In their pioneering paper [4], Gallager et al. introduced a distributed algorithm for constructing the minimum-weight spanning tree (MST), many authors have suggested ways to enhance their basic algorithm. Most of these improved algorithms have been shown to be very efficient in terms of reducing their worst-case communication and/or time complexity measures. In this paper, we address the probl...

Due to promulgation of data over internet significance of protection of one’s intellectual property is the important topic with technological and legal aspects. Watermarking scheme is used for establishing the ownership of dataset containing multiple objects. As watermarking scheme distorts distance relationship graph, methodology preserves utility of dataset by preserving important distance pr...

The identification of clusters or communities in complex networks is a reappearing problem. The minimum spanning tree (MST), the tree connecting all nodes with minimum total weight, is regarded as an important transport backbone of the original weighted graph. We hypothesize that the clustering of the MST reveals insight in the hierarchical structure of weighted graphs. However, existing theori...

An enhanced heuristic for the GOSST (Grade of Services Steiner Minimum Tree) problem is proposed in this paper. GOSST problem is to look for a network topology satisfying the G-condition with minimum construction cost of the network. In previous research, we proposed a heuristic for the problem, which employed two Steiner point locating strategies with Naïve MST (Minimum Spanning Tree) building...

We consider the minimum spanning tree (MST) problem under the restriction that for every vertex v, the edges of the tree that are adjacent to v satisfy a given family of constraints. A famous example thereof is the classical degree-bounded MST problem, where for every vertex v, a simple upper bound on the degree is imposed. Iterative rounding/relaxation algorithms became the tool of choice for ...

Motivated by practical VLSI routing applications, we study the maximum vertex degree of a minimum spanning tree (MST). We prove that under the Lp norm, the maximum vertex degree over all MSTs is equal to the Hadwiger number of the corresponding unit ball; we show an even tighter bound for MSTs where the maximum degree is minimized. We give the best-known bounds for the maximum MST degree for ar...

Minimum Spanning Tree (MST) problem is of high importance in network optimization. The multi-criteria MST (mc-MST) is a more realistic representation of the practical problem in the real-world, but it is diicult for the traditional network optimization technique to deal with. In this paper, a genetic algorithm (GA) approach is developed to deal with this problem. Without neglecting its network ...

Given n uniformly and independently distributed points in a ball of unit volume in dimension d, it is well established that the length of several combinatorial optimization problems (including the minimum spanning tree (MST), the minimum matching (M), the traveling salesman problem (TSP), etc.) on these n points obeys laws of large numbers. It has been a long open conjecture that a central limi...

The minimum spanning tree (MST) is widely used in planning the most economical network. algorithm for finding MST of a connected graph essential. In this paper, new proposed based on deduced theorem MST. first sorts edges according to their weight, from large small. Next, premise ensuring connectivity graph, it deletes order until number equal vertexes minus 1. Finally, remaining an This equiva...

This paper presents a lower bound of ~ (D + p n) on the time required for the distributed construction of a minimum-weight spanning tree (MST) in n-vertex networks of diameter D = (logn), in the bounded message model. This establishes the asymptotic near-optimality of existing time-e cient distributed algorithms for the problem, whose complexity is O(D + p n log n).