Showing papers on "Prim's algorithm published in 1979"
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 $O(n^2 \cdot p^2 )$.
1,333 citations
01 Oct 1979
TL;DR: In this paper, a distributed algorithm is presented that constructs the minimum weight spanning tree in a connected undirected graph with distinct edge weights, where a processor exists at each node of the graph, knowing initially only the weights of the adjacent edges.
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