Approximation schemes for covering and packing problems in image processing and VLSI

Authors:
Dorit S. Hochbaum;Wolfgang Maass
Affiliations:
School of Business Administration, 350 Barrows Hall, University of California at Berkeley, Berkeley, CA;Department of Mathematics, University of Illinois, Chicago, IL
Venue:
Journal of the ACM (JACM)
Year:
1985

Citing 1
Cited 188

Computers and Intractability: A Guide to the Theory of NP-Completeness

Computers and Intractability: A Guide to the Theory of NP-Completeness

On the complexity of some geometric problems in unbounded dimension

Journal of Symbolic Computation
Almost optimal set covers in finite VC-dimension: (preliminary version)

SCG '94 Proceedings of the tenth annual symposium on Computational geometry
Covering points in the plane by k-tours: towards a polynomial time approximation scheme for general k

STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Incremental clustering and dynamic information retrieval

STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Point set labeling with sliding labels

Proceedings of the fourteenth annual symposium on Computational geometry
Efficient algorithms for geometric optimization

ACM Computing Surveys (CSUR)
Map labeling and its generalizations

SODA '97 Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms
On approximating rectangle tiling and packing

Proceedings of the ninth 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
Discrete mobile centers

SCG '01 Proceedings of the seventeenth annual symposium on Computational geometry
Algorithms for congruent sphere packing and applications

SCG '01 Proceedings of the seventeenth annual symposium on Computational geometry
Selecting forwarding neighbors in wireless Ad Hoc networks

DIALM '01 Proceedings of the 5th international workshop on Discrete algorithms and methods for mobile computing and communications
A polynomial-time approximation scheme for base station positioning in UMTS networks

DIALM '01 Proceedings of the 5th international workshop on Discrete algorithms and methods for mobile computing and communications
On point covers of c-oriented polygons

Theoretical Computer Science
Parallel approximation schemes for a class of planar and near planar combinatorial optimization problems

Information and Computation
Slice and dice: a simple, improved approximate tiling recipe

SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Efficient integration of multi-hop wireless and wired networks with QoS constraints

Proceedings of the 8th annual international conference on Mobile computing and networking
Approximation algorithms for the mobile piercing set problem with applications to clustering in ad-hoc networks

DIALM '02 Proceedings of the 6th international workshop on Discrete algorithms and methods for mobile computing and communications
Simple heuristics and PTASs for intersection graphs in wireless ad hoc networks

DIALM '02 Proceedings of the 6th international workshop on Discrete algorithms and methods for mobile computing and communications
Approximations for Steiner Trees with Minimum Number of Steiner Points

Journal of Global Optimization
Approximating uniform triangular meshes in polygons

Theoretical Computer Science
Exact Algorithms and Approximation Schemes for Base Station Placement Problems

SWAT '02 Proceedings of the 8th Scandinavian Workshop on Algorithm Theory
Approximation Algorithms for Partial Covering Problems

ICALP '01 Proceedings of the 28th International Colloquium on Automata, Languages and Programming,
Towards a Predictive Computational Complexity Theory

ICALP '02 Proceedings of the 29th International Colloquium on Automata, Languages and Programming
Station Layouts in the Presence of Location Constraints

ISAAC '99 Proceedings of the 10th International Symposium on Algorithms and Computation
Robustness of regional matching scheme over global matching scheme

Artificial Intelligence
Approximation algorithms for aligning points

Proceedings of the nineteenth annual symposium on Computational geometry
Smooth kinetic maintenance of clusters

Proceedings of the nineteenth annual symposium on Computational geometry
Polynomial-time approximation schemes for packing and piercing fat objects

Journal of Algorithms
Approximation Algorithms for the Class Cover Problem

Annals of Mathematics and Artificial Intelligence
A Geometric Theorem for Network Design

IEEE Transactions on Computers
Selecting forwarding neighbors in wireless ad hoc networks

Mobile Networks and Applications - Discrete algorithms and methods for mobile computing and communications
Approximation algorithms for the mobile piercing set problem with applications to clustering in ad-hoc networks

Mobile Networks and Applications - Discrete algorithms and methods for mobile computing and communications
On rectangle packing: maximizing benefits

SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Approximation algorithms for partial covering problems

Journal of Algorithms
Efficient integration of multihop wireless and wired networks with QoS constraints

IEEE/ACM Transactions on Networking (TON)
Antipole Tree Indexing to Support Range Search and K-Nearest Neighbor Search in Metric Spaces

IEEE Transactions on Knowledge and Data Engineering
Packing a trunk: now with a twist!

