New Algorithms for Position Heaps

TL;DR

This paper introduces new algorithms and techniques for position heaps, improving their construction, size limitations, and integration with suffix arrays, thus enhancing their efficiency and applicability in string processing tasks.

Contribution

It presents novel algorithms for limiting heap height, linear-time construction independent of alphabet size, and methods to connect position heaps with suffix arrays.

Findings

Linear-time construction of position heaps

Heap height can be limited by pattern length

Efficient simulation of position heaps with compressed suffix arrays

Abstract

We present several results about position heaps, a relatively new alternative to suffix trees and suffix arrays. First, we show that, if we limit the maximum length of patterns to be sought, then we can also limit the height of the heap and reduce the worst-case cost of insertions and deletions. Second, we show how to build a position heap in linear time independent of the size of the alphabet. Third, we show how to augment a position heap such that it supports access to the corresponding suffix array, and vice versa. Fourth, we introduce a variant of a position heap that can be simulated efficiently by a compressed suffix array with a linear number of extra bits.