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Optimal algorithms for the vertex updating problem of a minimum spanning tree

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2 Author(s)
D. B. Johnson ; Dept. of Math. & Comput. Sci., Dartmouth Coll., Hanover, NH, USA ; P. Metaxas

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. The authors 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(log n) parallel time using n/lgn EREW PRAMs where n=|V|. These rules can also be used to derive simple linear-time sequential algorithms for the same problem. It is also shown how this 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(lgk.lgn) parallel time using lgk.lgn k.n EREW PRAM processors

Published in:

Parallel Processing Symposium, 1992. Proceedings., Sixth International

Date of Conference:

23-26 Mar 1992