Submatrix maximum queries in monge matrices are equivalent to predecessor search

Paweł Gawrychowski, Shay Mozes, Oren Weimann

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

Abstract

We present an optimal data structure for submatrix maximum queries in n×n Monge matrices. Our result is a two-way reduction showing that the problem is equivalent to the classical predecessor problem in a universe of polynomial size. This gives a data structure of O(n) space that answers submatrix maximum queries in O(log log n) time, as well as a matching lower bound, showing that O(log log n) query-time is optimal for any data structure of size O(n polylog(n)). Our result settles the problem, improving on the O(log2 n) query-time in SODA’12, and on the O(log n) query-time in ICALP’14. In addition, we show that partial Monge matrices can be handled in the same bounds as full Monge matrices. In both previous results, partial Monge matrices incurred additional inverse-Ackerman factors.

Original languageEnglish
Title of host publicationAutomata, Languages, and Programming - 42nd International Colloquium, ICALP 2015, Proceedings
EditorsMagnus M. Halldorsson, Naoki Kobayashi, Bettina Speckmann, Kazuo Iwama
PublisherSpringer Verlag
Pages580-592
Number of pages13
ISBN (Print)9783662476710
DOIs
StatePublished - 2015
Event42nd International Colloquium on Automata, Languages and Programming, ICALP 2015 - Kyoto, Japan
Duration: 6 Jul 201510 Jul 2015

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume9134
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference42nd International Colloquium on Automata, Languages and Programming, ICALP 2015
Country/TerritoryJapan
CityKyoto
Period6/07/1510/07/15

Bibliographical note

Funding Information:
Shay Mozes, Oren Weimann—SM and OW partially supported by Israel Science Foundation grant 794/13. SM partially supported by the Israeli ministry of absorption.

Publisher Copyright:
© Springer-Verlag Berlin Heidelberg 2015.

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science (all)

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