Proceedings of the 2005 ACM symposium on Solid and physical modeling
Low-coordination topologies for redundancy in sensor networks

Proceedings of the 6th ACM international symposium on Mobile ad hoc networking and computing
An effective hybrid algorithm for the problem of packing circles into a larger containing circle

Computers and Operations Research
Improved approximation algorithms for geometric set cover

SCG '05 Proceedings of the twenty-first annual symposium on Computational geometry
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
Polynomial time approximation schemes for base station coverage with minimum total radii

Computer Networks and ISDN Systems
Smooth kinetic maintenance of clusters

Computational Geometry: Theory and Applications - Special issue on the 19th annual symposium on computational geometry - SoCG 2003
The complexity of base station positioning in cellular networks

Discrete Applied Mathematics
Local approximation schemes for ad hoc and sensor networks

DIALM-POMC '05 Proceedings of the 2005 joint workshop on Foundations of mobile computing
Near-optimal sensor placements in Gaussian processes

ICML '05 Proceedings of the 22nd international conference on Machine learning
Mobile backbone networks --: construction and maintenance

Proceedings of the 7th ACM international symposium on Mobile ad hoc networking and computing
Minimum-cost coverage of point sets by disks

Proceedings of the twenty-second annual symposium on Computational geometry
New heuristics for packing unequal circles into a circular container

Computers and Operations Research
A new heuristic recursive algorithm for the strip rectangular packing problem

Computers and Operations Research
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
On the complexity of scheduling in wireless networks

Proceedings of the 12th annual international conference on Mobile computing and networking
Relay Node Placement in Wireless Sensor Networks

IEEE Transactions on Computers
MiFi: a framework for fairness and QoS assurance for current IEEE 802.11 networks with multiple access points

IEEE/ACM Transactions on Networking (TON)
The inverse protein folding problem on 2D and 3D lattices

Discrete Applied Mathematics
Improved approximation algorithms for connected sensor cover

Wireless Networks
Packing to angles and sectors

Proceedings of the nineteenth annual ACM symposium on Parallel algorithms and architectures
A two-level search algorithm for 2D rectangular packing problem

Computers and Industrial Engineering
A recursive branch-and-bound algorithm for the rectangular guillotine strip packing problem

Computers and Operations Research
PERM for solving circle packing problem

Computers and Operations Research
Polynomial-time approximation schemes for piercing and covering with applications in wireless networks

Computational Geometry: Theory and Applications
Approximating geometric coverage problems

Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Minimum-Energy Broadcast and disk cover in grid wireless networks

Theoretical Computer Science
Self-monitoring for sensor networks

Proceedings of the 9th ACM international symposium on Mobile ad hoc networking and computing
Optimizing active ranges for consistent dynamic map labeling

Proceedings of the twenty-fourth annual symposium on Computational geometry
Coloring kk-free intersection graphs of geometric objects in the plane

Proceedings of the twenty-fourth annual symposium on Computational geometry
Providing location privacy in assisted living environments

Proceedings of the 1st international conference on PErvasive Technologies Related to Assistive Environments
Near-Optimal Sensor Placements in Gaussian Processes: Theory, Efficient Algorithms and Empirical Studies

The Journal of Machine Learning Research
On the complexity of bandwidth allocation in radio networks

Theoretical Computer Science
An Almost Linear Time 2.8334-Approximation Algorithm for the Disc Covering Problem

AAIM '07 Proceedings of the 3rd international conference on Algorithmic Aspects in Information and Management
Spectrum Bidding in Wireless Networks and Related

COCOON '08 Proceedings of the 14th annual international conference on Computing and Combinatorics
On Covering Problems of Rado

SWAT '08 Proceedings of the 11th Scandinavian workshop on Algorithm Theory
Stabbing Convex Polygons with a Segment or a Polygon

ESA '08 Proceedings of the 16th annual European symposium on Algorithms
Covering a line segment with variable radius discs

Computers and Operations Research
PTAS for Minimum Connected Dominating Set in Unit Ball Graph

WASA '08 Proceedings of the Third International Conference on Wireless Algorithms, Systems, and Applications
A Better Theoretical Bound to Approximate Connected Dominating Set in Unit Disk Graph

WASA '08 Proceedings of the Third International Conference on Wireless Algorithms, Systems, and Applications
Maximum independent set of rectangles

SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Multiflows in multihop wireless networks

Proceedings of the tenth ACM international symposium on Mobile ad hoc networking and computing
Near-linear approximation algorithms for geometric hitting sets

Proceedings of the twenty-fifth annual symposium on Computational geometry
On grids in topological graphs

