Algorithms for VLSI artwork

Thesis/Dissertation · Sun Jan 01 04:00:00 EST 1989

OSTI ID:6037406

Wu, San-Yuan

The specific problems that the author studies in this thesis are painting and drawing of rectilinear polygons, covering rectilinear polygons by rectangles, and partitioning rectilinear polygons into rectangles. These problems have application to VLSI design, computer graphics, etc. He considers three display devices, one-dimensional and two dimensional pen plotters, and video screens, for the problem of painting and covering. An 0 (n log n) time algorithm to obtain an optimal drawing strategy on one-dimensional plotters is obtained (n is the number of the vertices of the polygons). Fore the case of a two-dimensional plotter, the strategy to optimally draw the contour of a rectilinear polygon can be found in linear time. However, for a collection of rectilinear polygons, this problem is NP-hard. For screen type displays, he formulates three strategies to paint a rectilinear polygon using a rectangle as a primitive. For two of these, he shows the problem NP-hard. Performance bounds for these strategies are also obtained. Three approximation algorithms to cover a rectilinear polygon that is neither horizontally nor vertically convex by rectangles are developed. All three guarantee covers that have at most twice as many rectangles as in an optimal cover. The complexities of those algorithms are O (n log n), O(n{sup 2}), and O(n{sup 4}), respectively. Finally, he develops two algorithms to obtain the optimal partition of simple rectilinear polygons. Their time complexities are {approximately} O (kn) and O (n log k), where k is the number of the inversions of the polygon. Both are significantly faster than the existing best algorithm on polygons whose size is large relative to k.

• Research Organization: Minnesota Univ., Minneapolis, MN (USA)
• OSTI ID: 6037406
• Country of Publication: United States
• Language: English

Related Subjects

99 GENERAL AND MISCELLANEOUS
990200* -- Mathematics & Computers
ALGORITHMS
BENCH-SCALE EXPERIMENTS
COMPUTER GRAPHICS
COMPUTER OUTPUT DEVICES
COMPUTER-GRAPHICS DEVICES
DESIGN
DISPLAY DEVICES
ELECTRONIC CIRCUITS
INTEGRATED CIRCUITS
MATHEMATICAL LOGIC
MICROELECTRONIC CIRCUITS
PERFORMANCE TESTING
TESTING
TWO-DIMENSIONAL CALCULATIONS