Topic

# Prim's algorithm

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

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TL;DR: An algorithm is presented which finds a p-median of a tree (for $p > 1$) in time $O(n^2 \cdot p^2 )$.

Abstract: It is shown that the problem of finding a p-median of a network is an $NP$-hard problem even when the network has a simple structure (e.g., planar graph of maximum vertex degree 3). However, results leading to efficient algorithms are presented when the network is a tree: In particular, we first show that a 1-median of a tree is identical to its w-centroid, and obtain Goldman’s $O(n)$ algorithm for finding a 1-median of a tree out of more general considerations. Then, we present an algorithm which finds a p-median of a tree (for $p > 1$) in time $O(n^2 \cdot p^2 )$.

1,297 citations

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TL;DR: A distributed algorithm is presented that constructs the minimum weight spanning tree in a connected undirected graph with distinct edge weights that can be initiated spontaneously at any node or at any subset of nodes.

Abstract: Abstract : A distributed algorithm is presented that constructs the minimum weight spanning tree in a connected undirected graph with distinct edge weights. A processor exists at each node of the graph, knowing initially only the weights of the adjacent edges. The processors obey the same algorithm and exchange messages with neighbors until the tree is constructed. The total number of messages required for a graph of N nodes and E edges is at most 5N log of N to the base 2 + 2E and a message contains at most one edge weight plus log of 8N to the base 2 bits. The algorithm can be initiated spontaneously at any node or at any subset of nodes.

1,111 citations

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01 Oct 1979

Abstract: : A distributed algorithm is presented that constructs the minimum weight spanning tree in a connected undirected graph with distinct edge weights. A processor exists at each node of the graph, knowing initially only the weights of the adjacent edges. The processors obey the same algorithm and exchange messages with neighbors until the tree is constructed. The total number of messages required for a graph of N nodes and E edges is at most 5N log of N to the base 2 + 2E and a message contains at most one edge weight plus log of 8N to the base 2 bits. The algorithm can be initiated spontaneously at any node or at any subset of nodes.

1,059 citations

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TL;DR: There are several apparently independent sources and algorithmic solutions of the minimum spanning tree problem and their motivations, and they have appeared in Czechoslovakia, France, and Poland, going back to the beginning of this century.

Abstract: It is standard practice among authors discussing the minimum spanning tree problem to refer to the work of Kruskal(1956) and Prim (1957) as the sources of the problem and its first efficient solutions, despite the citation by both of Boruvka (1926) as a predecessor. In fact, there are several apparently independent sources and algorithmic solutions of the problem. They have appeared in Czechoslovakia, France, and Poland, going back to the beginning of this century. We shall explore and compare these works and their motivations, and relate them to the most recent advances on the minimum spanning tree problem.

714 citations

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TL;DR: A linear time algorithm for computing, given the component tree of a function, the dynamics of all its maxima, and a link between the dynamics, minimum spanning trees, and component trees is established.

Abstract: We show several properties of the ordered dynamics. In particular, we give necessary and sufficient conditions which indicate when a transformation preserves the dynamics of the regional maxima. We also establish a link between the dynamics, minimum spanning trees, and component trees. At last, we propose a linear time algorithm for computing, given the component tree of a function, the dynamics of all its maxima.

434 citations