# The soft heap: an approximate priority queue with optimal error rate

@article{Chazelle2000TheSH, title={The soft heap: an approximate priority queue with optimal error rate}, author={Bernard Chazelle}, journal={J. ACM}, year={2000}, volume={47}, pages={1012-1027} }

A simple variant of a priority queue, called a soft heap, is introduced. The data structure supports the usual operations: insert, delete, meld, and findmin. Its novelty is to beat the logarithmic bound on the complexity of a heap in a comparison-based model. To break this information-theoretic barrier, the entropy of the data structure is reduced by artifically raising the values of certain keys. Given any mixed sequence of n operations, a soft heap with error rate ε (for any 0 < ε ≤ 1/2…

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## 77 Citations

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A simpler and more direct implementation of soft heaps in which each priority queue is composed of a collection of standard binary trees is described, which has the advantage that no clean-up operations similar to the ones used in Chazelle's implementation are required.

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An external memory version of soft heap that is presented, which supports Insert, Findmin, Deletemin and Meld operations and guarantees that the number of corrupt elements in it is never more than eN, where N is the total number of items inserted in it, and e is a parameter of it called the error-rate.

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The presented data structure uses soft heaps of Chazelle, biased search trees, and efficient priority queues in a non-trivial way, approaching the theoretically-best data structure for ordered data.

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The presented data structure makes fundamental use of soft heaps, biased search trees, and efficient priority queues, approaching the theoretically-best data structure for ordered data.

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