Proceedings of the twenty-fifth annual symposium on Computational geometry
Cheap or Flexible Sensor Coverage

DCOSS '09 Proceedings of the 5th IEEE International Conference on Distributed Computing in Sensor Systems
Construction and Maintenance of Wireless Mobile Backbone Networks

IEEE/ACM Transactions on Networking (TON)
Latency Constrained Aggregation in Chain Networks Admits a PTAS

AAIM '09 Proceedings of the 5th International Conference on Algorithmic Aspects in Information and Management
A PTAS for Node-Weighted Steiner Tree in Unit Disk Graphs

COCOA '09 Proceedings of the 3rd International Conference on Combinatorial Optimization and Applications
Variable-Size Rectangle Covering

COCOA '09 Proceedings of the 3rd International Conference on Combinatorial Optimization and Applications
Approximating the Spanning k-Tree Forest Problem

FAW '09 Proceedings of the 3d International Workshop on Frontiers in Algorithmics
An optimal local approximation algorithm for max-min linear programs

Proceedings of the twenty-first annual symposium on Parallelism in algorithms and architectures
Maximizing the number of obnoxious facilities to locate within a bounded region

Computers and Operations Research
Simultaneous placement and scheduling of sensors

IPSN '09 Proceedings of the 2009 International Conference on Information Processing in Sensor Networks
A Scheme for Computing Minimum Covers within Simple Regions

WADS '09 Proceedings of the 11th International Symposium on Algorithms and Data Structures
Optimizing active ranges for consistent dynamic map labeling

Computational Geometry: Theory and Applications
A PTAS for minimum connected dominating set in 3-dimensional Wireless sensor networks

Journal of Global Optimization
Smooth kinetic maintenance of clusters

Computational Geometry: Theory and Applications - Special issue on the 19th annual symposium on computational geometry - SoCG 2003
Relay node placement in large scale wireless sensor networks

Computer Communications
Polynomial time approximation schemes for base station coverage with minimum total radii

Computer Networks: The International Journal of Computer and Telecommunications Networking
Optimization for first order Delaunay triangulations

Computational Geometry: Theory and Applications
Subspace Discovery for Promotion: A Cell Clustering Approach

DS '09 Proceedings of the 12th International Conference on Discovery Science
Practical Discrete Unit Disk Cover Using an Exact Line-Separable Algorithm

ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
Shifting Strategy for Geometric Graphs without Geometry

ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
Minimum Covering with Travel Cost

ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
The complexity of base station positioning in cellular networks

Discrete Applied Mathematics
An on-line algorithm for the rectangle packing problem with rejection

WEA'03 Proceedings of the 2nd international conference on Experimental and efficient algorithms
Coordinating concurrent transmissions: a constant-factor approximation of maximum-weight independent set in local conflict graphs

ADHOC-NOW'07 Proceedings of the 6th international conference on Ad-hoc, mobile and wireless networks
Maximizing the number of independent labels in the plane

FAW'07 Proceedings of the 1st annual international conference on Frontiers in algorithmics
Sensor-mission assignment in wireless sensor networks

ACM Transactions on Sensor Networks (TOSN)
Covering points by unit disks of fixed location

ISAAC'07 Proceedings of the 18th international conference on Algorithms and computation
Local approximation algorithms for scheduling problems in sensor networks

ALGOSENSORS'07 Proceedings of the 3rd international conference on Algorithmic aspects of wireless sensor networks
Assigning sensors to missions with demands

ALGOSENSORS'07 Proceedings of the 3rd international conference on Algorithmic aspects of wireless sensor networks
Maximal breach in wireless sensor networks: geometric characterization and algorithms

ALGOSENSORS'07 Proceedings of the 3rd international conference on Algorithmic aspects of wireless sensor networks
Online distributed sensor selection

Proceedings of the 9th ACM/IEEE International Conference on Information Processing in Sensor Networks
Domination in geometric intersection graphs

LATIN'08 Proceedings of the 8th Latin American conference on Theoretical informatics
Constant factor approximation algorithms for the densest k-subgraph problem on proper interval graphs and bipartite permutation graphs

Information Processing Letters
Pattern mutation in wireless sensor deployment

INFOCOM'10 Proceedings of the 29th conference on Information communications
Constructing low-connectivity and full-coverage three dimensional sensor networks

IEEE Journal on Selected Areas in Communications - Special issue on simple wireless sensor networking solutions
On improved relay nodes placement in two-tiered wireless sensor networks

MILCOM'09 Proceedings of the 28th IEEE conference on Military communications
Solving the constrained coverage problem

Applied Soft Computing
Optimal scheduling for dynamic channel allocation in wireless LANs

