Dominating set of rectangles intersecting a straight line

The Minimum Dominating Set ( MDS ) problem is one of the well-studied problems in computer science. It is well-known that this problem is NP -hard for simple geometric objects; unit disks, axis-parallel unit squares, and axis-parallel rectangles to name a few. An interesting variation of the MDS pro...

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Vydáno v:Journal of combinatorial optimization Ročník 41; číslo 2; s. 414 - 432
Hlavní autor: Pandit, Supantha
Médium: Journal Article
Jazyk:angličtina
Vydáno: New York Springer US 01.02.2021
Springer Nature B.V
Témata:
Algorithms
Combinatorics
Convex and Discrete Geometry
Disks
Dynamic programming
Mathematical Modeling and Industrial Mathematics
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Optimization
Polynomials
Rectangles
Straight lines
Theory of Computation
Squares
Inclined line
Straight line
Rectangles
Diagonal line
Intersecting a line
Touching a line
hard
Minimum dominating set
ISSN:1382-6905, 1573-2886
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Popis
Shrnutí:The Minimum Dominating Set ( MDS ) problem is one of the well-studied problems in computer science. It is well-known that this problem is NP -hard for simple geometric objects; unit disks, axis-parallel unit squares, and axis-parallel rectangles to name a few. An interesting variation of the MDS problem with rectangles is when there exists a straight line that intersects each of the given rectangles. In the recent past researchers have studied the maximum independent set, minimum hitting set problems on this setting with different geometric objects. We study the MDS problem with axis-parallel rectangles, unit-height rectangles, and unit squares in the plane. These geometric objects are constrained to be intersected by a straight line. For axis-parallel rectangles, we prove that this problem is NP -hard. When the objects are axis-parallel unit squares, we present a polynomial time algorithm using dynamic programming. We provide a polynomial time algorithm for unit-height rectangles as well. For unit squares that touch the straight line at a single point from either side of the straight line, we show that there is an O ( n log n ) -time algorithm.
Bibliografie:ObjectType-Article-1
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ISSN:1382-6905
1573-2886
DOI:10.1007/s10878-020-00685-y