Optimal Algorithms for the Vertex Updating Problem of a Minimum Spanning Tree (1992)
| Venue: | In Proc. of the 6th Intl Parallel Proccessing Symposium (IPPS '92 |
| Citations: | 3 - 2 self |
BibTeX
@INPROCEEDINGS{Johnson92optimalalgorithms,
author = {Donald B. Johnson and Panagiotis Metaxas},
title = {Optimal Algorithms for the Vertex Updating Problem of a Minimum Spanning Tree},
booktitle = {In Proc. of the 6th Intl Parallel Proccessing Symposium (IPPS '92},
year = {1992},
pages = {306--314},
publisher = {IEEE Press}
}
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Abstract
The vertex updating problem for a minimum spanning tree (MST) is defined as follows: Given a graph G = (V; EG ) and its MST T , update T when a new vertex z is introduced along with weighted edges that connect z with the vertices of G. We present a set of rules that, together with a valid tree-contraction schedule, are used to produce simple optimal parallel algorithms that run in O(lgn) parallel time using n= lg n EREW PRAMs where n = jV j. These rules can also be used to derive simple linear-time sequential algorithms for the same problem. The previously best known parallel result was a rather complicated algorithm that used n processors of the more powerful CREW PRAM model. Furthermore, we show how our solution can be used to solve the multiple vertex updating problem: Update a given MST when k new vertices are introduced simultaneously. This problem is solved in O(lg k \Delta lg n) parallel time using k \Deltan lg k \Deltalg n EREW PRAM processors. 1 Introduction Definition. ...
