Show simple item record Mahajan, Sahil Raman, Rajiv (Advisor) 2016-09-13T11:04:49Z 2016-09-13T11:04:49Z 2016-09-13T11:04:49Z
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

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