my work computational geometry - hong kong university of
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My Work
Computational Geometry
Siu-Wing Cheng CSE, HKUST
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Planar point location
Manifold and surface reconstruction
Shape matching
Approximate shortest path
Prove theorems.
Sometimes complement the theorems with software.
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Which state am I in?
There are O(n) space and O(log n) query time solutions.
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What if the access frequencies of the states are different and changing?
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What are the largest subsets that can be overlaid under translation and rotation so that the bottleneck distance is smaller than eps?
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Find subsets A and B such that |A| = |B| � optimal size
such that the bottleneck distance is at most (1 + ⌘)".
• In O
✓n2m2
⌘(n+m) log n
◆time for rigid motions in
the plane.
• In O
✓nm
⌘5(n+m)
1.5log n
◆time for translations in R3
1
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Efficient Polynomial-Time (1+eps)-Approximation Algorithms
Approx. shortest descending path, SODA13 Approx. shortest path in the plane with direction-dependent travel costs, SODA07 Approx. shortest path on a terrain with a linear combination cost of length and total ascent, STOC14 Approx. shortest path through weighted regions, SODA15