Wireless Networks
Polynomial time approximation schemes for minimum disk cover problems

Journal of Combinatorial Optimization
PTAS for weighted set cover on unit squares

APPROX/RANDOM'10 Proceedings of the 13th international conference on Approximation, and 14 the International conference on Randomization, and combinatorial optimization: algorithms and techniques
Exact and approximation algorithms for geometric and capacitated set cover problems

COCOON'10 Proceedings of the 16th annual international conference on Computing and combinatorics
Minimum vertex cover in rectangle graphs

ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part I
Optimal cover of points by disks in a simple polygon

ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part I
A SAT-based Method for Solving the Two-dimensional Strip Packing Problem

Fundamenta Informaticae - RCRA 2008 Experimental Evaluation of Algorithms for Solving Problems with Combinatorial Explosion
Distributed antipole clustering for efficient data search and management in Euclidean and metric spaces

IPDPS'06 Proceedings of the 20th international conference on Parallel and distributed processing
New approximations for minimum-weighted dominating sets and minimum-weighted connected dominating sets on unit disk graphs

Theoretical Computer Science
Theory and application of width bounded geometric separators

Journal of Computer and System Sciences
Lifetime maximization of monitoring sensor networks

ALGOSENSORS'10 Proceedings of the 6th international conference on Algorithms for sensor systems, wireless adhoc networks, and autonomous mobile entities
The train delivery problem: vehicle routing meets bin packing

WAOA'10 Proceedings of the 8th international conference on Approximation and online algorithms
A Parallel Branch-and-Bound Approach to the Rectangular Guillotine Strip Cutting Problem

INFORMS Journal on Computing
On the complexity of scheduling in wireless networks

EURASIP Journal on Wireless Communications and Networking - Special issue on adaptive cross-layer strategies for fourth generation wireless communications
Optimal deployment patterns for full coverage and k- connectivity (k ≤ 6) wireless sensor networks

IEEE/ACM Transactions on Networking (TON)
On the discrete unit disk cover problem

WALCOM'11 Proceedings of the 5th international conference on WALCOM: algorithms and computation
Minimum vertex cover in rectangle graphs

Computational Geometry: Theory and Applications
Maximising lifetime for fault-tolerant target coverage in sensor networks

Proceedings of the twenty-third annual ACM symposium on Parallelism in algorithms and architectures
Clique clustering yields a PTAS for max-coloring interval graphs

ICALP'11 Proceedings of the 38th international colloquim conference on Automata, languages and programming - Volume Part I
Minimum-cost linear coverage by sensors with adjustable ranges

WASA'11 Proceedings of the 6th international conference on Wireless algorithms, systems, and applications
Two sides approximation algorithms for channel assignments in wireless network

WASA'11 Proceedings of the 6th international conference on Wireless algorithms, systems, and applications
Wireless coverage via dynamic programming

WASA'11 Proceedings of the 6th international conference on Wireless algorithms, systems, and applications
Consistent labeling of rotating maps

WADS'11 Proceedings of the 12th international conference on Algorithms and data structures
Hitting sets online and vertex ranking

ESA'11 Proceedings of the 19th European conference on Algorithms
PTAS for minimum weighted connected vertex cover problem with c-local condition in unit disk graphs

Journal of Combinatorial Optimization
A maximum profit coverage algorithm with application to small molecules cluster identification

WEA'06 Proceedings of the 5th international conference on Experimental Algorithms
Bidimensionality and geometric graphs

Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Minimum energy broadcast and disk cover in grid wireless networks

SIROCCO'06 Proceedings of the 13th international conference on Structural Information and Communication Complexity
Better approximation schemes for disk graphs

SWAT'06 Proceedings of the 10th Scandinavian conference on Algorithm Theory
Efficient approximation schemes for geometric problems?

ESA'05 Proceedings of the 13th annual European conference on Algorithms
A PTAS for the minimum dominating set problem in unit disk graphs

WAOA'05 Proceedings of the Third international conference on Approximation and Online Algorithms
Wireless coverage with disparate ranges

MobiHoc '11 Proceedings of the Twelfth ACM International Symposium on Mobile Ad Hoc Networking and Computing
Approximation algorithms for free-label maximization

Computational Geometry: Theory and Applications
Fault-tolerant relay node placement in wireless sensor networks

COCOON'05 Proceedings of the 11th annual international conference on Computing and Combinatorics
A polynomial-time approximation algorithm for a geometric dispersion problem

COCOON'06 Proceedings of the 12th annual international conference on Computing and Combinatorics
Computing the independence number of intersection graphs

Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
The set cover with pairs problem

