TY - GEN
T1 - Submatrix maximum queries in monge matrices are equivalent to predecessor search
AU - Gawrychowski, Paweł
AU - Mozes, Shay
AU - Weimann, Oren
N1 - Publisher Copyright: © Springer-Verlag Berlin Heidelberg 2015.
PY - 2015
Y1 - 2015
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=84950114846&partnerID=8YFLogxK
U2 - https://doi.org/10.1007/978-3-662-47672-7_47
DO - https://doi.org/10.1007/978-3-662-47672-7_47
M3 - Conference contribution
SN - 9783662476710
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 580
EP - 592
BT - Automata, Languages, and Programming - 42nd International Colloquium, ICALP 2015, Proceedings
A2 - Halldorsson, Magnus M.
A2 - Kobayashi, Naoki
A2 - Speckmann, Bettina
A2 - Iwama, Kazuo
PB - Springer Verlag
T2 - 42nd International Colloquium on Automata, Languages and Programming, ICALP 2015
Y2 - 6 July 2015 through 10 July 2015
ER -