Given a weighted graph, let W 1 ; W 2 ; W 3 ; : : : denote the increasing sequence of all possible distinct spanning tree weights. Settling a conjecture due to Kano, we prove that every spanning tree of weight W 1 is at most k ? 1 edge swaps away from some spanning tree of weight W k. Three other conjectures posed by Kano are proven for two special classes of graphs. Finally, we consider the al...

We study a probabilistic optimization model for MIN SPANNING TREE, where any vertex vi of the input-graph G(V, E) has some presence probability pi in the final instance G′ ⊂ G that will effectively be optimized. Supposing that when this “real” instance G′ becomes known, a decision maker might have no time to perform computation from scratch, we assume that a spanning tree T , called anticipator...

A number of minimum spanning tree algorithms have been proposed for lossy compression of image sets. In these algorithms, a complete graph is constructed from the entire image set and possibly an average image, and a minimum spanning tree is used to determine which difference images to encode. In this paper, we propose a hierarchical minimum spanning tree algorithm in which the minimum spanning...

An inverse minimum spanning tree problem makes the least modification on the edge weights such that a predetermined spanning tree is a minimum spanning tree with respect to the new edge weights. In this paper, the concept of uncertain α-minimum spanning tree is initiated for minimum spanning tree problem with uncertain edge weights. Using different decision criteria, two uncertain programming m...

The information content of the minimum spanning tree (MST), used to capture higher-order statistics and from cosmic web, is compared that power spectrum for a $\nu\Lambda$CDM model. measurements are made in redshift space using haloes Quijote simulation mass $\geq 3.2\times 10^{13}\,h^{-1}{\rm M}_{\odot}$ box length $L_{\rm box}=1\,h^{-1}{\rm Gpc}$. multipoles (monopole quadrupole) computed Fou...

An inverse minimum spanning tree problem is to make the least modification on the edge weights such that a predetermined spanning tree is a minimum spanning tree with respect to the new edge weights. In this paper, a type of fuzzy inverse minimum spanning tree problem is introduced from a LAN reconstruction problem, where the weights of edges are assumed to be fuzzy variables. The concept of fu...

Minimum spanning tree problem is a very important problem in VLSI CAD. Given n points in a plane, a minimum spanning tree is a set of edges which connects all the points and has a minimum total length. A naive approach enumerates edges on all pairs of points and takes at least (n 2) time. More eecient approaches nd a minimum spanning tree only among edges in the Delaunay triangulation of the po...

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...