On demand string sorting over unbounded alphabets

  • Authors:
  • Carmel Kent;Moshe Lewenstein;Dafna Sheinwald

  • Affiliations:
  • IBM Research Lab, Haifa, Israel;Department of Computer Science, Bar-Ilan University, Ramat Gan, Israel;IBM Research Lab, Haifa, Israel

  • Venue:
  • Theoretical Computer Science
  • Year:
  • 2012

Quantified Score

Hi-index 5.23

Visualization

Abstract

On-demand string sorting is the problem of preprocessing a set of strings to allow subsequent queries for finding the k lexicographically smallest strings (and afterward the next k etc.) This on-demand variant strongly resembles the search engine queries which give you the best k-ranked pages recurringly. We present a data structure that supports this in O(n) preprocessing time, where n is the number of strings, and answer queries in O(logn) time. There is also a cost of O(N) time amortized over all operations, where N is the total length of the strings. Our data structure is a heap of strings, which supports heapify and delete-mins. As it turns out, implementing a full heap with all operations is not that simple. For the sake of completeness, we propose a heap with full operations based on balanced indexing trees that supports the heap operations in optimal times.