NDLI: Self-Adjusting Heaps

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Sleator, Daniel Dominic Tarjan, Robert Endre
Copyright Year	1986
Abstract	In this paper we explore two themes in data structure design: amortized computational complexity and self adjustment. We are motivated by the following observations. In most applications of data structures, we wish to perform not just a single operation but a sequence of operations, possibly having correlated behavior. By averaging the running time per operation over a worst-case sequence of operations, we can sometimes obtain an overall time bound much smaller than the worst-case time per operation multiplied by the number of operations. We call this kind of averaging amortization.Standard kinds of data structures, such as the many varieties of balanced trees, are specifically designed so that the worst-case time per operation is small. Such efficiency is achieved by imposing an explicit structural constraint that must be maintained during updates, at a cost of both running time and storage space. However, if amortized running time is the complexity measure of interest, we can guarantee efficiency without maintaining a structural constraint. Instead, during each access or update operation we adjust the data structure in a simple, uniform way. We call such a data structure self adjusting.In this paper we develop the skew heap, a self-adjusting form of heap related to the leftist heaps of Crane and Knuth. (What we mean by a heap has also been called a priority queue or a mergeable heap.) Skew heaps use less space than leftist heaps and similar worst-case-efficient data structures and are competitive in running time, both in theory and in practice, with worst-case structures. They are also easier to implement. We derive an information-theoretic lower bound showing that skew heaps have minimum possible amortized running time, to within a constant factor, on any sequence of certain heap operations.
Starting Page	52
Ending Page	69
Page Count	18
File Format	PDF
ISSN	00975397
DOI	10.1137/0215004
e-ISSN	10957111
Journal	SIAM Journal on Computing (SMJCAT)
Issue Number	1
Volume Number	15
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2006-08-02
Access Restriction	Subscribed
Subject Keyword	amortized complexity priority queue Self-organizing data structure heap
Content Type	Text
Resource Type	Article
Subject	Mathematics Computer Science

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