46528104
Optimal Tetrahedralizations of Some Convex Polyhedra
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.
586755
Mixed symbolic representations for model checking software programs
We present an efficient symbolic search algorithm for software model checking. The algorithm combines multiple symbolic representations to efficiently represent the transition relation and reachable states and uses a combination of decision procedures for Boolean and integer representations. Our main contributions include: (1) mixed symbolic representations to model C programs with rich data types and complex expressions; and (2) new symbolic search strategies and optimization techniques specific to sequential programs that can significantly improve the scalability of model checking algorithms. Our controlled experiments on real-world software programs show that the new symbolic search algorithm can achieve several orders-of-magnitude improvements over existing methods. The proposed techniques are extremely competitive in handling sequential models of non-trivial sizes, and also compare favorably to popular Boolean-level model checking algorithms based on BDDs and SAT
8882975
Locating Sensors in Concave Areas
In sensor network localization, multihop based approaches were proposed to approximate the shortest paths to Euclidean distances between pairwise sensors. A good approximation can be achieved when sensors are densely deployed in a convex area, where the shortest paths are close to straight lines connecting pairwise sensors. However, in a concave network, the shortest paths may deviate far away from straight lines, which leads to erroneous distance estimation and inaccurate localization results. In this paper, we propose an improved multihop algorithm which can recognize and filter out the erroneous distance estimation, and therefore achieve accurate localization results even in a concave network.
7877505
Three forbidden subgraphs for line graphs
We construct a set of three graphs with the property that a 3-connected graph with minimum degree at least 7 is a line graph if and only if it does not contain any of the three graphs as an induced subgraph. We also show that the number of excluded subgraphs cannot be reduced no matter what connectivity is specified.
14588645
Community Tools for Repurposing Learning Objects
A critical success factor for the reuse of learning objects is the ease by which they may be repurposed in order to enable reusability in a different teaching context from which they were originally designed. The current generation of tools for creating, storing, describing and locating learning objects are best suited for users with technical expertise. Such tools are an obstacle to teachers who might wish to perform alterations to learning objects in order to make them suitable for their context. In this paper we describe a simple set of tools to enable practitioners to adapt the content of existing learning objects and to store and modify metadata describing the intended teaching context of these learning objects. We are deploying and evaluating these tools within the UK language teaching community.
28695934
Alternating walks in partially 2-edge-colored graphs and optimal strength of graph labeling
Abstract A graph is partially 2-edge-colored if edges of G are colored by two colors, possibly with some edges uncolored. A walk is alternating in a partially 2-edge-colored graph if the given 2-edge-coloring can be extended to all edges of G such that colors alternate as the walk is traversed. We present a polynomial-time algorithm to decide, given a partially 2-edge-colored graph and two distinct vertices, whether there is an alternating walk connecting the two vertices. We apply the algorithm to solve problems in graph labeling. In particular, we show that the regularizable strength of a graph can be determined in polynomial time.