On hardness of jumbled indexing

Amihood Amir, Timothy M. Chan, Moshe Lewenstein, Noa Lewenstein

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


Jumbled indexing is the problem of indexing a text T for queries that ask whether there is a substring of T matching a pattern represented as a Parikh vector, i.e., the vector of frequency counts for each character. Jumbled indexing has garnered a lot of interest in the last four years; for a partial list see [2,6,13,16,17,20,22,24,26,30,35,36]. There is a naive algorithm that preprocesses all answers in O(n2|∑|) time allowing quick queries afterwards, and there is another naive algorithm that requires no preprocessing but has O(nlog|∑|) query time. Despite a tremendous amount of effort there has been little improvement over these running times. In this paper we provide good reason for this. We show that, under a 3SUM-hardness assumption, jumbled indexing for alphabets of size ω(1) requires Ω(n2-ε) preprocessing time or Ω(n1-δ) query time for any ε,δ > 0. In fact, under a stronger 3SUM-hardness assumption, for any constant alphabet size r ≥ 3 there exist describable fixed constant εr and δr such that jumbled indexing requires Ω(n2-εr) preprocessing time or Ω(n 1-δr) query time.

Original languageEnglish
Title of host publicationAutomata, Languages, and Programming - 41st International Colloquium, ICALP 2014, Proceedings
PublisherSpringer Verlag
Number of pages12
EditionPART 1
ISBN (Print)9783662439470
StatePublished - 2014
Event41st International Colloquium on Automata, Languages, and Programming, ICALP 2014 - Copenhagen, Denmark
Duration: 8 Jul 201411 Jul 2014

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
NumberPART 1
Volume8572 LNCS


Conference41st International Colloquium on Automata, Languages, and Programming, ICALP 2014

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • General Computer Science


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