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Approximation algorithms for TSP with neighborhoods in the plane
Separating points by axis-parallel lines
This problem of separating n points in the plane, no two of which have the same x- or y-coordinate, is studied, and it is proved that this problem and some variants of it are APX-hard.
On the Fréchet distance of a set of curves
A measure for the resemblance of curves, Alt and Godau have considered the so-called Frechet distance 243, which is a continuous mapping of curves with values of "0/1$".
Packing anchored rectangles
This work constructs n pairwise interior-disjoint axis-aligned empty rectangles such that the lower left corner of each rectangle is a point in S, and the rectangles jointly cover at least a positive constant area.
Pushing Squares Around
The feasibility of motion planning in a rectangular model consisting of square modules that are allowed to slide along or rotate about one another is guaranteed and it is shown that any two connected configurations can be transformed into each other by a sequence of moves.
Minimum Clique Partition in Unit Disk Graphs
Two improved approximation algorithms for MCP in UDGs with a realization of a polynomial time approximation scheme and a randomized quadratic-time algorithm.
Sliding Disks in the Plane
Efficient algorithms for this task are discussed and the number of moves under different assumptions on disk radii and disk placements is estimated.
Bounds on the Maximum Multiplicity of Some Common Geometric Graphs
- A. Dumitrescu, A. Schulz, Adam Sheffer, Csaba D. Tóth
- MathematicsSIAM J. Discret. Math.
- 27 December 2010
We obtain new lower and upper bounds for the maximum multiplicity of some weighted and, respectively, nonweighted common geometric graphs drawn on $n$ points in the plane in general position (with no…
Matching colored points in the plane: Some new results
Formations for Fast Locomotion of Metamorphic Robotic Systems
The formations presented here achieve a constant ratio guarantee on the time to reach a given target in the asymptotic sense and prove upper and lower bounds on the speed of locomotion.