A k-clustering of a given set of points in the plane is a partition of the points into k subsets ("clusters"). For any fixed k, we can find a k-clustering which minimizes any monotone function of the diameters or the radii of the clusters in polynomial time. The algorithm is based

We consider, for each exchange matrix B, a category of geometric cluster algebras over B and coefficient specializations between the cluster algebras. The category also depends on an underlying ring R, usually Z, Q, or R. We broaden the definition of geometric cluster algebras slightly over

) in the abovementioned existing research, propose using geometric clustering algorithms for...

This paper investigates the computational complexity of several clustering problems with special objective functions for point sets in the Euclidean plane. Our strongest negative result is that clustering a set of 3k points in the plane into k triangles with minimum total circumference is NP

Abstract. We discuss a new Monte Carlo algorithm for the simulation of complex fluids. This algorithm employs geometric operations to identify clusters of particles that can be moved in a rejection-free way. It is demonstrated that this geometric cluster algorithm (GCA) constitutes the continuum

Figure 1: Lines of the initial drawing (left) are first automatically clustered into groups that can be merged at a scale ε (middle). A new line is then generated for each group in an application-dependent style (at right, line thickness indicates the mean thickness of the cluster). 1

Abstract. A universal geometric cluster algebra over an exchange matrix B is a universal object in the category of geometric cluster algebras over B re-lated by coefficient specializations. (Following an earlier paper on universal geometric cluster algebras, we broaden the definition of geometric

Figure 1: The two stages of our method. Lines of the initial drawing (left) are first automatically clustered into groups that can be merged at a scale ε (each group is assigned a unique color). A new line is then generated for each group in an applicationdependent style (at right, line thickness

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Abstract Drawing on the correspondence between the graph Laplacian, the Laplace-Beltrami op erator on a manifold , and the connections to the heat equation , we propose a geometrically motivated algorithm for constructing a representation for data sampled from a low dimensional manifold embedded