# Recognition of Largest Empty Ortho Convex Polygon in a Point Set.

December 2008

## Date of Award

Winter 12-12-2009

## Institute Name (Publisher)

Indian Statistical Institute

## Document Type

Master's Dissertation

## Degree Name

Master of Technology

Computer Science

## Department

Advance Computing and Microelectronics Unit (ACMU-Kolkata)

## Supervisor

Nandy, Subhas Chandra (ACMU-Kolkata; ISI)

## Abstract (Summary of the Work)

The objective of this report is to study the algorithm for computing the maximum area empty isothetic orthoconvex polygon (MEOP) among a set of n points on a rectangular region in 2D. A polygon is said to be isothetic if its sides are parallel to coordinate axes. An isothetic polygon is said to be orthoconvex if the intersection of the polygon with a horizontal or a vertical line is a single line segment. Orthoconvexity has importance in robotic visibility, and VLSI. Datta and Ramkumar [1], proposed algorithms for recognizing largest empty orthoconvex polygon of some specified shapes among a point set in 2D. These include (i) L-shape, (ii) cross-shape, (iii) point visible, and (iv) edge-visible polygons. The time complexity of these algorithms are all O(n2 ). Another variant in this class of problems is recognizing the largest empty staircase polygon among point and isothetic polygonal obstacles, which can also be solved in O(n2 ) time and space complexity [2]. But the problem of finding an maximum area orthoconvex polygon MEOP of arbitrary shape is not studied yet. Here, we propose an algorithm to compute an MEOP in O(n5 ) time and O(n3 ) space.The thesis is organized as follows. In Chapter 2, we introduce some preliminary concepts and the overview of the algorithm. The algorithm for computing the maximum area edge-visible polygon is discussed in Chapter 3. The algorithm for finding the maximum area empty staircase polygon is discussed in Chapter 4. Finally the conclusion of the work appears in Chapter 5.

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:28843274

## Control Number

ISI-DISS-2008-217