In this paper, we present the first differentially private clustering method for arbitrary-shaped node clusters in a graph. This algorithm takes as input only an approximate Minimum Spanning Tree (MST) T released under weight differential privacy constraints from the graph. Then, the underlying nonconvex clustering partition is successfully recovered from cutting optimal cuts on T . As opposed ...

In this paper, the authors present a robust three-dimensional fingerprint algorithm for verification, indexing, and identification. The core idea behind our technique is to apply the eigen-decomposition to the mesh Laplacian matrix, and then compute minimum spanning trees (MST) of several concentrations of the mesh shape structure. The fixed size hash vector of a 3D mesh is defined in terms of ...

This paper studies the sum-of-ratios version of the classical minimum spanning tree (MST) problem. We develop a branch-and-bound algorithm for solving the general version of the problem based on its image space representation. The suggested approach specifically addresses the difficulties arising in the case when the number of ratios exceeds two. The efficacy of our approach is demonstrated on ...

The most popular algorithms for generation of minimal spanning tree are Kruskal’s[2] and Prim’s[2] algorithm. Many algorithms have been proposed for generation of all spanning tree. This paper deals with generation of all possible spanning trees in increasing cost of a weighted graph. This approach uses one matrix called Difference Weighted Circuit Matrix (DWCM); it is little bit modification o...

A minimum spanning tree (MST) with a small diameter is required in numerous practical situations. It is needed, for example, in distributed mutual exclusion algorithms in order to minimize the number of messages communicated among processors per critical section. The DiameterConstrained MST (DCMST) problem can be stated as follows: given an undirected, edge-weighted graph G with n nodes and a p...

Given a set S of n points, we show that the length of 1) the minimum weight triangulation (MWT ) of the minimum weight convex partition (MWCP ) of S (TMWCP ) is at most Θ(n) longer than the MWT of S if collinearity of two or more edges is allowed and Θ(log n) otherwise, 2) the MWT of the minimum spanning tree (MST ) of the MWCP of S (Tmst(MWCP )) is at most Θ(n) longer than the MWT of S if coll...

The changes in the population, gross domestic product (GDP) and exports of goods services 32 countries that we have selected for 25 years annually been examined. In this study, use hierarchical structure methods such as minimum spanning tree (MST) (HT) to explain relationship between countries' GDP, annual from 1991 2016. Using MST HT, obtained with same economic development level some variable...

Let P be a set of n points in a metric space. A Steiner Minimal Tree (SMT) on P is a shortest network interconnecting P while a Minimum Spanning Tree (MST) is a shortest network interconnecting P with all edges between points of P . The Steiner ratio is the infimum over P of ratio of the length of SMT over that of MST. Steiner ratio problem is to determine the value of the ratio. In this paper ...