Computing the largest empty rectangle
SIAM Journal on Computing
Progressive approximate aggregate queries with a multi-resolution tree structure
SIGMOD '01 Proceedings of the 2001 ACM SIGMOD international conference on Management of data
CRB-Tree: An Efficient Indexing Scheme for Range-Aggregate Queries
ICDT '03 Proceedings of the 9th International Conference on Database Theory
Efficient OLAP Operations in Spatial Data Warehouses
SSTD '01 Proceedings of the 7th International Symposium on Advances in Spatial and Temporal Databases
Online maintenance of very large random samples
SIGMOD '04 Proceedings of the 2004 ACM SIGMOD international conference on Management of data
Progressive computation of the min-dist optimal-location query
VLDB '06 Proceedings of the 32nd international conference on Very large data bases
Covering Many or Few Points with Unit Disks
Theory of Computing Systems
Dynamic external hashing: the limit of buffering
Proceedings of the twenty-first annual symposium on Parallelism in algorithms and architectures
Efficient method for maximizing bichromatic reverse nearest neighbor
Proceedings of the VLDB Endowment
New results on two-dimensional orthogonal range aggregation in external memory
Proceedings of the thirtieth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Optimal location queries in road network databases
ICDE '11 Proceedings of the 2011 IEEE 27th International Conference on Data Engineering
ICDE '11 Proceedings of the 2011 IEEE 27th International Conference on Data Engineering
SSTD'05 Proceedings of the 9th international conference on Advances in Spatial and Temporal Databases
A scalable algorithm for maximizing range sum in spatial databases
Proceedings of the VLDB Endowment
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In the maximizing range sum (MaxRS) problem, given (i) a set P of 2D points each of which is associated with a positive weight, and (ii) a rectangle r of specific extents, we need to decide where to place r in order to maximize the covered weight of r - that is, the total weight of the data points covered by r. Algorithms solving the problem exactly entail expensive CPU or I/O cost. In practice, exact answers are often not compulsory in a MaxRS application, where slight imprecision can often be comfortably tolerated, provided that approximate answers can be computed considerably faster. Motivated by this, the present paper studies the (1 - ε)-approximate MaxRS problem, which admits the same inputs as MaxRS, but aims instead to return a rectangle whose covered weight is at least (1-ε)m*, where m* is the optimal covered weight, and ε can be an arbitrarily small constant between 0 and 1. We present fast algorithms that settle this problem with strong theoretical guarantees.