When several objects are moved about by computer ani-marion, there is the chance that they will interpenetrate. This is often an undesired state, particularly if the animation is seeking to model a realistic world. Two issues are involved: detecting that a collision has occurred, and responding to it. The former is fundamentally a kinematic problem, involving the positional relationship of objects in the world. The latter is a dynamic problem, in that it involves predicting behavior according to physical laws. This paper discusses collision detection and response in general, presents two collision detection algorithms, describes modeling collisions of arbi-trary bodies using springs, and presents an analytical collision response algorithm for articulated rigid bodies that conserves linear and angular momentum.

On the basis of regular tree grammars, we present a formal framework for XML schema languages. This framework helps to describe, compare, and implement such schema languages in a rigorous manner. Our main results are as follows: (1) a simple framework to study three classes of tree languages (local, single-type, and regular); (2) classification and comparison of schema languages (DTD, W3C XML Schema, and RELAX NG) based on these classes; (3) efficient document validation algorithms for these classes; and (4) other grammatical concepts and advanced validation algorithms relevant to an XML model (e.g., binarization, derivative-based validation).

Abstract. It is demonstrated that the linear programming problem in d variables and n constraints can be solved in O(n) time when d is fixed. This bound follows from a multidimensional search technique which is applicable for quadratic programming as well. There is also developed an algorithm that is polynomial in both n and d provided d is bounded by a certain slowly growing function of n. Categories and Subject Descriptors: F.2.1 [Analysis of Algorithms and Problem Complexity]: Numerical Algorithms and Problems-computations on matrices; F.2.2 [Analysis of Algorithms and Problem Complexity]: Nonnumerical Algorithms and Problems-geometrical problems and computations; sort-ing and searching; G. 1.6 [Mathematics of Computing]: Optimization-linear programming

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Recent studies on frequent itemset mining algorithms resulted in significant performance improvements. However, if the minimal support threshold is set too low, or the data is highly correlated, the number of frequent itemsets itself can be prohibitively large. To overcome this problem, recently several proposals have been made to construct a concise representation of the frequent itemsets, instead of mining all frequent itemsets. The main goal of this paper is to identify redundancies in the set of all frequent itemsets and to exploit these redundancies in order to reduce the result of a mining operation. We present deduction rules to derive tight bounds on the support of candidate itemsets. We show how the deduction rules allow for constructing a minimal representation for all frequent itemsets. We also present connections between our proposal and recent proposals for concise representations and we give the results of experiments on real-life datasets that show the effectiveness of the deduction rules. In fact, the experiments even show that in many cases, first mining the concise representation, and then creating the frequent itemsets from this representation outperforms existing frequent set mining algorithms.

Abstract. It has become increasingly common to implement discrete-logarithm based public-key protocols on elliptic curves over finite fields. The basic operation is scalar multiplication: taking a given integer multiple of a given point on the curve. The cost of the protocols depends on that of the elliptic scalar multiplication operation. Koblitz introduced a family of curves which admit especially fast elliptic scalar multiplication. His algorithm was later modified by Meier and Staffelbach. We give an improved version of the algorithm which runs 50 % faster than any previous version. It is based on a new kind of representation of an integer, analogous to certain kinds of binary expansions. We also outline further speedups using precomputation and storage.

We analyze the line simplification algorithm reported by Douglas and Peucker and show that its worst case is quadratic in n, the number of input points. Then we give a algorithm, based on path hulls, that uses the geometric structure of the problem to attain a worst-case running time proportional to n log 2 n, which is the best case of the Douglas algorithm. We give complete C code and compare the two algorithms theoretically, by operation counts, and practically, by machine timings.

Mathematical notation evolves like all languages do. As new experiments are made, we sometimes witness the survival of the fittest, sometimes the survival of the most familiar. A healthy conservatism keeps things from changing too rapidly; a healthy radicalism keeps things in tune with new theoretical emphases. Our mathematical language continues to improve, just as “the d-ism of Leibniz overtook the dotage of Newton ” in past centuries [4, Chapter 4]. In 1970 I began teaching a class at Stanford University entitled Concrete Mathematics. The students and I studied how to manipulate formulas in continuous and discrete mathematics, and the problems we investigated were often inspired by new developments in computer science. As the years went by we began to see that a few changes in notational traditions would greatly facilitate our work. The notes from that class have recently been published in a book [15], and as I wrote the final drafts of that book I learned to my surprise that two of the notations we had been using were considerably more useful than I had previously realized. The ideas “clicked ” so well, in fact, that I’ve decided to write this article, blatantly attempting to promote these notations among the mathematicians who have no use for [15]. I hope that within five years everybody will be able to use these notations in published papers without needing to explain what they mean.

Consider a given pattern H and a random text T generated by a Markovian source. We study the frequency of pattern occurrences in a random text when overlapping copies of the pattern are counted separately. We present exact and asymptotic formulae for all moments (including the variance), and probability of r pattern occurrences for three different regions of r, namely: (i) r = O(1), (ii) central limit regime, and (iii) large deviations regime. In order to derive these results, we first construct some language expressions that characterize pattern occurrences which are later translated into generating functions. Finally, we use analytical methods to extract asymptotic behaviors of the pattern frequency. Applications of these results include molecular biology, source coding, synchronization, wireless communications, approximate pattern matching, game theory, and stock market analysis. These findings are of particular interest to information theory (e.g., second-order properties of the re...

Abstract. In a general sequential model of computation, no restrictions are placed on theway in which the computation may proceed, except that parallel operations are not allowed. We show that in such an unrestricted environment TIME.SPACE fl(N2/logN) in order to sort N integers, each in the range [,N]. Key words, time-space tradeoffs, conputational complexity, sorting, time lower bounds, space lower bounds