A simpler implementation and analysis of Chazelle's Soft Heaps

Haim Kaplan*, Uri Zwick

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

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, may be corrupted, 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.

Original languageEnglish
Title of host publicationProceedings of the 20th Annual ACM-SIAM Symposium on Discrete Algorithms
PublisherAssociation for Computing Machinery (ACM)
Pages477-485
Number of pages9
ISBN (Print)9780898716801
DOIs
StatePublished - 2009
Event20th Annual ACM-SIAM Symposium on Discrete Algorithms - New York, NY, United States
Duration: 4 Jan 20096 Jan 2009

Publication series

NameProceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms

Conference

Conference20th Annual ACM-SIAM Symposium on Discrete Algorithms
Country/TerritoryUnited States
CityNew York, NY
Period4/01/096/01/09

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