Proceedings on STACS 85 2nd annual symposium on theoretical aspects of computer science
Communication complexity
Optimal bounds for the predecessor problem
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
The discrepancy method: randomness and complexity
The discrepancy method: randomness and complexity
Improved lower bound on testing membership to a polyhedron by algebraic decision trees
FOCS '95 Proceedings of the 36th Annual Symposium on Foundations of Computer Science
Optimal bounds for the predecessor problem and related problems
Journal of Computer and System Sciences - STOC 1999
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We revisit classical geometric search problems under the assumption of rational coordinates. Our main result is a tight bound for point separation, ie, to determine whether n given points lie on one side of a query line. We show that with polynomial storage the query time is 驴(log b/ log log b), where b is the bit length of the rationals used in specifying the line and the points. The lower bound holds in Yao's cell probe model with storage in nO(1) and word size in bO(1). By duality, this provides a tight lower bound on the complexity on the polygon point enclosure problem: given a polygon in the plane, is a query point in it?