Computational geometry: an introduction
Computational geometry: an introduction
Fast heuristics for minimum length rectangular partitions of polygons
SCG '86 Proceedings of the second annual symposium on Computational geometry
Beyond Steiner's problem: a VLSI oriented generalization
WG '89 Proceedings of the fifteenth international workshop on Graph-theoretic concepts in computer science
The complexity of computing minimum separating polygons
Pattern Recognition Letters - Special issue on computational geometry
A pedestrian approach to ray shooting: shoot a ray, take a walk
SODA '93 Selected papers from the fourth annual ACM SIAM symposium on Discrete algorithms
Approximation algorithms for the geometric covering salesman problem
Discrete Applied Mathematics
Approximation algorithms for geometric tour and network design problems (extended abstract)
Proceedings of the eleventh annual symposium on Computational geometry
Bounds for partitioning rectilinear polygons
SCG '85 Proceedings of the first annual symposium on Computational geometry
Nearly linear time approximation schemes for Euclidean TSP and other geometric problems
FOCS '97 Proceedings of the 38th Annual Symposium on Foundations of Computer Science
Some NP-complete geometric problems
STOC '76 Proceedings of the eighth annual ACM symposium on Theory of computing
Approximation algorithms for TSP with neighborhoods in the plane
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Balanced Partition of Minimum Spanning Trees
ICCS '02 Proceedings of the International Conference on Computational Science-Part III
TSP with Neighborhoods of Varying Size
ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
Approximation algorithms for TSP with neighborhoods in the plane
Journal of Algorithms - Special issue: Twelfth annual ACM-SIAM symposium on discrete algorithms
TSP with neighborhoods of varying size
Journal of Algorithms
On the complexity of approximating tsp with neighborhoods and related problems
Computational Complexity
A PTAS for TSP with neighborhoods among fat regions in the plane
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Finding the Optimal Path in 3D Spaces Using EDAs --- The Wireless Sensor Networks Scenario
ICANNGA '07 Proceedings of the 8th international conference on Adaptive and Natural Computing Algorithms, Part I
Minimum Spanning Tree with Neighborhoods
AAIM '07 Proceedings of the 3rd international conference on Algorithmic Aspects in Information and Management
Node-Weighted Steiner Tree and Group Steiner Tree in Planar Graphs
ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
TSP with neighborhoods of varying size
Journal of Algorithms
Theoretical Computer Science
Proceedings of the twenty-sixth annual symposium on Computational geometry
A QPTAS for TSP with fat weakly disjoint neighborhoods in doubling metrics
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Fast track article: Designing hierarchical sensor networks with mobile data collectors
Pervasive and Mobile Computing
Optimizing data collection path in sensor networks with mobile elements
International Journal of Automation and Computing
On approximating the TSP with intersecting neighborhoods
ISAAC'06 Proceedings of the 17th international conference on Algorithms and Computation
The kissing problem: how to end a gathering when everyone kisses everyone else goodbye
FUN'12 Proceedings of the 6th international conference on Fun with Algorithms
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In TSP with neighborhoods (TSPN) we are given a collection X of k polygonal regions in the plane, called neighborhoods, with totally n vertices, and we seek the shortest tour that visits each neighborhood. In this paper we present a simple and fast algorithm that, given a start point, computes a TSPN tour of length O(log k) times the optimum in time O(n+k log k). When no start point is given we show how to compute a "good" start point in time O(n2 logn), hence we obtain a logarithmic approximation algorithm that runs in time O(n2 log n). We also present an algorithm which performs at least one of the following two tasks (which of these tasks is performed depends on the given input): (1) It outputs in time O(n log n) a TSPN tour of length O(log k) times the optimum. (2) It outputs a TSPN tour of length less than (1 + ε) times the optimum in time O(n3), where ε is an arbitrary real constant given as an optional parameter.The same approach can be used for the Red-Blue Separation Problem. We show an algorithm with logarithmic approximation ratio that runs in time O(n log n), where n is the total number of points.