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A Simpler Implementation and Analysis of Chazelle’s Soft Heaps (2009)
| Venue: | In Proc. of the 19th ACM-SIAM Symposium on Discrete Algorithms |
| Citations: | 3 - 0 self |
BibTeX
@INPROCEEDINGS{Kaplan09asimpler,
author = {Haim Kaplan and Uri Zwick},
title = {A Simpler Implementation and Analysis of Chazelle’s Soft Heaps},
booktitle = {In Proc. of the 19th ACM-SIAM Symposium on Discrete Algorithms},
year = {2009},
pages = {477--485}
}
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Abstract
Chazelle (JACM 47(6), 2000) devised an approximate meldable priority queue data structure, called Soft Heaps, and used it to obtain the fastest known deterministic comparison-based algorithm for computing minimum spanning trees, as well as some new algorithms for selection and approximate sorting problems. If n elements are inserted into a collection of soft heaps, then up to εn of the elements still contained in these heaps, for a given error parameter ε, maybecorrupted, i.e., have their keys artificially increased. In exchange for allowing these corruptions, each soft heap operation is performed in O(log 1 ε) amortized time. Chazelle’s soft heaps are derived from the binomial heaps data structure in which each priority queue is composed of a collection of binomial trees. We describe a simpler and more direct implementation of soft heaps in which each priority queue is composed of a collection of standard binary trees. Our implementation has the advantage that no clean-up operations similar to the ones used in Chazelle’s implementation are required. We also present a concise and unified potential-based amortized analysis of the new implementation. 1
Keyphrases
soft heap simpler implementation priority queue binomial tree minimum spanning tree clean-up operation standard binary tree approximate sorting problem direct implementation new algorithm unified potential-based amortized analysis new implementation chazelle implementation error parameter soft heap operation deterministic comparison-based algorithm binomial heap data structure
