Prim's algorithm

About: Prim's algorithm is a research topic. Over the lifetime, 775 publications have been published within this topic receiving 17971 citations. The topic is also known as: DJP algorithm & Jarník algorithm.

A linear algorithm for analysis of minimum spanning and shortest-path trees of planar graphs

Abstract: We give a linear time and space algorithm for analyzing trees in planar graphs. The algorithm can be used to analyze the sensitivity of a minimum spanning tree to changes in edge costs, to find its replacement edges, and to verify its minimality. It can also be used to analyze the sensitivity of a single-source shortest-path tree to changes in edge costs, and to analyze the sensitivity of a minimum-cost network flow. The algorithm is simple and practical. It uses the properties of a planar embedding, combined with a heap-ordered queue data structure.

An Exact Algorithm for the Maximum Leaf Spanning Tree Problem

Abstract: Given an undirected graph G with n nodes, the Maximum Leaf Spanning Tree problem asks to find a spanning tree of G with as many leaves as possible. When parameterized in the number of leaves k, this problem can be solved in time O(4 k poly(n)) using a simple branching algorithm introduced by a subset of the authors [13]. Daligault, Gutin, Kim, and Yeo [6] improved this branching algorithm and obtained a running time of O(3.72 k poly(n)). In this paper, we study the problem from an exact exponential time point of view, where it is equivalent to the Connected Dominating Set problem. For this problem Fomin, Grandoni, and Kratsch showed how to break the ?(2 n ) barrier and proposed an O(1.9407 n ) time algorithm [10]. Based on some properties of [6] and [13], we establish a branching algorithm whose running time of O(1.8966 n ) has been analyzed using the Measure-and-Conquer technique. Finally we provide a lower bound of ?(1.4422 n ) for the worst case running time of our algorithm.

Linear time algorithms for computing the most reliable source on an unreliable tree network

Abstract: Given a tree network with n vertices where each edge has an operational probability, we are interested in finding a vertex on the tree whose expected number of reachable vertices is maximum. This problem was studied in Networks 27 (1996) 219-237, where an O(n 3 ) time algorithm and an O(n 2 ) time algorithm were proposed. In this paper, we present an O(n) time algorithm for the same problem, improving the previously best algorithm by a factor of O(n). We also study a max-min version of the problem and propose an O(n) time algorithm for this problem as well. Examples are provided to illustrate the algorithms.

An efficient delay-constrained minimum spanning tree heuristic

Abstract: We formulate the problem of constructing broadcast trees for real-time traffic with delay constraints in networks with asymmetric link loads as a delay-constrained minimum spanning tree (DCMST) problem in directed networks. Then we prove that this problem is NP-complete, and we propose an efficient heuristic to solve the problem based on Prim’s algorithm for the unconstrained minimum spanning tree problem. This is the first heuristic designed specifically for solving the DCMST problem. Simulation results under realistic networking conditions show that our heuristic’s performance is close to optimal when the link loads are symmetric as well as when asymmetric link loads are used. Delay-constrained minimum Steiner tree heuristics can be used to solve the DCMST problem. Simulation results indicate that the fastest delay-constrained minimum Steiner tree heuristic, DMCT [1], is not as efficient as the heuristic we propose, while the most efficient delay-constrained minimum Steiner tree heuristic, BSMA [2], is much slower than our proposed heuristic and does not construct cheaper delay-constrained broadcast trees.