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)
NC-approximation schemes for NP- and PSPACE-hard problems for geometric graphs
Journal of Algorithms
Unit disk graph recognition is NP-hard
Computational Geometry: Theory and Applications - Special issue on geometric representations of graphs
Polynomial time approximation schemes for Euclidean traveling salesman and other geometric problems
Journal of the ACM (JACM)
Robust algorithms for restricted domains
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Calibration as parameter estimation in sensor networks
WSNA '02 Proceedings of the 1st ACM international workshop on Wireless sensor networks and applications
Approximation Schemes Using L-Reductions
Proceedings of the 14th Conference on Foundations of Software Technology and Theoretical Computer Science
A tight bound on approximating arbitrary metrics by tree metrics
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Polynomial-time approximation schemes for packing and piercing fat objects
Journal of Algorithms
Bypassing the embedding: algorithms for low dimensional metrics
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Localization and routing in sensor networks by local angle information
Proceedings of the 6th ACM international symposium on Mobile ad hoc networking and computing
Polynomial-Time Approximation Schemes for Geometric Intersection Graphs
SIAM Journal on Computing
On the locality of bounded growth
Proceedings of the twenty-fourth annual ACM symposium on Principles of distributed computing
Local approximation schemes for ad hoc and sensor networks
DIALM-POMC '05 Proceedings of the 2005 joint workshop on Foundations of mobile computing
On a conjecture related to geometric routing
Theoretical Computer Science - Algorithmic aspects of wireless sensor networks
Greedy drawings of triangulations
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Approximating geometric coverage problems
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Approximation schemes for wireless networks
ACM Transactions on Algorithms (TALG)
The intrinsic dimensionality of graphs
Combinatorica
A log-star distributed maximal independent set algorithm for growth-bounded graphs
Proceedings of the twenty-seventh ACM symposium on Principles of distributed computing
On Metric Clustering to Minimize the Sum of Radii
SWAT '08 Proceedings of the 11th Scandinavian workshop on Algorithm Theory
Some Results on Greedy Embeddings in Metric Spaces
FOCS '08 Proceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer Science
Maximum independent set of rectangles
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Approximation algorithms for maximum independent set of pseudo-disks
Proceedings of the twenty-fifth annual symposium on Computational geometry
Polynomial time approximation schemes for base station coverage with minimum total radii
Computer Networks: The International Journal of Computer and Telecommunications Networking
Succinct Greedy Geometric Routing in the Euclidean Plane
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
Organizing a global coordinate system from local information on an ad hoc sensor network
IPSN'03 Proceedings of the 2nd international conference on Information processing in sensor networks
Good quality virtual realization of unit ball graphs
ESA'07 Proceedings of the 15th annual European conference on Algorithms
Efficient approximation schemes for geometric problems?
ESA'05 Proceedings of the 13th annual European conference on Algorithms
Geometric clustering to minimize the sum of cluster sizes
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
A weakly robust PTAS for minimum clique partition in unit disk graphs
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
Fast deterministic distributed maximal independent set computation on growth-bounded graphs
DISC'05 Proceedings of the 19th international conference on Distributed Computing
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We give a simple framework which is an alternative to the celebrated and widely used shifting strategy of Hochbaum and Maass (J. ACM 32(1):103---136, 1985) which has yielded efficient algorithms with good approximation bounds for numerous optimization problems in low-dimensional Euclidean space. Our framework does not require the input graph/metric to have a geometric realization--it only requires that the input graph satisfy some weak property referred to as growth boundedness. Growth bounded graphs form an important graph class that has been used to model wireless networks. We show how to apply the framework to obtain a polynomial time approximation scheme (PTAS) for the maximum (weighted) independent set problem on this important graph class; the problem is W[1]-complete.Via a more sophisticated application of our framework, we show how to obtain a PTAS for the maximum (weighted) independent set for intersection graphs of (low-dimensional) fat objects that are expressed without geometry. Erlebach et al. (SIAM J. Comput. 34(6):1302---1323, 2005) and Chan (J. Algorithms 46(2):178---189, 2003) independently gave a PTAS for maximum weighted independent set problem for intersection graphs of fat geometric objects, say ball graphs, which required a geometric representation of the input. Our result gives a positive answer to a question of Erlebach et al. (SIAM J. Comput. 34(6):1302---1323, 2005) who asked if a PTAS for this problem can be obtained without access to a geometric representation.