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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02 Sep 2009
TL;DR: A new distributed algorithm, which finds a good approximation of the Minimum Spanning Tree in the Unit Disc Graphs, in O(d2) synchronous rounds, where d is an input parameter.
Abstract: We present a new distributed algorithm, which finds a good approximation of the Minimum Spanning Tree in the Unit Disc Graphs. Our algorithm, in O(d2) synchronous rounds, where d is an input parameter, finds a subgraph H of the Unit Disc Graph G which contains a Minimum Spanning Tree of G. Moreover, H is planar, does not contain cycles of weight smaller than d/3 and the weight of H is (1 + O(1/d)) approximation of the weight of the Minimum Spanning Tree of G.
2 citations
Proceedings Article•
07 Nov 2008TL;DR: An optimal algorithm to solve the problem for tree topology graphs in polynomial time is proposed, where n is the number of nodes in a k-terminal graph, with the Goldberg-Tarjan's network flow algorithm.
Abstract: Geometrical k-cut problem has numerous applications, particularly in clustering-related setups such as task assignment and VLSI cell placement. This problem is NP-hard in general. We propose an optimal algorithm to solve the problem for tree topology graphs in polynomial time. The time complexity of the algorithm is O(kn3), where n is the number of nodes in a k-terminal graph, with the Goldberg-Tarjan's network flow algorithm.
2 citations
01 Jan 2012
TL;DR: A modified version of prim's algorithm which is a minimum spanning tree algorithm, where root node is chosen with minimum edge weight so that from the beginning of forest creation, only minimum weight edges are included.
Abstract: 1 Abstract— This paper proposes a modified version of prim's algorithm which is a minimum spanning tree algorithm. Minimum spanning tree algorithms are greedy algorithms as they choose the best path available at that moment. Prim's algorithm chooses a root node randomly and starts processing it but choosing any node randomly as a root node is not efficient. So, in modified prim's algorithm, root node is chosen with minimum edge weight so that from the beginning of forest creation, only minimum weight edges are included. Minimum spanning tree is generated differently as of prim's algorithm. Although modified prim's algorithm is a special case of original prims algorithm with randomly chosen node is of minimum weight. With this modification in original prims algorithm, modified prim's algorithm maintains the complexity same as original prim's algorithm.
2 citations
15 Aug 2007
TL;DR: It is shown that the O*(2√k) complexity is hard to improve under a hypothesis of the complexity of 3-SAT, and more sophisticated algorithms based on graph separators are given, with a novel technique to ensure connectivity.
Abstract: We consider the problem of computing non-crossing spanning trees in topological graphs. It is known that it is NP-hard to decide whether a topological graph has a non-crossing spanning tree, and that it is hard to approximate the minimum number of crossings in a spanning tree. We consider the parametric complexities of the problem for the following natural input parameters: the number k of crossing edge pairs, the number µ of crossing edges in the given graph, and the number l of vertices in the interior of the convex hull of the vertex set. We start with an improved strategy of the simple search-tree method to obtain an O*(1.93k) time algorithm. We then give more sophisticated algorithms based on graph separators, with a novel technique to ensure connectivity. The time complexities of our algorithms are O*(2O(√k)), O*(µO(µ2/3)), and O*(2O(√l)). By giving a reduction from 3-SAT, we show that the O*(2√k) complexity is hard to improve under a hypothesis of the complexity of 3-SAT.
2 citations