On Piercing Set of Axis-Parallel Rectangles in 2D.

Date of Submission

December 2011

Date of Award

Winter 12-12-2012

Institute Name (Publisher)

Indian Statistical Institute

Document Type

Master's Dissertation

Degree Name

Master of Technology

Subject Name

Computer Science


Advance Computing and Microelectronics Unit (ACMU-Kolkata)


Nandy, Subhas Chandra (ACMU-Kolkata; ISI)

Abstract (Summary of the Work)

Piercing problems often arises in facility location, and is a well-studied area of research in computational geometry. The specific piercing problem discussed in this dissertation asks for the minimum number of points required to stab a set of possibly overlapping rectangles. In other words, to determine the minimum number of facilities and their positions such that each rectangular demand region contains at least one facility located inside it. It is already proved that even if all regions are uniform sized squares, the problem is NP-hard. Therefore we concentrate on designing efficient heuristic algorithms for solving this problem. In this dissertation we do experimental studies of the piercing problem on randomly generated axis-parallel rectangles. We have implemented two approaches for piercing on random rectangles generated in a random manner (i) Greedy approach (ii) Divide-and-Conquer approach and compared the two results. We have also studied the computation of maximum independent set and minimum clique cover problems and plotted the ratio of minimum clique cover and maximum independent set for a set of n rectangles for different values of n. It is observed that Greedy Clique Cover is a 2 factor approximation of the Maximum Independent Set problem for randomly generated rectangles.


ProQuest Collection ID: http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&res_dat=xri:pqm&rft_dat=xri:pqdiss:28843248

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Creative Commons License

Creative Commons Attribution 4.0 International License
This work is licensed under a Creative Commons Attribution 4.0 International License.



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