Verification and Sensitivity Analysis Of Minimum Spanning Trees In Linear Time (1992)
| Venue: | SIAM J. Comput |
| Citations: | 48 - 2 self |
BibTeX
@ARTICLE{Dixon92verificationand,
author = {Brandon Dixon and Monika Rauch and Robert and Robert E. Tarjan},
title = {Verification and Sensitivity Analysis Of Minimum Spanning Trees In Linear Time},
journal = {SIAM J. Comput},
year = {1992},
volume = {21},
pages = {1184--1192}
}
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Abstract
. Koml'os has devised a way to use a linear number of binary comparisons to test whether a given spanning tree of a graph with edge costs is a minimum spanning tree. The total computational work required by his method is much larger than linear, however. We describe a linear-time algorithm for verifying a minimum spanning tree. Our algorithm combines the result of Koml'os with a preprocessing and table look-up method for small subproblems and with a previously known almost-linear-time algorithm. Additionally, we present an optimal deterministic algorithm and a linear-time randomized algorithm for sensitivity analysis of minimum spanning trees. 1. Introduction. Suppose we wish to solve some problem for which we know in advance the size of the input data, using an algorithm from some well-defined class of algorithms. For example, consider sorting n numbers, when n is fixed in advance, using a binary comparison tree. Given a sufficient amount of preprocessing time and storage space, we ca...
