We describe a construction of LR-spaces whose bases are composed of locally linearly independent B-splines which also form a partition of unity. The construction conforms to given refinement requirements associated to subdomains. In contrast to the original LRpaper (Dokken et al., 2013) and similarly to the hierarchical B-spline framework (Forsey and Bartels, 1988) the construction of the mesh ...

The partition reenement algorithm 10, 6] is the basis for most of the tools for checking bisimulation equivalences and for computing minimal realisations of CCS-like nite state processes. In this paper, we present a partition reenement algorithm for the-calculus 7], a development of CCS where channel names can be communicated. It can be used to check bisimilarity and to compute minimal realisat...

This paper deals with evaluating constant terms of a special class of rational functions, the Elliott-rational functions. The constant term of such a function can be read off immediately from its partial fraction decomposition. We combine the theory of iterated Laurent series and a new algorithm for partial fraction decompositions to obtain a fast algorithm for MacMahon’s Omega calculus, which ...

Determining the shortest path from one node to another in a graph is probably the most popular question in graph theory. If the graph is non-negatively weighted, Dijkstra’s algorithm is the classic algorithm used to answer this question. Because of its breadth-first-search character, this algorithm usually spreads circularly around the source node of the search and hence the search space can be...

A skew partition as defined by Chvátal is a partition of the vertex set of a graph into four nonempty parts A B C D such that there are all possible edges between A and B and no edges between C and D. We present a polynomial-time algorithm for testing whether a graph admits a skew partition. Our algorithm solves the more general list skew partition problem, where the input contains, for each ve...

H.266/Versatile Video Coding (VVC) is the latest international video coding standard to encode ultra-high-definition effectively. The quadtree with nested multi-type tree (QT-MTT) structure provides various sizes of partitioning and allows binary (BT) split ternary (TT) at each QT level. Furthermore, numerous advanced tools are equipped in H.266/VVC encoder. However, encoding time increases tre...

The NP-hard graph bisection problem is to partition the nodes of an undirected graph into two equal-sized groups so as to minimize the number of edges that cross the partition. The more general graph l-partition problem is to partition the nodes of an undirected graph into l equal-sized groups so as to minimize the total number of edges that cross between groups. We present a simple, linear-tim...

Radiologists perform a CT Angiography procedure to examine vascular structures and associated pathologies such as aneurysms. Volume rendering is used to exploit volumetric capabilities of CT that provides complete interactive 3-D visualization. However, bone forms an occluding structure and must be segmented out. The anatomical complexity of the head creates a major challenge in the segmentatio...

Increasing amount of RDF data on the Web drives the need for its efficient and effective management. In this light, numerous researchers have proposed to use RDBMSs to store and query RDF annotations using the SQL and SPARQL query languages. The first few attempts at SPARQL-to-SQL translation revealed non-trivial challenges related to correctness and efficiency of such translation in the presen...