TY - JOUR
T1 - Two dimensional range minimum queries and Fibonacci lattices
AU - Stølting Brodal, Gerth
AU - Davoodi, Pooya
AU - Lewenstein, Moshe
AU - Raman, Rajeev
AU - Satti, Srinivasa Rao
N1 - Publisher Copyright:
© 2016.
PY - 2016/7/25
Y1 - 2016/7/25
N2 - Given a matrix of size N, two dimensional range minimum queries (2D-RMQs) ask for the position of the minimum element in a rectangular range within the matrix. We study trade-offs between the query time and the additional space used by indexing data structures that support 2D-RMQs. Using a novel technique-the discrepancy properties of Fibonacci lattices-we give an indexing data structure for 2D-RMQs that uses O(N/c) bits additional space with O(clog c(log log c)2) query time, for any parameter c, 4≤c≤N. Also, when the entries of the input matrix are from {0, 1}, we show that the query time can be improved to O(clog c) with the same space usage.
AB - Given a matrix of size N, two dimensional range minimum queries (2D-RMQs) ask for the position of the minimum element in a rectangular range within the matrix. We study trade-offs between the query time and the additional space used by indexing data structures that support 2D-RMQs. Using a novel technique-the discrepancy properties of Fibonacci lattices-we give an indexing data structure for 2D-RMQs that uses O(N/c) bits additional space with O(clog c(log log c)2) query time, for any parameter c, 4≤c≤N. Also, when the entries of the input matrix are from {0, 1}, we show that the query time can be improved to O(clog c) with the same space usage.
KW - Fibonacci lattices
KW - Pattern matching
KW - Range minimum queries
UR - http://www.scopus.com/inward/record.url?scp=84979465407&partnerID=8YFLogxK
U2 - 10.1016/j.tcs.2016.02.016
DO - 10.1016/j.tcs.2016.02.016
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AN - SCOPUS:84979465407
SN - 0304-3975
VL - 638
SP - 33
EP - 43
JO - Theoretical Computer Science
JF - Theoretical Computer Science
ER -