On the union of Jordan regions and collision-free translational motion amidst polygonal obstacles
Discrete & Computational Geometry
Partition trees for triangle counting and other range searching problems
SCG '88 Proceedings of the fourth annual symposium on Computational geometry
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
On arrangements of Jordan arcs with three intersections per pair
Discrete & Computational Geometry - Selected papers from the fourth ACM symposium on computational geometry, Univ. of Illinois, Urbana-Champaign, June 6 8, 1988
How to net a lot with little: small &egr;-nets for disks and halfspaces
SCG '90 Proceedings of the sixth annual symposium on Computational geometry
Reporting points in halfspaces
Computational Geometry: Theory and Applications
On the union of fat wedges and separating a collection of segments by a line
Computational Geometry: Theory and Applications
Four results on randomized incremental constructions
Computational Geometry: Theory and Applications
Fat Triangles Determine Linearly Many Holes
SIAM Journal on Computing
Las Vegas algorithms for linear and integer programming when the dimension is small
Journal of the ACM (JACM)
Approximation schemes for covering and packing problems in image processing and VLSI
Journal of the ACM (JACM)
Separation and approximation of polyhedral objects
Computational Geometry: Theory and Applications
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)
The complexity of the union of (&agr;, &bgr;)-covered objects
SCG '99 Proceedings of the fifteenth annual symposium on Computational geometry
On the hardness of approximating minimization problems
Journal of the ACM (JACM)
Algorithms for Polytope Covering and Approximation
WADS '93 Proceedings of the Third Workshop on Algorithms and Data Structures
Covering Rectilinear Polygons with Axis-Parallel Rectangles
SIAM Journal on Computing
Selecting forwarding neighbors in wireless ad hoc networks
Mobile Networks and Applications - Discrete algorithms and methods for mobile computing and communications
A constant-factor approximation algorithm for optimal terrain guarding
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Guarding a terrain by two watchtowers
SCG '05 Proceedings of the twenty-first annual symposium on Computational geometry
Approximately dominating representatives
Theoretical Computer Science
Proceedings of the nineteenth annual ACM symposium on Parallel algorithms and architectures
Computational Geometry: Theory and Applications
On guarding the vertices of rectilinear domains
Computational Geometry: Theory and Applications
Relaxation in text search using taxonomies
Proceedings of the VLDB Endowment
An Approximation Scheme for Terrain Guarding
APPROX '09 / RANDOM '09 Proceedings of the 12th International Workshop and 13th International Workshop on Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques
Covering points by unit disks of fixed location
ISAAC'07 Proceedings of the 18th international conference on Algorithms and computation
Pattern mutation in wireless sensor deployment
INFOCOM'10 Proceedings of the 29th conference on Information communications
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Exact and approximation algorithms for geometric and capacitated set cover problems
COCOON'10 Proceedings of the 16th annual international conference on Computing and combinatorics
Pervasive and Mobile Computing
Optimal deployment patterns for full coverage and k- connectivity (k ≤ 6) wireless sensor networks
IEEE/ACM Transactions on Networking (TON)
Bandwidth provisioning in infrastructure-based wireless networks employing directional antennas
ICDCN'10 Proceedings of the 11th international conference on Distributed computing and networking
On isolating points using disks
ESA'11 Proceedings of the 19th European conference on Algorithms
On guarding rectilinear domains
SWAT'06 Proceedings of the 10th Scandinavian conference on Algorithm Theory
Towards faster linear-sized nets for axis-aligned boxes in the plane
JCDCG'04 Proceedings of the 2004 Japanese conference on Discrete and Computational Geometry
Approximate guarding of monotone and rectilinear polygons
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
CAAN'06 Proceedings of the Third international conference on Combinatorial and Algorithmic Aspects of Networking
A 4-approximation algorithm for guarding 1.5-dimensional terrains
LATIN'06 Proceedings of the 7th Latin American conference on Theoretical Informatics
Pattern mutation in wireless sensor deployment
IEEE/ACM Transactions on Networking (TON)
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Given a collection S of subsets of some set U, and M ⊂ U, the set cover problem is to find the smallest subcollection C ⊂ S such that M is a subset of the union of the sets in C. While the general problem is NP-hard to solve, even approximately, here we consider some geometric special cases, where usually U = Rd. Combining previously known techniques [3, 4], we show that polynomial time approximation algorithms with provable performance exist, under a certain general condition: that for a random subset R ⊂ S and function f(), there is a decomposition of the complement U ∖ ∪Y ∈ R Y into an expected f(|R|) regions, each region of a particular simple form. Under this condition, a cover of size O(f(|C|)) can be found in polynomial time. Using this result, and combinatorial geometry results implying bounding functions f(c) that are nearly linear, we obtain o(log c) approximation algorithms for covering by fat triangles, by pseudodisks, by a family of fat objects, and others. Similarly, constant-factor approximations follow for similar-sized fat triangles and fat objects, and for fat wedges. With more work, we obtain constant-factor approximation algorithms for covering by unit cubes in R3, and for guarding an x-monotone polygonal chain.