Algorithms for Covering Points with Lines Aman Anand Department of - - PowerPoint PPT Presentation

Algorithms for Covering Points with Lines

Aman Anand

Department of Computer Science and Engineering, Indian Institute of Technology, Kanpur, India 4th November, 2014

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Outline

1

Introduction What is this paper about? Why

2

2nd Section How novel are these ideas compared to the previous research? References

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Introduction

Outline

1

Introduction What is this paper about? Why

2

2nd Section How novel are these ideas compared to the previous research? References

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Introduction What is this paper about?

Overview

The inputs are n points in the plane and a positive integer k, and we are asked to answer if we can cover these n points with at most k lines.

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Introduction What is this paper about?

Overview

The inputs are n points in the plane and a positive integer k, and we are asked to answer if we can cover these n points with at most k lines. Our approach is based on fixed-parameter tractability and, in particular, kernelization.

Aman Anand (CSE, IITK) Algorithms for Covering Points with Lines 04/11/14 4 / 9

Introduction What is this paper about?

Overview

The inputs are n points in the plane and a positive integer k, and we are asked to answer if we can cover these n points with at most k lines. Once instances are no longer susceptible to these reduction rules, we

• btain a problem kernel whose size is bounded by a polynomial

function of the parameter k and does not depend on the size n of the input.

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Introduction Why

Why I choose this paper?

Much research has been done on covering point with lines. In this article, approximation algorithms or probabilistic algorithms that give an answer with a high probability of correctness were not considered. This paper discuss all the previous work done on this topic. Overall the proof style is nice and the proofs are easy to understand if you have basic knowledge of geometry.

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2nd Section

Outline

1

Introduction What is this paper about? Why

2

2nd Section How novel are these ideas compared to the previous research? References

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2nd Section How novel are these ideas compared to the previous research?

How novel are these ideas compared to the previous research?

This research is the latest and most detailed paper one could find on this topic.It’s making,working are clearly explained with some examples. This algorithms can handle large instances in practice.

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2nd Section How novel are these ideas compared to the previous research?

How novel are these ideas compared to the previous research?

This research is the latest and most detailed paper one could find on this topic.It’s making,working are clearly explained with some examples. This algorithms can handle large instances in practice. Although this idea did not improve the theoretical time complexity (asymptotically, the O-notation is the same), it improved significantly the running time in practice.

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2nd Section References

References

AGARWAL, P. 1990. Partitioning arrangements of lines II:

• applications. Discrete Comput. Geom. 5, 533573.

http://www.cgal.org/Manual/3.3/doc html/cgal manual/packages.html. APPLEGATE, D., BIXBY, R., CHVATAL , V., AND COOK, W. 2006. The Traveling Salesman Problem. Princeton University Press, Princeton, NJ, ARKIN, E., BENDER, M., DEMAINE, E., FEKETE, S., MITCHELL, J., AND SETHIA, S. 2005. Optimal covering tours with turn costs. SIAM J. Comput. 35, 3, 531566. ARKIN, E., FEKETE, S., AND MITCHELL, J. 2000. Approximation algorithms for lawn mowing and milling. Comput. Geom. 17, 1-2, 2550.

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2nd Section References

Thank You

Thank You!

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