1893362
Minimal Tetrahedralizations of a Class of Polyhedra
Given a simple polyhedron P in the three dimensional Euclidean space, different tetrahedralizations of P may contain different numbers of tetrahedra. The minimal tetrahedralization is a tetrahedralization with the minimum number of tetrahedra. In this paper, we present some properties of the graph of polyhedra. Then we identify a class of polyhedra and show that this kind of polyhedra can be minimally tetrahedralized in O(n2) time.
18478446
On Parallel Complexity of Planar Triangulations
The greedy triangulation of a finite planar point set is obtained by repeatedly inserting a shortest diagonal that doesn't intersect those already in the plane. We show that the problem of constructing the greedy triangulation of a finite set of points with integer coordinates in the plane is P-complete. This is the first known geometric P-complete problem where the input is given as a set of points. On the other hand, we provide general NC-methods for testing whether a given triangulation of a set of points and/or line segments can be built by inserting the diagonals in a given partial order, and for constructing such triangulations for simple polygons. As corollaries, we obtain NC-algorithms for testing whether a triangulation is respectively the greedy triangulation or the so called sweep-line triangulation, and for constructing respectively the greedy triangulation or the sweep-line triangulation of a simple polygon. The latter result solves the open problem posed by Atallah et al.
35234330
A Parallel Algorithm for Finding the Constrained Voronoi Diagram of Line Segments in the Plane
In this paper, we present an O(1/αlog n) (for any constant 0 ≤ α ≤ 1) time parallel algorithm for constructing the constrained Voronoi diagram of a set L of n non-crossing line segments in E2, using O(n1+α) processors on a CREW PRAM model. This parallel algorithm also constructs the constrained Delaunay triangulation of L in the same time and processor bound by the duality. 
 
Our method established the conversions from finding the constrained Voronoi diagram L to finding the Voronoi diagram of S, the endpoint set of L. We further showed that this conversion can be done in O(log n) time using n processors in CREW PRAM model. The complexity of the conversion implies that any improvement of the complexity for finding the Voronoi diagram of a point set will automatically bring the improvement of the one in question.
46528104
Optimal Tetrahedralizations of Some Convex Polyhedra
38065257
Tetrahedralization of Two Nested Convex Polyhedra
In this paper, we present an algorithm to tetrahedralize the region between two nested convex polyhedra without introducing Steiner points. The resulting tetrahedralization consists of linear number of tetrahedra. Thus, we answer the open problem raised by Chazelle and Shouraboura: "whether or not one can tetrahedralize the region between two nested convex polyhedra into linear number of tetrahedra, avoiding Steiner points?". Our algorithm runs in O((n+m)3 log(n+m)) time and produces 2(m+n-3) tetrahedra, where n and m are the numbers of the vertices in the two given polyhedra, respectively.
31866645
Optimal Processor Mapping for Linear-Complement Communication on Hypercubes
In this paper, we address the problem of minimizing channel contention of linear-complement communication on wormhole-routed hypercubes. Our research reveals that, for traditional routing algorithms, the degree of channel contention of a linear-complement communication can be quite large. To solve this problem, we propose an alternative approach, which applies processor reordering mapping at compile time. In this compiler approach, processors are logically reordered according to the given communication(s) so that the new communication(s) can be efficiently realized on the hypercube network. It is proved that, for any linear-complement communication, there exists a reordering mapping such that the new communication has minimum channel contention. An O(n/sup 3/) algorithm is proposed to find such a mapping for an n-dimensional hypercube. An algorithm based on dynamic programming is also proposed to find an optimal reordering mapping for a set of linear-complement communications. Several computer simulations have been conducted and the results clearly show the advantage of the proposed approach.
13092959
Whodunit? Causal Analysis for Counterexamples
Although the counterexample returned by a model checker can help in reproducing the symptom related to a defect, a significant amount of effort is often required for the programmer to interpret it in order to locate the cause. In this paper, we provide an automated procedure to zoom in to potential software defects by analyzing a single concrete counterexample. Our analysis relies on extracting from the counterexample a syntactic-level proof of infeasibility, i.e., a minimal set of word-level predicates that contradict with each other. The procedure uses an efficient weakest pre-condition algorithm carried out on a single concrete execution path, which is significantly more scalable than other model checking based approaches. Unlike most of the existing methods, we do not need additional execution traces other than the buggy one. We use public-domain examples to demonstrate the effectiveness of our new algorithm.
386
Density evolution for asymmetric memoryless channels
Density evolution (DE) is one of the most powerful analytical tools for low-density parity-check (LDPC) codes and graph codes with message passing decoding algorithms. With channel symmetry as one of its fundamental assumptions, density evolution has been widely and successfully applied to different channels, including binary erasure channels (BECs), binary symmetric channels (BSCs), binary additive white Gaussian noise (BiAWGN) channels, etc. This paper generalizes density evolution for asymmetric memoryless channels, which in turn broadens the applications to general memoryless channels, e.g., z-channels, composite white Gaussian noise channels, etc. The central theorem underpinning this generalization is the convergence to perfect projection for any fixed-size supporting tree. A new iterative formula of the same complexity is then presented and the necessary theorems for the performance concentration theorems are developed. Several properties of the new density evolution method are explored, including stability results for general asymmetric memoryless channels. Simulations, code optimizations, and possible new applications suggested by this new density evolution method are also provided. This result is also used to prove the typicality of linear LDPC codes among the coset code ensemble when the minimum check node degree is sufficiently large. It is shown that the convergence to perfect projection is essential to the belief propagation (BP) algorithm even when only symmetric channels are considered. Hence, the proof of the convergence to perfect projection serves also as a completion of the theory of classical density evolution for symmetric memoryless channels.
7101460
On the Difference Method for Drawing Conic Arcs
Abstract The difference method is an efficient way to generate an inscribed polygon of a conic section. We address the implementation issues of the difference method, that is, how to choose the difference parameter and initial points so that the inscribed polygon has a minimal number of line segments and is within a given tolerance of the conic arc. We also discuss how the difference method can be used to draw conic arcs represented by rational quadratic Bezier curves.
36109723
Generation and Matching of Ontology Data for the Semantic Web in a Peer-to-Peer Framework
The abundance of ontology data is very crucial to the emerging semantic web. This paper proposes a framework that supports the generation of ontology data in a peer-to-peer environment. It not only enables users to convert existing structured data to ontology data aligned with given ontology schemas, but also allows them to publish new ontology data with ease. Besides ontology data generation, the common issue of data overlapping over the peers is addressed by the process of ontology data matching in the framework. This process helps turn the implicitly related data among the peers caused by overlapping into explicitly interlinked ontology data, which increases the overall quality of the ontology data. To improve matching accuracy, we explore ontology related features in the matching process. Experiments show that adding these features achieves better overall performance than using traditional features only.