FSTTCS '05 Proceedings of the 25th international conference on Foundations of Software Technology and Theoretical Computer Science
A meta-heuristic algorithm for the strip rectangular packing problem

ICNC'05 Proceedings of the First international conference on Advances in Natural Computation - Volume Part III
On the minimization of the number of forwarding nodes for multicast in wireless ad hoc networks

ICCNMC'05 Proceedings of the Third international conference on Networking and Mobile Computing
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 hybrid heuristic algorithm for the rectangular packing problem

ICCS'05 Proceedings of the 5th international conference on Computational Science - Volume Part I
Capacitated max -batching with interval graph compatibilities

SWAT'10 Proceedings of the 12th Scandinavian conference on Algorithm Theory
Approximation algorithms for free-label maximization

SWAT'10 Proceedings of the 12th Scandinavian conference on Algorithm Theory
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
A (4+ε)-approximation for the minimum-weight dominating set problem in unit disk graphs

WAOA'09 Proceedings of the 7th international conference on Approximation and Online Algorithms
Constant-factor approximation for minimum-weight (connected) dominating sets in unit disk graphs

APPROX'06/RANDOM'06 Proceedings of the 9th international conference on Approximation Algorithms for Combinatorial Optimization Problems, and 10th international conference on Randomization and Computation
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
Radar placement along banks of river

Journal of Global Optimization
A probability collectives approach with a feasibility-based rule for constrained optimization

Applied Computational Intelligence and Soft Computing
In-situ soil moisture sensing: Optimal sensor placement and field estimation

ACM Transactions on Sensor Networks (TOSN)
Disjoint edges in complete topological graphs

Proceedings of the twenty-eighth annual symposium on Computational geometry
Polynomial time solution to minimum forwarding set problem in wireless networks under disk coverage model

Ad Hoc Networks
Shifting strategy for geometric graphs without geometry

Journal of Combinatorial Optimization
Minimum covering with travel cost

Journal of Combinatorial Optimization
Optimal Cover of Points by Disks in a Simple Polygon

SIAM Journal on Computing
Providing and finding k-road-coverage efficiently in wireless sensor networks

Wireless Communications & Mobile Computing
A polynomial-time approximation scheme for the geometric unique coverage problem on unit squares

SWAT'12 Proceedings of the 13th Scandinavian conference on Algorithm Theory
Sparse WiFi deployment for vehicular internet access with bounded interconnection gap

IEEE/ACM Transactions on Networking (TON)
On the impact of symmetry-breaking constraints on spatial Branch-and-Bound for circle packing in a square

Discrete Applied Mathematics
An improved algorithm for online unit clustering

COCOON'07 Proceedings of the 13th annual international conference on Computing and Combinatorics
Optimization for first order delaunay triangulations

WADS'07 Proceedings of the 10th international conference on Algorithms and Data Structures
Solving a 2-covered path problem with variable radii for wireless sensor networks

ICA3PP'12 Proceedings of the 12th international conference on Algorithms and Architectures for Parallel Processing - Volume Part II
Pattern mutation in wireless sensor deployment

IEEE/ACM Transactions on Networking (TON)
Dynamic router node placement in wireless mesh networks: A PSO approach with constriction coefficient and its convergence analysis

Information Sciences: an International Journal
Density theorems for intersection graphs of t-monotone curves

GD'12 Proceedings of the 20th international conference on Graph Drawing
Topological graphs: empty triangles and disjoint matchings

Proceedings of the twenty-ninth annual symposium on Computational geometry
Approximating hitting sets of axis-parallel rectangles intersecting a monotone curve

Computational Geometry: Theory and Applications
Maximum lifetime connected coverage with two active-phase sensors

Journal of Global Optimization
Relay node placement in two-tiered wireless sensor networks with base stations

Journal of Combinatorial Optimization

Quantified Score

Hi-index	0.02

Visualization

Abstract

A unified and powerful approach is presented for devising polynomial approximation schemes for many strongly NP-complete problems. Such schemes consist of families of approximation algorithms for each desired performance bound on the relative error &egr; &Ogr;, with running time that is polynomial when &egr; is fixed. Though the polynomiality of these algorithms depends on the degree of approximation &egr; being fixed, they cannot be improved, owing to a negative result stating that there are no fully polynomial approximation schemes for strongly NP-complete problems unless NP = P.The unified technique that is introduced here, referred to as the shifting strategy, is applicable to numerous geometric covering and packing problems. The method of using the technique and how it varies with problem parameters are illustrated. A similar technique, independently devised by B. S. Baker, was shown to be applicable for covering and packing problems on planar graphs.