Man-Kwun Chiu

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We present a novel approach to estimate the dimension m of an unknown manifold M ⊂ R d with positive reach from a set of point samples P ⊂ M. It works by analyzing the shape of simplices formed by point samples. Suppose that P is drawn from M according to a Poisson process with an unknown parameter λ. Let k be some fixed positive integer. When λ is large(More)
This paper studies a cooperative card game called Hanabi from an algorithmic combinatorial game theory viewpoint. The aim of the game is to play cards from 1 to n in increasing order (this has to be done independently in c different colors). Cards are drawn from a deck one by one. Drawn cards are either immediately played, discarded or stored for future use(More)
Let M be an m-dimensional smooth compact manifold embedded in R d , where m is a constant known to us. Suppose that a dense set of points are sampled from M according to a Poisson process with an unknown parameter. Let p be any sample point, let be the local feature size at p, and let ε be the distance from p to the (n + 1)th nearest sample point for some n(More)
We propose an algorithm for finding a (1 + ε)-approximate shortest path through a weighted 3D simplicial complex T. The weights are integers from the range [1, W ] and the vertices have integral coordinates. Let N be the largest vertex coordinate magnitude, and let n be the number of tetrahedra in T. Let ρ be some arbitrary constant. Let κ be the size of(More)
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