Property testing algorithms are highly efficient algorithms that come with probabilistic accuracy guarantees. For a property P, the goal is to distinguish inputs that have P from those that are far from having P with ...
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Property testing algorithms are highly efficient algorithms that come with probabilistic accuracy guarantees. For a property P, the goal is to distinguish inputs that have P from those that are far from having P with high probability correctly, by querying only a small number of local parts of the input. In property testing on graphs, the distance is measured by the number of edge modifications (additions or deletions) that are necessary to transform a graph into one with property P. Much research has focused on the query complexity of such algorithms, i. e., the number of queries the algorithm makes to the input, but in view of applications, the running time of the algorithm is equally relevant. In (Adler, Harwath, STACS 2018), a natural extension of the bounded degree graph model of property testing to relational databases of bounded degree was introduced, and it was shown that on databases of bounded degree and bounded tree-width, every property that is expressible in monadic second-order logic with counting (CMSO) is testable with constant query complexity and sublinear running time. It remains open whether this can be improved to constant running time. In this article we introduce a new model, which is based on the bounded degree model, but the distance measure allows both edge (tuple) modifications and vertex (element) modifications. We show that every property that is testable in the classical model is testable in our model with the same query complexity and running time, but the converse is not true. Our main theorem shows that on databases of bounded degree and bounded tree-width, every property that is expressible in CMSO is testable with constant query complexity and constant running time in the new model. Our proof methods include the semilinearity of the neighborhood histograms of databases having the property and a result by Alon (Proposition 19.10 in Lovasz, Large networks and graph limits, 2012) that states that for every bounded degree graph G there
Code based cryptosystems often need to encode either a message or a random bitstring into one of fixed length and fixed (Hamming) weight. The lack of an efficient and reliable bijective map presents a problem in build...
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ISBN:
(纸本)9781450379564
Code based cryptosystems often need to encode either a message or a random bitstring into one of fixed length and fixed (Hamming) weight. The lack of an efficient and reliable bijective map presents a problem in building constructions around the said cryptosystems to attain security against active attackers. We present an efficiently computable, bijective function which yields the desired mapping. Furthermore, we delineate how the said function can be computed in constanttime. We experimentally validate the effectiveness and efficiency of our approach, comparing it against the current state of the art solutions, achieving three to four orders of magnitude improvements in computation time, and validate its constant runtime.
In 2008 Nguyen and Onak constructed the first constant-time algorithm for the approximation of the size of the maximum matching in bounded degree graphs. The Borel oracle machinery is a tool that can be used to conver...
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In 2008 Nguyen and Onak constructed the first constant-time algorithm for the approximation of the size of the maximum matching in bounded degree graphs. The Borel oracle machinery is a tool that can be used to convert some statements in Borel graph theory to theorems in the field of constant-timealgorithms. In this paper we illustrate the power of this tool to prove the existence of the above mentioned constant-time approximation algorithm.
A number of applications in computer-aided manufacturing, CAD, and computer-aided geometric design ask for triangulating pieces of material with defects. These tasks are known collectively as constrained triangulation...
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A number of applications in computer-aided manufacturing, CAD, and computer-aided geometric design ask for triangulating pieces of material with defects. These tasks are known collectively as constrained triangulations. Recently, a powerful architecture called the reconfigurable mesh has been proposed: In essence, a reconfigurable mesh consists of a mesh-connected architecture augmented by a dynamically reconfigurable bus system. The main contribution of this paper is to show that the flexibility of the reconfigurable mesh can be exploited for the purpose of obtaining constant-timealgorithms for a number of constrained triangulation problems. These include triangulating a convex planar region containing any constant number of convex holes, triangulating a convex planar region in the presence of a collection of rectangular holes, and triangulating a set of ordered line segments. Specifically, with a collection of O(n) such objects as input, our algorithms run in O(1) time on a reconfigurable mesh of size n x n. To the best of our knowledge, this is the first timeconstanttime solutions to constrained triangulations are reported on this architecture.
Mathematical Morphology (MM) is a general method for image processing based on set theory. The two basic morphological operators are dilation and erosion. From these, several non linear filters have been developed usu...
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Mathematical Morphology (MM) is a general method for image processing based on set theory. The two basic morphological operators are dilation and erosion. From these, several non linear filters have been developed usually with polynomial complexity, and this because the two basic operators depend strongly on the definition of the structural element. Most efforts to improve the algorithm's speed for each operator are based on structural element decomposition and/or efficient codification. A new framework and a theoretical basis toward the construction of fast morphological operators (of zero complexity) for an infinite (countable) family of regular metric spaces are presented in work. The framework is completely defined by the three axioms of metric. The theoretical basis here developed points out properties of some metric spaces and relationships between metric spaces in the same family, just in terms of the properties of the four basic metrics stated in this work. Concepts such as bounds, neighborhoods and contours are also related by the same framework. The presented results, are general in the sense that they cover the most commonly used metrics such as the chamfer, the city block and the chess board metrics. Generalizations and new results related with distances and distance transforms, which in turn are used to develop the morphologic operations in constanttime, in contrast with the polynomial timealgorithms are also given.
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