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 self-stabilizing 3-approximation for the maximum leaf spanning tree problem in arbitrary networks

Abstract: The maximum leaf spanning tree (MLST) is a good candidate for constructing a virtual backbone in self-organized multihop wireless networks, but is practically intractable (NP-complete). Self-stabilization is a general technique that permits to recover from catastrophic transient failures in self-organized networks without human intervention. We propose a fully distributed self-stabilizing approximation algorithm for the MLST problem in arbitrary topology networks. Our algorithm is the first self-stabilizing protocol that is specifically designed to approximate an MLST. It builds a solution whose number of leaves is at least 1/3 of the maximum possible in arbitrary graphs. The time complexity of our algorithm is O(n 2) rounds.

Parallel algorithms for the degree-constrained minimum spanning tree problem using nearest-neighbor chains and the heap-traversal technique

Abstract: The degree-constrained minimum spanning tree (d-MST) 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 /spl les/ d /spl les/ (n - 2), where n denotes the total number of nodes. Several approximate algorithms (heuristics) have been proposed in the literature. We have previously proposed three approximate algorithms, IR, TC-RNN, and TC-NNC, for solving the d-MST problem, the last two (TC-RNN and TC-NNC) take advantage of nearest neighbors and their properties. Our experimental results showed that both the TC-RNN and TC-NNC algorithms consistently produce spanning trees with a smaller weight (better quality-of-solution) than that of IR, but using slightly longer execution time. We propose a new heap traversal technique that further improves the time efficiency of TC-RNN and TC-NNC. Our experiments using randomly generated, weighted graphs as inputs show that the TC-NNC algorithm outperforms the other two approximate algorithms in terms of the execution time and quality-of-solution.

Efficient algorithms for finding the k most vital edges for the minimum spanning tree problem

Abstract: We study in this paper the problem of finding in a graph a subset of k edges whose deletion causes the largest increase in the weight of a minimum spanning tree. We propose for this problem an explicit enumeration algorithm whose complexity, when compared to the current best algorithm, is better for general k but very slightly worse for fixed k. More interestingly, unlike in the previous algorithms, we can easily adapt our algorithm so as to transform it into an implicit exploration algorithm based on a branch and bound scheme. We also propose a mixed integer programming formulation for this problem. Computational results show a clear superiority of the implicit enumeration algorithm both over the explicit enumeration algorithm and the mixed integer program.

Spanning Tree Construction for Nameless Networks

Abstract: Two types of distributed fully asynchronous probabilistic algorithms are given in the present paper which elect a leader and find a spanning tree in arbitrary anonymous networks of processes. Our algorithms are simpler than in [11] and slightly improve on those in [9,11] with respect to communication complexity. So far, the present algorithms are very likely to be the first fully and precisely specified distributed communication protocols for nameless networks. They are basically patterned upon the spanning tree algorithm designed in [7,8], and motivated by the previous works proposed in [9,11].