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 Aman Anand (CSE, IITK) Algorithms for Covering Points with Lines 04/11/14 1 / 9

Outline Introduction 1 What is this paper about? Why 2nd Section 2 How novel are these ideas compared to the previous research? References Aman Anand (CSE, IITK) Algorithms for Covering Points with Lines 04/11/14 2 / 9

Introduction Outline Introduction 1 What is this paper about? Why 2nd Section 2 How novel are these ideas compared to the previous research? References Aman Anand (CSE, IITK) Algorithms for Covering Points with Lines 04/11/14 3 / 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. 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. 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 obtain 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. Aman Anand (CSE, IITK) Algorithms for Covering Points with Lines 04/11/14 4 / 9

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. Aman Anand (CSE, IITK) Algorithms for Covering Points with Lines 04/11/14 5 / 9

2nd Section Outline Introduction 1 What is this paper about? Why 2nd Section 2 How novel are these ideas compared to the previous research? References Aman Anand (CSE, IITK) Algorithms for Covering Points with Lines 04/11/14 6 / 9

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. Aman Anand (CSE, IITK) Algorithms for Covering Points with Lines 04/11/14 7 / 9

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. Aman Anand (CSE, IITK) Algorithms for Covering Points with Lines 04/11/14 7 / 9

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. Aman Anand (CSE, IITK) Algorithms for Covering Points with Lines 04/11/14 8 / 9

2nd Section References Thank You Thank You! Aman Anand (CSE, IITK) Algorithms for Covering Points with Lines 04/11/14 9 / 9