This paper presents a lower bound of Ω(D+ √ n/ logn) on the time required for the distributed construction of a minimum-weight spanning tree (MST) in weighted n-vertex networks of diameter D = Ω(logn), in the bounded message model. This establishes the asymptotic nearoptimality of existing time-efficient distributed algorithms for the problem, whose complexity is O(D + √ n log∗ n).

The connection between sense of direction and communication complexity in distributed complete networks is studied for two basic problems: finding a minimum-weight spanning tree (MST) and finding a spanning tree (SP). Several models of the complete network are defined, the difference being the amount (and type) of sense of direction available, forming a hierarchy which includes the models previ...

Salah satu contoh masalah dalam graf adalah pencarian pohon merentang. Terdapat dua kasus yang pada umumnya dibahas merentang, yaitu merentang maksimum dan minimum. Ada beberapa algoritma dapat digunakan untuk mencari minimum dari sebuah berbobot atau dikenal dengan istilah Minimum Spanning Tree (MST). Pada penelitian ini dilakukan jaringan pipa air PDAM perumahan mendalo asri, menggunakan Algo...

This paper proposes an eflcient distributed multicast routing algorithm that provides quality of service (QoS) guarantees for real-time applications. It focuses on the delay-constrained minimum cost tree (or constrained Steiner tree) problem; that is, it constructs a multicast tree that not only meets the constrained end-to-end delay requirements but also is the minimum cost multicast tree. Thi...

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 weighted n-vertex networks of diameter D = (log n), in the bounded message model. This establishes the asymptotic near-optimality of existing time-eecient distributed algorithms for the problem, whose complexity is O(D + p n log n).

Minimum spanning tree can be obtained for connected weighted edges with no negative weight using classical algorithms such as Boruvka’s, Prim’s and Kruskal. This paper presents a survey on the classical and the more recent algorithms with different techniques. This survey paper also contains comparisons of MST algorithm and their advantages and disadvantages.

We present an (1+ε)-approximation algorithm for computing the minimum-spanning tree of points in a planar arrangement of lines, where the metric is the number of crossings between the spanning tree and the lines. The expected running time of the algorithm is near linear. We also show how to embed such a crossing metric of hyperplanes in d-dimensions, in subquadratic time, into high-dimensions s...

We study the problem of constructing minimum power-p Euclidean k-Steiner trees in the plane. The problem is to find a tree of minimum cost spanning a set of given terminals where, as opposed to the minimum spanning tree problem, at most k additional nodes (Steiner points) may be introduced anywhere in the plane. The cost of an edge is its length to the power of p (where p ≥ 1), and the cost of ...

For any ǫ > 0 we give a (2+ǫ)-approximation algorithm for the problem of finding a minimum tree spanning any k vertices in a graph (k-MST), improving a 3-approximation algorithm by Garg [5]. As in [5] the algorithm extends to a (2+ǫ)-approximation algorithm for the minimum tour that visits any k vertices, provided the edge costs satisfy the triangle inequality.

The Degree-Constrained Minimum Spanning Tree (dMST) problem attempts to find a minimum spanning tree with an added constraint that no nodes in the tree have a degree larger than a specified integer d. It is known that computing the d-MST is NP-hard for every d in the range 2 ≤ d ≤ (n − 2), where n denotes the total number of nodes. Several approximate algorithms (heuristics) have been proposed ...