In this paper we present an algorithm for detecting and repairing defects in the boundary of a polyhedron. These defects, usually caused by problems in CAD software, consist of small gaps bounded by edges that are incident to only one polyhedron face. The algorithm uses a partial curve matching technique for matching parts of the defects, and an optimal triangulation of 3-D polygons for resolving the unmatched parts. It is also shown that finding a consistent set of partial curve matches with maximum score, a subproblem which is related to our repairing process, is NP-Hard. Experimental results on several polyhedra are presented. Keywords: CAD, polyhedra, gap filling, curve matching, geometric hashing, triangulation. 1 Introduction The problem studied in this paper is the detection and repair of "gaps" in the boundary of a polyhedron. This problem usually appears in polyhedral approximations of CAD objects, whose boundaries are described using curved entities of higher leve...

Despite extensive study over the last four decades and numerous applications, no I/O-efficient algorithm is known for the union-find problem. In this paper we present an I/O-efficient algorithm for the batched (off-line) version of the union-find problem. Given any sequence of N union and find operations, where each union operation joins two distinct sets, our algorithm uses O(SORT(N)) = O ( N B log M/B N I/Os, where M is the memory size and B is the disk block size. This bound is asymptotically optimal in the worst case. If there are union operations that join a set with itself, our algorithm uses O(SORT(N) + MST(N)) I/Os, where MST(N) is the number of I/Os needed to compute the minimum spanning tree of a graph with N edges. We also describe a simple and practical O(SORT(N) log ( N M))-I/O algorithm for this problem, which we have implemented. We are interested in the union-find problem because of its applications in terrain analysis. A terrain can be abstracted as a height function defined over R2, and many problems that deal with such functions require a union-find data structure. With the emergence of modern mapping technologies, huge amount of elevation data is being generated that is too large to fit in memory, thus I/O-efficient algorithms are needed to process this data efficiently. In this paper, we study two terrain-analysis problems that benefit from a union-find data structure: (i) computing topological persistence and (ii) constructing the contour tree. We give the first O(SORT(N))-I/O algorithms for these two problems, assuming that the input terrain is represented as a triangular mesh with N vertices. Finally, we report some preliminary experimental results, showing that our algorithms give order-ofmagnitude improvement over previous methods on large data sets that do not fit in memory. 1

Abstract. In this paper we consider the dictionary problem in the scalable distributed data structure paradigm introduced by Litwin, Neimat and Schneider and analyze costs for insert and exact searches in an amortized framework. We show that both for the 1-dimensional and the kdimensional case insert and exact searches have an amortized almost constant costs, namely O � log (1+A) n � messages, where n is the total number of servers of the structure, b is the capacity of each server, and A = b. Considering that A is a large value in real applications, in the 2 order of thousands, we can assume to have a constant cost in real distributed structures. Only worst case analysis has been previously considered and the almost constant cost for the amortized analysis of the general k-dimensional case appears to be very promising in the light of the well known difficulties in proving optimal worst case bounds for k-dimensions.

DiscFinder is a scalable approach for identifying large-scale astronomical structures, such as galaxy clusters, in massive observation and simulation astrophysics datasets. It is designed to operate on datasets with tens of billions of astronomical objects, even in the case when the dataset is much larger than the aggregate memory of compute cluster used for the processing. 1.

In this paper we present a saturation-based decision procedure for basic hybrid logic extended with the universal modality. Termination of the procedure is guaranteed by constraints that are conceptually simpler than the loop-checks commonly used with related tableau-based decision methods in that they do not rely on the order in which new formulas are introduced. At the same time, our constraints allow us to limit the worst-case asymptotic complexity of the procedure more tightly than it seems to be possible for methods using conventional loop-checks. The procedure is based on Hardt and Smolka’s higher-order formulation of hybrid logic [10]. 1

Morphological attribute filters have not previously been parallelized mainly because they are both global and nonseparable. We propose a parallel algorithm that achieves efficient parallelism for a large class of attribute filters, including attribute openings, closings, thinnings, and thickenings, based on Salembier’s Max-Trees and Min-trees. The image or volume is first partitioned in multiple slices. We then compute the Max-trees of each slice using any sequential Max-Tree algorithm. Subsequently, the Max-trees of the slices can be merged to obtain the Max-tree of the image. A C-implementation yielded good speed-ups on both a 16-processor MIPS 14000 parallel machine and a dual-core Opteron-based machine. It is shown that the speed-up of the parallel algorithm is a direct measure of the gain with respect to the sequential algorithm used. Furthermore, the concurrent algorithm shows a speed gain of up to 72 percent on a single-core processor due to reduced cache thrashing.

The problem of checking or optimally simplifying bisimulation formulas is likely to be computationally very hard. We take a different view at the problem: we set out to define a very fast algorithm, and then see what we can obtain. Sometimes our algorithm can simplify a formula perfectly, sometimes it cannot. However, the algorithm is extremely fast and can, therefore, be added to formula-based bisimulation model checkers at practically no cost. When the formula can be simplified by our algorithm, this can have a dramatic positive effect on the better, but also more time consuming, theorem provers which will finish the job. 1 Introduction The need for validity checking or optimal simplification of first order bisimulation formulas has arisen from recent work on symbolic bisimulation checking of value-passing calculi [4, 9, 15]. The NP-completeness of checking satisfiability of propositional formulas [3] implies that validity checking of that class of formulas is co-NP complete. Addit...

Contents 1 Introduction 3 2 Models of computation 6 3 The Set Union Problem 9 4 The Worst--Case Time Complexity of a Single Operation 15 5 The Set Union Problem with Deunions 18 6 Split and the Set Union Problem on Intervals 22 7 The Set Union Problem with Unlimited Backtracking 26 1 Introduction An equivalence relation on a finite set S is a binary relation that is reflexive symmetric and transitive. That is, for s; t and u in S, we have that sRs, if sRt then tRs, and if sRt and tRu then sRu. Set S is partitioned by R into equivalence classes where each class cointains all and only the elements that obey R pairwise. Many computational problems involve representing, modifying and tracking the evolution of equivalenc

Moving Objects Databases (MOD) have gained popularity as a subject for research due to the latest developments in the positioning technologies and mobile networking. Analysis of mobility data can be used to discover and deliver knowledge that can enhance public welfare. For instance, a study of traffic patterns and congestion trends can reveal some information that can be used to improve routing and scheduling of public transit vehicles. To enable analysis of mobility data, a MOD must be published. However, publication of MOD can pose a threat to location privacy of users, whose movement is recorded in the database. A user’s location at one or more time points can be publicly available prior to the publication of MOD. Based on this public knowledge, an attacker can potentially find the user’s entire trajectory and learn his/her positions at other time points, which constitutes privacy breach. This public knowledge is a user’s quasi-identifier (QID), i.e. a set of attributes that can uniquely identify the user’s trajectory in the published database. We argue that unlike in relational microdata, where all

an allocation of advanced computing resources supported by the NSF and the TeraGrid Advanced Support Program. The computations were performed on on Kraken at the National Institute for Computational Sciences (NICS)