kruskal. Penelitian ini bersifat eksperimental dimana pendekatan yang dilakukan adalah menggunakan matrik ketetanggaan berbobot, dari bobot yang ada diambil sisi yang paling minimum di tiap pasangan matriks untuk menghasilkan minimum spanning tree. Solusi baru ini dapat menjadi alternatif dalam menyelesaikan permasalahan minimum spanning tree.

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Listing all the minimum spanning trees in an undirected graph

Cited by 14 publications

References 12 publications

Ranked Enumeration of Minimal Triangulations

Ranked Enumeration of Minimal Triangulations

Characterization of Supernovae Based on the Spectral–Temporal Energy Distribution: Two Possible SN Ib Subtypes

Pendekatan Matriks Ketetanggaan Berbobot untuk Solusi Minimum Spanning Tree (MST)

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