Topic
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.
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03 Jul 1996
TL;DR: In this article, a fast algorithm for enumerating all distinct minimum spanning trees in a graph whose edge weights vary linearly with a parameter is given. And an asymptotically optimal algorithm for the minimum ratio spanning tree problem, as well as other search problems, on dense graphs.
Abstract: Two applications of sparsification to parametric computing are given. The first is a fast algorithm for enumerating all distinct minimum spanning trees in a graph whose edge weights vary linearly with a parameter. The second is an asymptotically optimal algorithm for the minimum ratio spanning tree problem, as well as other search problems, on dense graphs.
18 citations
13 Sep 2010
TL;DR: This algorithm improves the convergence time of all previously known self-stabilizing asynchronous MST algorithms by a multiplicative factor Θ(n), to the price of increasing the best known space complexity by a factor O(log n).
Abstract: We present a novel self-stabilizing algorithm for minimum spanning tree (MST) construction. The space complexity of our solution is O(log2 n) bits and it converges in O(n2) rounds. Thus, this algorithm improves the convergence time of all previously known self-stabilizing asynchronous MST algorithms by a multiplicative factor Θ(n), to the price of increasing the best known space complexity by a factor O(log n). The main ingredient used in our algorithm is the design, for the first time in self-stabilizing settings, of a labeling scheme for computing the nearest common ancestor with only O(log2 n) bits.
18 citations
TL;DR: There is enough evidence to conclude that for sparse graphs, Char's original implementation is superior to MOD-CHAR, and for dense graphs of any order the time complexity of MOD- CHAR is O(t), where t is the number of spanning trees generated.
Abstract: Two complexity analyses of MOD-CHAR are presented. It is shown that MOD-CHAR leads to better complexity results for J.P. Char's algorithm than what could be obtained using the straightforward implementation implied in Char's original presentation (see IEEE Trans. Circuit Theory, Vol.15, p.228-38, 1968). The class of graphs for which MOD-CHAR and, hence, Char's algorithm, has linear time complexity per spanning tree generated is identified. This class is more general than the corresponding one identified in R. Jayakumar et al. (see ibid., vol.31, no.10, p.853-60, 1984). Using a result on random graphs, it is proved that for almost all graphs MOD-CHAR has linear worst-case time complexity per spanning tree generated. It is also shown that for any complete graph MOD-CHAR requires, on the average, at most seven computational steps to generate a spanning tree. This result and computational experiences provide evidence to believe that for dense graphs of any order the time complexity of MOD-CHAR is O(t), where t is the number of spanning trees generated. On the other hand, there is enough evidence to conclude that for sparse graphs, Char's original implementation is superior to MOD-CHAR. >
18 citations
07 Mar 2011
TL;DR: In this paper, a computer program has been developed for planning and operation in service restoration of distribution network, which has been tested on 16 bus IEEE Power Distribution System and the results obtained have reduced the losses considerably without using any optimization techniques and the amount of load shed is less when compared to the reference papers.
Abstract: The distribution network can undergo outages, during which the supply of power is either partially or completely isolated from distribution network to the load centres. To achieve minimum deficit of power supply, proper switching of power lines is required. The power flow path identification in the network is the complicated task of the distribution operators. Based on the survey the papers published have always used some predefined rules in identifying the power flow path, sometimes it may lead to cascaded outage. Hence the identification of the path was the major drawback of other proposed methodologies. The scope of the proposed work is to find the path using Prim's algorithm for a power distribution network. The algorithm is used here because it provides a path which consists of all the possible buses through which the power will flow. A computer program has been, developed for planning and operation in service restoration of distribution network. The validity of this new approach has been tested on 16 bus IEEE Power Distribution System. The results obtained have reduced the losses considerably without using any optimization techniques and the amount of load shed is less when compared to the reference papers.
18 citations
TL;DR: The Stackelberg Minimum Spanning Tree Game is a two-level combinatorial pricing problem played on a graph representing a network that is NP-hard on planar graphs but can be solved in polynomial time on graphs of bounded treewidth.
Abstract: The Stackelberg Minimum Spanning Tree Game is a two-level combinatorial pricing problem played on a graph representing a network. Its edges are colored either red or blue, and the red edges have a given fixed cost, representing the competitor's prices. The first player chooses an assignment of prices to the blue edges, and the second player then buys the cheapest spanning tree, using any combination of red and blue edges. The goal of the first player is to maximize the total price of purchased blue edges.
We study this problem in the cases of planar and bounded-treewidth graphs. We show that the problem is NP-hard on planar graphs but can be solved in polynomial time on graphs of bounded treewidth.
18 citations