# On Covering Points with Minimum Turns

@inproceedings{Jiang2012OnCP, title={On Covering Points with Minimum Turns}, author={Minghui Jiang}, booktitle={Int. J. Comput. Geom. Appl.}, year={2012} }

We study the problem of finding a polygonal chain of line segments to cover a set of points in ℝd, d≥2, with the goal of minimizing the number of links or turns in the chain. A chain of line segments that covers all points in the given set is called a covering tour if the chain is closed, and is called a covering path if the chain is open. A covering tour or a covering path is rectilinear if all segments in the chain are axis-parallel. We prove that the two problems Minimum-Link Rectilinear…

## 6 Citations

### Covering Paths for Planar Point Sets

- Mathematics, Computer ScienceGraph Drawing
- 2012

It is shown that computing a noncrossing covering path for n points in the plane requires Ω(nlogn) time in the worst case, and it is proved that (1−ε)n straight line segments suffice for a small constant ε>0.

### On the Minimum Link-Length Rectilinear Spanning Path Problem: Complexity and Algorithms

- Computer Science, MathematicsIEEE Transactions on Computers
- 2014

A new parameterized algorithm with running time O*((2d )k) for the constrained -RSP problem is presented, which significantly improves the previous best result and is the first parameterized algorithms of running timeO*(2O(k))) for the constraints of the constrained d-R SP problem for a fixed .

### Minimum-Link Rectilinear Covering Tour is NP-hard in R4

- Mathematics, Computer ScienceArXiv
- 2018

The problems of defining a path and a tour with minimum number of links, also known as Minimum-link Covering Path and Minimum-Link Covering Tour respectively are proven to be NP-hard in $R^2 and the corresponding rectilinear versions are also NP- hard.

### Improved parameterized algorithms for minimum link-length rectilinear spanning path problem

- MathematicsTheor. Comput. Sci.
- 2014

### On the approximability of covering points by lines and related problems

- Computer Science, MathematicsComput. Geom.
- 2015

### Fixed-Parameter Tractable Algorithms for Corridor Guarding Problems

- Computer Science, MathematicsArXiv
- 2019

This work proves the fixed parameter tractability of the parameterized version of MCC, namely k-MCC with respect to the parameter k, where k is the number of rooms, and proposes a variant of CTSP, in which the link-distance of the closed walk has to be minimized.

### Size constrained k simple polygons

- Computer ScienceGeoInformatica
- 2020

This paper proposes a novel approach for finding k simple polygons that maximize the total weights under the size constraint and demonstrates that the proposed algorithm outperforms baseline approaches and reduces the computational cost to create a SCSP.

### REDUCING THE CLOCKWISE-ALGORITHM TO k LENGTH CLASSES

- Computer ScienceJournal of Fundamental Mathematics and Applications (JFMA)
- 2021

An optimization problem related to the extension in k-dimensions of the well known 3x3 points problem by Sam Loyd is considered, thanks to a variation of the so called “clockwise-algorithm”, it is shown how it is possible to visit all the 3^k points of the k-dimensional grid given by the Cartesian product of (0, 1, 2).

## References

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It is shown that computing a noncrossing covering path for n points in the plane requires Ω(nlogn) time in the worst case, and it is proved that (1−ε)n straight line segments suffice for a small constant ε>0.

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