NDLI: Performance Guarantees on a Sweep-Line Heuristic for Covering Rectilinear Polygons with Rectangles

Please wait, while we are loading the content...

Performance Guarantees on a Sweep-Line Heuristic for Covering Rectilinear Polygons with Rectangles

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Franzblau, D. S.
Copyright Year	1989
Abstract	Finding the minimum number of rectangles required to cover a rectilinear or orthogonal polygon, where overlapping of rectangles is allowed, is one of several well-known, hard geometric decomposition problems. This paper reports the first results known that give worst-case performance bounds for an approximation algorithm for this problem. It is proved that partitioning the polygon into rectangles (with no overlapping) produces at most $2\theta + h - 1$ rectangles, where $\theta $ is the minimum number of rectangles in a cover, and h is the number of holes. Examples are also given in which this bound is tight. The proof is based on counting arguments, and on Eulers formula for a planar graph. This paper shows that extending rectangles vertically and deleting duplicates produces at most $O(\theta \log \theta )$ rectangles. For the proof, geometric constraints are used to construct a large an-tirectangle, a set of points with no two contained in the same rectangle. This algorithm has an $O(n\log n)$ implementation using balanced trees, where n is the number of vertices.
Starting Page	307
Ending Page	321
Page Count	15
File Format	PDF
ISSN	08954801
DOI	10.1137/0402027
e-ISSN	10957146
Journal	SIAM Journal on Discrete Mathematics (SJDMEC)
Issue Number	3
Volume Number	2
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2006-08-08
Access Restriction	Subscribed
Subject Keyword	approximation Polyominoes heuristic rectilinear cover sweep-line orthogonal Analysis of algorithms and problem complexity polygon Packing and covering rectangle Combinatorics algorithm
Content Type	Text
Resource Type	Article
Subject	Mathematics

Sl.	Authority	Responsibilities	Communication Details
1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
5	Website/Portal (Helpdesk)	Queries regarding NDLI and its services	support@ndl.gov.in
6	Contents and Copyright Issues	Queries related to content curation and copyright issues	content@ndl.gov.in
7	National Digital Library of India Club (NDLI Club)	Queries related to NDLI Club formation, support, user awareness program, seminar/symposium, collaboration, social media, promotion, and outreach	clubsupport@ndl.gov.in
8	Digital Preservation Centre (DPC)	Assistance with digitizing and archiving copyright-free printed books	dpc@ndl.gov.in
9	IDR Setup or Support	Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops	idr@ndl.gov.in

Performance Guarantees on a Sweep-line Heuristic for Covering Rectilinear Polygons with Rectangles *

Covering rectilinear polygons with axis-parallel rectangles (2003).

Covering Rectilinear Polygons with Axis-Parallel Rectangles

Covering rectangles by few monotonous polyominoes

Partitioning orthogonal polygons into fat rectangles in polynomial time (2002).

Approximation Algorithms for the Orthogonal Z-Oriented Three-Dimensional Packing Problem

The structure of optimal partitions of orthogonal polygons into fat rectangles (2003).

Complexities of efficient solutions of rectilinear polygon cover problems

Covering Orthogonal Polygons with Sliding k-transmitters (2014)

Performance Guarantees on a Sweep-Line Heuristic for Covering Rectilinear Polygons with Rectangles

Similar Documents

Performance Guarantees on a Sweep-line Heuristic for Covering Rectilinear Polygons with Rectangles *

Covering rectilinear polygons with axis-parallel rectangles (2003).

Covering Rectilinear Polygons with Axis-Parallel Rectangles

Covering rectangles by few monotonous polyominoes

Partitioning orthogonal polygons into fat rectangles in polynomial time (2002).

Approximation Algorithms for the Orthogonal Z-Oriented Three-Dimensional Packing Problem

The structure of optimal partitions of orthogonal polygons into fat rectangles (2003).

Complexities of efficient solutions of rectilinear polygon cover problems

Covering Orthogonal Polygons with Sliding k-transmitters (2014)

Performance Guarantees on a Sweep-Line Heuristic for Covering Rectilinear Polygons with Rectangles