Guillotine cuts

Mahajan, Sahil; Raman, Rajiv (Advisor)

dc.contributor.author	Mahajan, Sahil
dc.contributor.author	Raman, Rajiv (Advisor)
dc.date.accessioned	2016-09-13T11:04:49Z
dc.date.available	2016-09-13T11:04:49Z
dc.date.issued	2016-09-13T11:04:49Z
dc.identifier.uri	https://repository.iiitd.edu.in/jspui/handle/123456789/422
dc.description.abstract	In guillotine cut problem, we are given non-intersecting convex sets in the plane and we are allowed straight line cuts. If a cut passes through an object, it kills that object. Can one always save a constant fraction or Ω(n) objects? For the general case, Pach and Tardos answered in the negative. We investigate the case where we have axis-parallel rectangles and only horizontal and vertical guillotine cuts are allowed. Ω(n) bound here would have interesting implications for the Maximum Independent Set of Rectangles problem - it would imply a constant factor or O(1) approximation for it. Unable to solve the problem in its totality, we discuss some approaches and small results.	en_US
dc.language.iso	en_US	en_US
dc.subject	Guillotine	en_US
dc.subject	Non-intersecting convex sets	en_US
dc.subject	Constant fraction	en_US
dc.subject	Independent Set	en_US
dc.title	Guillotine cuts	en_US
dc.type	Thesis	en_US