Showing papers on "Prim's algorithm published in 2003"

Greedy heuristics and an evolutionary algorithm for the bounded-diameter minimum spanning tree problem

Abstract: Given a connected, weighted, undirected graph G and a bound D, the bounded-diameter minimum spanning tree problem seeks a spanning tree on G of lowest weight in which no path between two vertices contains more than D edges. This problem is NP-hard for 4

Primal-dual meets local search: approximating MST's with nonuniform degree bounds

Abstract: We present a new bicriteria approximation algorithm for the degree-bounded minimum-cost spanning tree problem: Given an undirected graph with nonnegative edge weights and degree bounds Bv > 1 for all vertices v, find a spanning tree T of minimum total edge-cost such that the maximum degree of each node v in T is at most Bv. Our algorithm finds a tree in which the degree of each node v is O(Bv + log n) and the total edge-cost is at most a constant times the cost of any tree that obeys all degree constraints.Our previous algorithm[9] with similar guarantees worked only in the case of uniform degree bounds (i.e. Bv=B for all vertices v). While the new algorithm is based on ideas from Lagrangean relaxation as is our previous work, it does not rely on computing a solution to a linear program. Instead it uses a repeated application of Kruskal's MST algorithm interleaved with a combinatorial update of approximate Lagrangean node-multipliers maintained by the algorithm. These updates cause subsequent repetitions of the spanning tree algorithm to run for longer and longer times, leading to overall progress and a proof of the performance guarantee.

A Permutation-Coded Evolutionary Algorithm for the Bounded-Diameter Minimum Spanning Tree Problem

Abstract: The diameter of a tree is the largest number of edges on any path between two vertices in it Given a weighted, connected, undirected graph G and a bound D ≥ 2, the bounded-diameter minimum spanning tree problem seeks a spanning tree on G of minimum weight whose diameter does not exceed D An evolutionary algorithm for this NP-hard problem encodes candidate trees as permutations of their vertices The first vertex (if D is even) or the first two vertices (if D is odd) form the center of the tree a permutation represents A greedy heuristic appends the remaining vertices to the tree in their listed order, as economically as possible, while maintaining the diameter bound In tests on 25 Euclidean problem instances, this EA identifies shorter trees on average than does an EA that encodes trees as sets of their edges, though it takes longer

A distributed spanning tree algorithm for topology-aware networks

Abstract: . A topology-aware network is a dynamic network in which the nodes can detect whether locally topology changes occur. Many modern networks, like IEEE 1394.1, are topology-aware networks. We present a distributed algorithm for computing and maintaining an arbitrary spanning tree in such a topology-aware network. Although usually minimal spanning trees are studied, in practice arbitrary spanning trees are often sufficient. Since our algorithm is not involved in the detection of topology changes, it performs better than the spanning tree algorithms in standards like IEEE 802.1. Because reasoning about distributed algorithms is rather tricky, we use a systematic approach to prove our algorithm.

The first approximated distributed algorithm for the minimum degree spanning tree problem on general graphs

Abstract: In this paper we present the first distributed algorithm on general graphs for the minimum degree spanning tree problem. The problem is NP-hard in sequential. Our algorithm gives a spanning tree of a degree at most 1 from the optimal. The resulting distributed algorithm is asynchronous, it works for named asynchronous arbitrary networks and achieves O(|V|) time complexity and O(|V| |E|) message complexity.

An optimal PRAM algorithm for a spanning tree on trapezoid graphs

Abstract: Let G be a graph with n vertices and m edges. The problem of constructing a spanning tree is to find a connected subgraph of G with n vertices and n - 1 edges. In this paper, we propose an O(log n) time parallel algorithm with O(n/log n) processors on an EREW PRAM for constructing a spanning tree on trapezoid graphs.

A formal analysis of a dynamic distributed spanning tree algorithm

Abstract: We analyze the spanning tree algorithm in the IEEE 13941 draft standard, which correctness has not previously been proved This algorithm is a fully-dynamic distributed graph algorithm, which, in general, is hard to develop The approach we use is to formally develop an algorithm that is almost equivalent to it: First, based on a formal specification and an abstraction of the network, we systematically construct an algorithm including its correctness proof Afterwards we implement this algorithm in terms of IEEE 1394 devices under maintenance of its correctness

Quasi-polynomial Time Approximation Algorithm for Low-Degree Minimum-Cost Steiner Trees

Abstract: In a recent paper [5], we addressed the problem of finding a minimum-cost spanning tree T for a given undirected graph G=(V,E) with maximum node-degree at most a given parameter B>1. We developed an algorithm based on Lagrangean relaxation that uses a repeated application of Kruskal’s MST algorithm interleaved with a combinatorial update of approximate Lagrangean node-multipliers maintained by the algorithm.

A node-oriented branch and bound algorithm for the capacitated minimum spanning tree problem

Abstract: This paper studies the capacitated minimum spanning tree (CMST) problem, which is one of the most fundamental and significant problems in the optimal design of local computer networks. A solution method using a node-oriented branch and bound technique is introduced and its performance is presented. We show the advantages of the algorithm while illustrating the process of searching for the optimal solution. Techniques for finding tighter lower bounds are emphasized. Computational experiences demonstrate the algorithm's effectiveness.

Method and apparatus for determining communication path over network by using spanning tree and circuit detection

Abstract: A method and apparatus for determining a communication path over a network are provided. The method involves generating a spanning tree having connection devices over a network as vertices and having links among the connection devices as edges; allotting predetermined vertex information to each vertex on the spanning tree; detecting all circuits having a plurality of communication paths among the connection devices over the network corresponding to the spanning tree; and applying rapid ring spanning tree protocol (RRSTP) to links corresponding to the detected circuits and applying rapid spanning tree protocol (RSTP) to links not corresponding to the detected circuits.

On the inverse minimum spanning tree problem with minimum number of perturbed edges

Abstract: Let G=〈V, E, L〉 be a network with the vertex set V, the edge set E and the length vector L, and let T* be a prior determined spanning tree of G. The inverse minimum spanning tree problem with minimum number of perturbed edges is to perturb the length vector L to L+δ, such that T* is one of minimum spanning trees under the length vector L+δ and the number of perturbed edges is minimum. This paper establishes a mathematical model for this problem and transforms it into a minimum vertex covering problem in a bipartite graph G0, a path-graph. Thus a strongly polynomial algorithm with time complexity O(mn2) can be designed by using Hungarian method.

Minimum Spanning Tree Algorithm Based on Extended Double List Storage Structure

Abstract: This paper presents an extended double list storage structure based on a double list storage structure and then applies it to the minimum spanning tree algorithm. This storage structure has more agility as compared with the others storage structure.

Approximating the Geometric Minimum-Diameter Spanning Tree

Abstract: Given a set P of points in the plane, a geometric minimum-diameter spanning tree (GMDST) of P is a spanning tree of P such that the longest path through the tree is minimized. In this paper, we present an approximation algorithm that generates a tree whose diameter is no more than (1 + � ) times that of a GMDST, for any �> 0. Our algorithm reduces the problem to several grid-aligned versions of the problem and runs within time O(� −3 + n) and space O(n) improving the result by Gudmundsson et al. [4].