The minimum rectilinear Steiner tree (MRST) problem is very important for such aspects of physical layout as global routing and wiring estimation. Virtually all previous heuristics for computing rectilinear Steiner trees begin with a minimum spanning tree (MST) topology and rearrange edges to induce Steiner points. This paper gives a more direct approach which makes a significant departure from...

The Minimum Spanning Tree Problem (MSTP) is one of the most known combinatorial optimization problems. It concerns the determination of a minimum edge-cost subgraph spanning all the vertices of a given connected graph. The Quadratic Minimum Spanning Tree Problem (QMSTP) is a variant of the MST whose cost considers also the interaction between every pair of edges of the tree. In this paper we re...

We present a new efficient localized algorithm to construct, for any given quasi-unit disk graph G = (V ,E) and any ε > 0, a (1+ ε)-spanner for G of maximum degree O(1) and total weight O(ω(MST )), where ω(MST ) denotes the weight of a minimum spanning tree forV . We further show that similar localized techniques can be used to construct, for a given unit disk graphG = (V ,E), a planarCdel(1+ε)...

Most clustering algorithms become ineffective when provided with unsuitable parameters or applied to datasets which are composed of clusters with diverse shapes, sizes, and densities. To alleviate these deficiencies, we propose a novel split-and-merge hierarchical clustering method in which a minimum spanning tree (MST) and an MST-based graph are employed to guide the splitting and merging proc...

This first algorithm is quite simple. (Though this was probably known earlier, its proof can be found in Prof. Indyk’s 1999 paper “Sublinear Time Algorithms for Metric Space Problems”.) Let Dij denote the distance between a pair of points i and j, over m total points. The entries of Dij must satisfy the triangle inequality; additionally the matrix is symmetric. Note that the matrix size (i.e., ...

it is very important for managers, investors and financial policy-makers to detect and analyze factors affecting financial markets to obtain optimal decision and reduce risks. the importance of market analysis and attempt to improve its behavior understanding, has led analysts to use the experiences of other professionals in the fields such as social sciences and mathematics to examine the inte...

In recent years there has been a shift in focus from the study of local, mostly task-related activation to the exploration of the organization and functioning of large-scale structural and functional complex brain networks. Progress in the interdisciplinary field of modern network science has introduced many new concepts, analytical tools and models which allow a systematic interpretation of mu...

Choi et al. [2] introduced a minimum spanning tree (MST)-based method called CLGrouping, for constructing tree-structured probabilistic graphical models, a statistical framework that is commonly used for inferring phylogenetic trees. While CLGrouping works correctly if there is a unique MST, we observe an indeterminacy in the method in the case that there are multiple MSTs. We demonstrate the i...

We study the expected value of the length Ln of the minimum spanning tree of the complete graph Kn when each edge e is given an independent uniform [0, 1] edge weight. We sharpen the result of Frieze [6] that limn→∞ E(Ln) = ζ(3) and show that E(Ln) = ζ(3) + c1 n + c2+o(1) n4/3 where c1, c2 are explicitly defined constants.