Matrix multiplication via arithmetic progressions
Journal of Symbolic Computation - Special issue on computational algebraic complexity
Applications of random sampling in computational geometry, II
Discrete & Computational Geometry - Selected papers from the fourth ACM symposium on computational geometry, Univ. of Illinois, Urbana-Champaign, June 6 8, 1988
Randomized fully dynamic graph algorithms with polylogarithmic time per operation
Journal of the ACM (JACM)
Decremental dynamic connectivity
Journal of Algorithms
Near-optimal fully-dynamic graph connectivity
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Dynamic subgraph connectivity with geometric applications
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Lectures on Discrete Geometry
Semi-Online Maintenance of Geometric Optima and Measures
SIAM Journal on Computing
Logarithmic Lower Bounds in the Cell-Probe Model
SIAM Journal on Computing
Approximation algorithms for maximum independent set of pseudo-disks
Proceedings of the twenty-fifth annual symposium on Computational geometry
Dynamic Connectivity: Connecting to Networks and Geometry
SIAM Journal on Computing
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In this paper we give a fully dynamic data structure to maintain the connectivity of the intersection graph of n axis-parallel rectangles. The amortized update time (insertion and deletion of rectangles) is O (n10/11polylog n) and the query time (deciding whether two given rectangles are connected) is O(1). It slightly improves the update time (O (n0.94)) of the previous method while drastically reducing the query time (near O(n1/3)). Our method does not use fast matrix multiplication results and supports a wider range of queries.