Elsevier

Information Processing Letters

Volume 79, Issue 5, 15 September 2001, Pages 237-241
Information Processing Letters

Space-time trade-offs for some ranking and searching queries

https://doi.org/10.1016/S0020-0190(00)00226-XGet rights and content

Abstract

We study space/time tradeoffs for querying some combinatorial structures. In the first, given an arrangement of n lines in general position in the plane, a query for a real number t asks about Rank(t), the number of vertices of the arrangement with x-coordinates ⩽t. We show that for K=O(n/logn), after a preprocessing step that uses space S=O(n2/(KlogK)) the query can be answered in time O(nlogK). The second query involves the Cartesian sum of vectors a=(a1,…,an) and b=(b1,…,bn). For a given real t, it asks about Rank(t), the number of sums ai+bj which are ⩽t. We show that for some positive constant c and K⩽c(logn)/(log logn), after a preprocessing step that uses space S=O(n2/K2), the query may be answered in time O((n/K)logK). Both results fit neatly between two obvious extremes.

References (6)

There are more references available in the full text version of this article.

Cited by (2)

  • Time and space efficient collinearity indexing

    2023, Computational Geometry: Theory and Applications
  • Monitoring continuous band-join queries over dynamic data

    2005, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
View full text