[PDF] In-place Heap Construction with Optimized Comparisons, Moves, and Cache Misses | Semantic Scholar

Analysis of the behaviour of three methods for constructing a binary heap on a computer with a hierarchical memory shows that, under reasonable assumptions, repeated insertion and layerwise construction both incur at most at most cN/B cache misses, whereas repeated merging, as programmed by Floyd, can incur more than more than (<i>dN</i> log<inf>2</inf> <i>B</i>) cache misses.

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The task of performing the basic priority queue operations on a heap is considered and it is shown that in the worst case log log n comparisons are necessary and sufficient to insert an element into a heap.

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The study is carried out by investigating hardest instances of the problem and developing an algorithmic paradigm for the construction that produces comparison- and space-efficient construction algorithms for the heaplike structures, which improve over those previously fast known algorithms.

A data structure called aweak-heap is defined by relaxing the requirements for a heap and theoretical analysis and empirical results indicate that it is a competitive structure for sorting.

It is proved that an optimal cache-oblivious algorithm designed for two levels of memory is also optimal for multiple levels and that the assumption of optimal replacement in the ideal-cache model can be simulated efficiently by LRU replacement.