Performance engineering case study: heap construction

• Authors: Jesper Bojesen;Jyrki Katajainen;Maz Spork
• Venue: Journal of Experimental Algorithmics (JEA)
• Year: 2000

The behaviour of three methods for constructing a binary heap on a computer with a hierarchical memory is studied. The methods considered are the original one proposed by Williams [1964], in which elements are repeatedly inserted into a single heap; the improvement by Floyd [1964], in which small heaps are repeatedly merged to bigger heaps; and a recent method proposed, e.g., by Fadel et al. [1999] in which a heap is built layerwise. Both the worst-case number of instructions and that of cache misses are analysed. It is well-known that Floyd's method has the best instruction count. Let N denote the size of the heap to be constructed, B the number of elements that fit into a cache line, and let c and d be some positive constants. Our analysis shows that, under reasonable assumptions, repeated insertion and layerwise construction both incur at most cN/B cache misses, whereas repeated merging, as programmed by Floyd, can incur more than (dN log2 B)/B cache misses. However, for our memory-tuned versions of repeated insertion and repeated merging the number of cache misses incurred is close to the optimal bound N/B. In addition to these theoretical findings, we communicate many practical experiences which we hope to be valuable for others doing experimental algorithmic work.