Approximation schemes for covering and packing problems in image processing and VLSI
Journal of the ACM (JACM)
Davenport-Schinzel sequences and their geometric applications
Davenport-Schinzel sequences and their geometric applications
A threshold of ln n for approximating set cover
Journal of the ACM (JACM)
Handbook of discrete and computational geometry
SCG '85 Proceedings of the first annual symposium on Computational geometry
Approximation algorithms
Introduction to Algorithms
On approximating the depth and related problems
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Improved Approximation Algorithms for Geometric Set Cover
Discrete & Computational Geometry
Stabbing Convex Polygons with a Segment or a Polygon
ESA '08 Proceedings of the 16th annual European symposium on Algorithms
Stabbing Convex Polygons with a Segment or a Polygon
ESA '08 Proceedings of the 16th annual European symposium on Algorithms
Efficient Sensor Placement for Surveillance Problems
DCOSS '09 Proceedings of the 5th IEEE International Conference on Distributed Computing in Sensor Systems
The resilience of WDM networks to probabilistic geographical failures
IEEE/ACM Transactions on Networking (TON)
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Let $\mathcal{O} = \{O_1, \ldots, O_m\}$ be a set of mconvex polygons in 茂戮驴2with a total of nvertices, and let Bbe another convex k-gon. A placementof B, any congruent copy of B(without reflection), is called freeif Bdoes not intersect the interior of any polygon in $\mathcal{O}$ at this placement. A placement zof Bis called criticalif Bforms three "distinct" contacts with $\mathcal{O}$ at z. Let $\varphi(B, \mathcal{O})$ be the number of free critical placements. A set of placements of Bis called a stabbing setof $\mathcal{O}$ if each polygon in $\mathcal{O}$ intersects at least one placement of Bin this set.We develop efficient Monte Carlo algorithms that compute a stabbing set of size h= O(h*logm), with high probability, where h*is the size of the optimal stabbing set of $\mathcal{O}$. We also improve bounds on $\varphi(B, \mathcal{O})$ for the following three cases, namely, (i) Bis a line segment and the obstacles in $\mathcal{O}$ are pairwise-disjoint, (ii) Bis a line segment and the obstacles in $\mathcal{O}$ may intersect (iii) Bis a convex k-gon and the obstacles in $\mathcal{O}$ are disjoint, and use these improved bounds to analyze the running time of our stabbing-set algorithm.