Improved submatrix maximum queries in Monge matrices

Paweł Gawrychowski, Shay Mozes, Oren Weimann

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


We present efficient data structures for submatrix maximum queries in Monge matrices and Monge partial matrices. For n x n Monge matrices, we give a data structure that requires O(n) space and answers submatrix maximum queries in O(logn) time. The best previous data structure [Kaplan et al., SODA'12] required O(n logn) space and O(log2 n) query time. We also give an alternative data structure with constant query-time and O(n1+ε) construction time and space for any fixed ε < 1. For n x n partial Monge matrices we obtain a data structure with O(n) space and O(logn·α (n)) query time. The data structure of Kaplan et al. required O(n logn·α(n)) space and O(log2 n) query time. Our improvements are enabled by a technique for exploiting the structure of the upper envelope of Monge matrices to efficiently report column maxima in skewed rectangular Monge matrices. We hope this technique will be useful in obtaining faster search algorithms in Monge partial matrices. In addition, we give a linear upper bound on the number of breakpoints in the upper envelope of a Monge partial matrix. This shows that the inverse Ackermann α(n) factor in the analysis of the data structure of Kaplan et. al is superfluous.

Original languageEnglish
Title of host publicationAutomata, Languages, and Programming - 41st International Colloquium, ICALP 2014, Proceedings
PublisherSpringer Verlag
Number of pages13
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
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


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

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science


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