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Search: authors:"Hsien-Chih Chang"

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Near-Optimal Distance Emulator for Planar Graphs

, Poland 3 University of Illinois at Urbana-Champaign , USA 4 Hsien-Chih Chang Given a graph G and a set of terminals T , a distance emulator of G is another graph H (not necessarily a subgraph of G

Untangling Planar Curves

Any generic closed curve in the plane can be transformed into a simple closed curve by a finite sequence of local transformations called homotopy moves. We prove that simplifying a planar closed curve with n self-crossings requires Theta(n^{3/2}) homotopy moves in the worst case. Our algorithm improves the best previous upper bound O(n^2), which is already implicit in the...

From Proximity to Utility: A Voronoi Partition of Pareto Optima

We present an extension of Voronoi diagrams where not only the distance to the site is taken into account when considering which site the client is going to use, but additional attributes (i.e., prices or weights) are also considered. A cell in this diagram is then the loci of all clients that consider the same set of sites to be relevant. In particular, the precise site a client...