Given a graph G = (V,E), k natural numbers n1, n2, ..., nk such that ∑k i=1 ni = |V |, we wish to find a partition V1, V2, ..., Vk of the vertex set V such that |Vi| = ni and Vi induces a connected subgraph of G for each i, 1 ≤ i ≤ k. Such a partition is called a k-partition of G. The problem of finding a k-partition of a graph G is NP-hard in general. It is known that every k-connected graph h...

The order in which the variables of a linear system are processed determines the total amounts of fill and work to perform LU decomposition on the system. We identify a trade-off between the amounts of fill and work for a given order and the parallelism inherent in that order. We present two algorithms: one that tries to parallelize sequential orders, and another that tries to produce low-fill ...

The 8-tetrahedra longest-edge (8T-LE) partition of any tetrahedron is defined in terms of three consecutive edge bisections, the first one performed by the longest-edge. The associated local refinement algorithm can be described in terms of the polyhedron skeleton concept using either a set of precomputed partition patterns or by a simple edgemidpoint tetrahedron bisection procedure. An effecti...

Watershed from markers and hierarchical watershed are approaches suitable for interactive image segmentation: in the former, the user can edit markers to control the segmentation result; in the latter, the user can select an image partition from a nested set of partitions. We propose an interactive image segmentation tool that allows transition from one approach to other and thus the combinatio...

The approximation of stochastic processes by trees is an important topic in multistage stochastic programming. In this paper we focus on improving the approximation of large trees by smaller (tractable) trees. The quality of the approximation is measured by the nested distance, recently introduced in [Pflug, Pfl09]. The nested distance is derived from the Wasserstein distance. It additionally t...

shop on Sparse Matrix Computations: Graph Theory Issues and Algorithms, Institute for Mathematics and Its Applications, Springer-Verlag, 1992. [13] G. L. Miller, S. Teng, and S. A. Vavasis, A uni ed geometric approach to graph separators, in Proceedings of the 32nd Annual Symposiumon Foundations of Computer Science, IEEE, 1991, pp. 538{547. [14] G. L. Miller and W. Thurston, Separators in two a...

Frustrated antiferromagnets are important materials whose quantum Monte Carlo simulation suffers from a severe sign problem. We construct a nested cluster algorithm which uses a powerful strategy to address this problem. For the spin 1/2 Heisenberg antiferromagnet on a kagome and on a frustrated square lattice the sign problem is eliminated for large systems. The method is applicable to general...

The speed-up in program running time is investigated for problems of parameter estimation with nested sampling Monte Carlo methods. The example used in this study is to extract a polarisation observable from event-by-event data from meson photoproduction reactions. Various implementations of the basic algorithmwere compared, consisting of combinations of single threaded versus multi-threaded, a...