Introduction to algorithms
Approximate closest-point queries in high dimensions
Information Processing Letters
Approximation algorithms for NP-complete problems on planar graphs
Journal of the ACM (JACM)
Approximation schemes for covering and packing problems in image processing and VLSI
Journal of the ACM (JACM)
A tight analysis of the greedy algorithm for set cover
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
Separators for sphere-packings and nearest neighbor graphs
Journal of the ACM (JACM)
Realistic input models for geometric algorithms
SCG '97 Proceedings of the thirteenth annual symposium on Computational geometry
Approximating geometrical graphs via “spanners” and “banyans”
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Point set labeling with sliding labels
Proceedings of the fourteenth annual symposium on Computational geometry
A threshold of ln n for approximating set cover
Journal of the ACM (JACM)
NC-approximation schemes for NP- and PSPACE-hard problems for geometric graphs
Journal of Algorithms
Polynomial time approximation schemes for Euclidean traveling salesman and other geometric problems
Journal of the ACM (JACM)
An optimal algorithm for approximate nearest neighbor searching fixed dimensions
Journal of the ACM (JACM)
Efficient algorithms for geometric optimization
ACM Computing Surveys (CSUR)
Label placement by maximum independent set in rectangles
WADS '97 Selected papers presented at the international workshop on Algorithms and data structure
On approximating rectangle tiling and packing
Proceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms
Dynamic data structures for fat objects and their applications
Computational Geometry: Theory and Applications
Fast stabbing of boxes in high dimensions
Theoretical Computer Science
Improved approximation algorithms for rectangle tiling and packing
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Polynomial-time approximation schemes for geometric graphs
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Geometric Separator Theorems and Applications
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
Packing a trunk: now with a twist!
Proceedings of the 2005 ACM symposium on Solid and physical modeling
Approximation hardness of optimization problems in intersection graphs of d-dimensional boxes
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
A Characterization of the (natural) Graph Properties Testable with One-Sided Error
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Simple approximation algorithms and PTASs for various problems in wireless ad hoc networks
Journal of Parallel and Distributed Computing - Special issue: Algorithms for wireless and ad-hoc networks
Independent set of intersection graphs of convex objects in 2D
Computational Geometry: Theory and Applications
Randomized on-line algorithms and lower bounds for computing large independent sets in disk graphs
Discrete Applied Mathematics
Optimization problems in multiple-interval graphs
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Computational Geometry: Theory and Applications
Approximating geometric coverage problems
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Coloring kk-free intersection graphs of geometric objects in the plane
Proceedings of the twenty-fourth annual symposium on Computational geometry
Approximation schemes for wireless networks
ACM Transactions on Algorithms (TALG)
Cubage-Weight Balance Algorithm for the Scattered Goods Loading with Two Aims
ICCS '07 Proceedings of the 7th international conference on Computational Science, Part I: ICCS 2007
SWAT '08 Proceedings of the 11th Scandinavian workshop on Algorithm Theory
Approximating minimum independent dominating sets in wireless networks
Information Processing Letters
Maximum independent set of rectangles
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Near-linear approximation algorithms for geometric hitting sets
Proceedings of the twenty-fifth annual symposium on Computational geometry
Approximation algorithms for maximum independent set of pseudo-disks
Proceedings of the twenty-fifth annual symposium on Computational geometry
Independent set of intersection graphs of convex objects in 2D
Computational Geometry: Theory and Applications
Shifting Strategy for Geometric Graphs without Geometry
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
Optimization problems in multiple-interval graphs
ACM Transactions on Algorithms (TALG)
Domination in geometric intersection graphs
LATIN'08 Proceedings of the 8th Latin American conference on Theoretical informatics
A note about weak ε-nets for axis-parallel boxes in d-space
Information Processing Letters
Approximation algorithms for intersection graphs
APPROX/RANDOM'10 Proceedings of the 13th international conference on Approximation, and 14 the International conference on Randomization, and combinatorial optimization: algorithms and techniques
Algorithms for dominating set in disk graphs: breaking the log n Barrier
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part I
Minimum vertex cover in rectangle graphs
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part I
Truthful mechanisms for exhibitions
WINE'10 Proceedings of the 6th international conference on Internet and network economics
Minimum vertex cover in rectangle graphs
Computational Geometry: Theory and Applications
Closest pair and the post office problem for stochastic points
WADS'11 Proceedings of the 12th international conference on Algorithms and data structures
Coloring and maximum independent set of rectangles
APPROX'11/RANDOM'11 Proceedings of the 14th international workshop and 15th international conference on Approximation, randomization, and combinatorial optimization: algorithms and techniques
Bidimensionality and geometric graphs
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Better approximation schemes for disk graphs
SWAT'06 Proceedings of the 10th Scandinavian conference on Algorithm Theory
Coloring Kk-free intersection graphs of geometric objects in the plane
European Journal of Combinatorics
Approximation algorithms for unit disk graphs
WG'05 Proceedings of the 31st international conference on Graph-Theoretic Concepts in Computer Science
A robust PTAS for maximum weight independent sets in unit disk graphs
WG'04 Proceedings of the 30th international conference on Graph-Theoretic Concepts in Computer Science
Independence and coloring problems on intersection graphs of disks
Efficient Approximation and Online Algorithms
A randomized algorithm for online unit clustering
WAOA'06 Proceedings of the 4th international conference on Approximation and Online Algorithms
Geometric packing under non-uniform constraints
Proceedings of the twenty-eighth annual symposium on Computational geometry
Proceedings of the twenty-eighth annual symposium on Computational geometry
Shifting strategy for geometric graphs without geometry
Journal of Combinatorial Optimization
A constant-factor approximation for multi-covering with disks
Proceedings of the twenty-ninth annual symposium on Computational geometry
Computational geometry column 56
ACM SIGACT News
Approximating hitting sets of axis-parallel rectangles intersecting a monotone curve
Computational Geometry: Theory and Applications
Closest pair and the post office problem for stochastic points
Computational Geometry: Theory and Applications
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We consider two problems: given a collection of n fat objects in a fixed dimension, (1) (packing) find the maximum subcollection of pairwise disjoint objects, and (2) (piercing) find the minimum point set that intersects every object. Recently, Erlebach, Jansen, and Seidel gave a polynomial-time approximation scheme (PTAS) for the packing problem, based on a shifted hierarchical subdivision method. Using shifted quadtrees, we describe a similar algorithm for packing but with a smaller time bound. Erlebach et al.'s algorithm requires polynomial space. We describe a different algorithm, based on geometric separators, that requires only linear space. This algorithm can also be applied to piercing, yielding the first PTAS for that problem.