Data structures and network algorithms
Data structures and network algorithms
An optimal algorithm for finding a maximum independent set of a circular-arc graph
SIAM Journal on Computing
Stability in circular arc graphs
Journal of Algorithms
Parallel algorithms on circular-arc graphs
Information Processing Letters
Minimum cuts for circular-arc graphs
SIAM Journal on Computing
Linear time algorithms on circular-arc graphs
Information Processing Letters
Cutting hyperplanes for divide-and-conquer
Discrete & Computational Geometry
Fast Stabbing of Boxes in High Dimensions
Proceedings of the 8th Canadian Conference on Computational Geometry
Proceedings of the 8th Canadian Conference on Computational Geometry
Generalized shooter location problem
COCOON'99 Proceedings of the 5th annual international conference on Computing and combinatorics
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We show how to efficiently maintain a minimum piercing set for a set S of intervals on the line, under insertions and deletions to/from S. A linear-size dynamic data structure is presented, which enables us to compute a new minimum piercing set following an insertion or deletion in time O(c(S) log |S|), where c(S) is the size of the new minimum piercing set. We also show how to maintain a piercing set for S of size at most (1 + Ɛ)c(S), for 0 O(log |S|/Ɛ) amortized time per update. We then apply these results to obtain efficient (sometimes improved) solutions to the following three problems: (i) the shooter location problem, (ii) computing a minimum piercing set for arcs on a circle, and (iii) dynamically maintaining a box cover for a d-dimensional point set.