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Submatrix Maximum Queries in Monge Matrices are Equivalent to Predecessor Search | | Pawel Gawrychowski
; Shay Mozes
; Oren Weimann
; | | Date: |
26 Feb 2015 | | Abstract: | We present an optimal data structure for submatrix maximum queries in n x n
Monge matrices. Our result is a two-way reduction showing that the problem is
equivalent to the classical predecessor problem. This gives a data structure of
O(n) space that answers submatrix maximum queries in O(loglogn) time. It also
gives a matching lower bound, showing that O(loglogn) query-time is optimal for
any data structure of size O(n polylog(n)).
Our result concludes a line of improvements that started in SODA’12 with
O(log^2 n) query-time and continued in ICALP’14 with O(log n) query-time.
Finally, 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. | | Source: | arXiv, 1502.7663 | | Services: | Forum | Review | PDF | Favorites | |
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