A key aspect of the parallel partitioners of AMR codes based on meshes consisting of regularly refined patches lies in the choice of a load balancing algorithm. One of the current load balancing methods of choice is to use a space-filling curve. The need to apply load balancing in parallel on possibly hundreds of thousands of processors has led to the development of an algorithm which generates...

Let C ⊂ P be a smooth irreducible complete algebraic curve of degree d embedded in a projective 3-space over an algebraically closed field k. It is called n-regular if H(IC(n− 1)) = H(IC(n− 2)) = 0, where IC is the ideal sheaf of C. Among all this implies that the homogeneous ideal IC = ⊕ l H (IC(l)) ⊂ k[x0, x1, x2, x3] is generated in degree ≤ n ([7], Lecture 14) and C ⊂ P is (scheme-theoretic...

Space filling curves (SFCs) are widely used in the design of indexes for spatial and temporal data. Clustering is a key metric for an SFC, that measures how well the curve preserves locality in moving from higher dimensions to a single dimension. We present the onion curve, an SFC whose clustering performance is provably close to optimal for cube and nearcube shaped query sets, irrespective of ...