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Minimum Spanning Tree with Neighborhoods
2007We consider a natural generalization of the classical minimum spanning tree problem called Minimum Spanning Tree with Neighborhoods (MSTN)which seeks a tree of minimum length to span a set of 2D regions called neighborhoods. Each neighborhood contributes exact one node to the tree, and the MSTN has the minimum total length among all possible trees ...
Yang Yang 0012 +3 more
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On partitioning minimum spanning trees
Discrete Applied MathematicszbMATH Open Web Interface contents unavailable due to conflicting licenses.
Nili Guttmann-Beck +2 more
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The Minimum Spanning Tree Constraint
2006The paper introduces the MST(G,T,W) constraint, which is specified on two graph variables G and T and a vector W of scalar variables. The constraint is satisfied if T is a minimum spanning tree of G, where the edge weights are specified by the entries of W. We develop algorithms that filter the domains of all variables to bound consistency.
Dooms, Gregoire, Katriel, Irit
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On Steiner trees and minimum spanning trees in hypergraphs
Operations Research Letters, 2003zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Daneshmand, Siavash Vahdati +1 more
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On the History of the Minimum Spanning Tree Problem
IEEE Annals of the History of Computing, 1985Summary: It is standard practice among authors discussing the minimum spanning tree problem to refer to the work of \textit{J. B. Kruskal} [Proc. Am. Math. Soc. 7, 48-5- (1956; Zbl 0070.18404)] and \textit{R. C. Prim} [Bell Syst. Tech. J. 36, No. 6, 1389-1402 (1957)] as the sources of the problem and its first efficient solutions, despite the citation ...
Ronald L. Graham, Pavol Hell
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Counting Minimum Weight Spanning Trees
Journal of Algorithms, 1997Summary: We present an algorithm for counting the number of minimum weight spanning trees, based on the fact that the generating function for the number of spanning trees of a given graph, by weight, can be expressed as a simple determinant.
Andrei Z. Broder, Ernst W. Mayr
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Minimum Spanning Trees with Sums of Ratios
Journal of Global Optimization, 2001zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Christopher C. Skiscim +1 more
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The saga of minimum spanning trees
Computer Science Review, 2008zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Finding Minimum Congestion Spanning Trees
ACM Journal of Experimental Algorithmics, 1999Given a weighted graph <i>G = (V, E)</i>, a positive integer <i>k</i>, and a penalty function <i>w<inf>p</inf></i>, we want to find <i>k</i> spanning trees on <i>G</i>, not necessarily disjoint, of minimum total weight, such that the weight of each edge is subject to a penalty ...
Renato Fonseca F. Werneck +2 more
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Contractors' minimum spanning tree
Australas. J Comb., 2019Summary: We consider the following problem. Given a graph \(G=(V,E)\), a partition of \(E\) into \(k\) color classes, \(E=\cup^k_{i=1}E_i\), and a cost function for each class \(f_i:2^{E_i}\rightarrow\mathbb{R}^+\), find a spanning tree \(T=(V,F)\) whose total cost is minimal, where the cost of \(T\) is defined as the sum of the costs of the color ...
Irith Ben-Arroyo Hartman, Ilan Newman
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