Bootstrapping one-sided flexible arrays

ABSTRACT

The abstract data type one-sided flexible array, also called random-access list, supports look-up and update of elements and can grow and shrink at one end. We describe a purely functional implementation based on weight-balanced multiway trees that is both simple and versatile. A novel feature of the representation is that the running time of the operations can be tailored to one's needs---even dynamically at array-creation time. In particular, one can trade the running time of look-up operations for the running time of update operations. For instance, if the multiway trees have a fixed degree, the operations take θ(log n) time, where n is the size of the flexible array. If the degree doubles levelwise, look-up speeds up to θ(sqrtlog n) while update slows down to θ(2^{sqrt log n}). We show that different tree shapes can be conveniently modelled after mixed-radix number systems.

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INDEX TERMS

Primary Classification:
  D. Software
  D.1 PROGRAMMING TECHNIQUES
      D.1.1 Applicative (Functional) Programming

Additional Classification:
  D. Software
  D.3 PROGRAMMING LANGUAGES
      D.3.2 Language Classifications
          Subjects: Applicative (functional) languages
      D.3.3 Language Constructs and Features

  E. Data
  E.1 DATA STRUCTURES
      Subjects: Trees; Arrays

  I. Computing Methodologies
  I.1 SYMBOLIC AND ALGEBRAIC MANIPULATION
      I.1.2 Algorithms
          Subjects: Analysis of algorithms

General Terms:
Algorithms, Design, Performance

Keywords:
Haskell, flexible arrays, mixed-radix number systems, purely functional data structures, sub-logarithmic look-up