Generic Subsequence Matching Framework: Modularity, Flexibility, Efficiency

Subsequence matching has appeared to be an ideal approach for solving many problems related to the fields of data mining and similarity retrieval. It has been shown that almost any data class (audio, image, biometrics, signals) is or can be represented by some kind of time series or string of symbols, which can be seen as an input for various subsequence matching approaches. The variety of data types, specific tasks and their partial or full solutions is so wide that the choice, implementation and parametrization of a suitable solution for a given task might be complicated and time-consuming; a possibly fruitful combination of fragments from different research areas may not be obvious nor easy to realize. The leading authors of this field also mention the implementation bias that makes difficult a proper comparison of competing approaches. Therefore we present a new generic Subsequence Matching Framework (SMF) that tries to overcome the aforementioned problems by a uniform frame that simplifies and speeds up the design, development and evaluation of subsequence matching related systems. We identify several relatively separate subtasks solved differently over the literature and SMF enables to combine them in straightforward manner achieving new quality and efficiency. This framework can be used in many application domains and its components can be reused effectively. Its strictly modular architecture and openness enables also involvement of efficient solutions from different fields, for instance efficient metric-based indexes. This is an extended version of a paper published on DEXA 2012.Comment: This is an extended version of a paper published on DEXA 201

Designing optimal- and fast-on-average pattern matching algorithms

Given a pattern $w$ and a text $t$, the speed of a pattern matching algorithm over $t$ with regard to $w$, is the ratio of the length of $t$ to the number of text accesses performed to search $w$ into $t$. We first propose a general method for computing the limit of the expected speed of pattern matching algorithms, with regard to $w$, over iid texts. Next, we show how to determine the greatest speed which can be achieved among a large class of algorithms, altogether with an algorithm running this speed. Since the complexity of this determination make it impossible to deal with patterns of length greater than 4, we propose a polynomial heuristic. Finally, our approaches are compared with 9 pre-existing pattern matching algorithms from both a theoretical and a practical point of view, i.e. both in terms of limit expected speed on iid texts, and in terms of observed average speed on real data. In all cases, the pre-existing algorithms are outperformed

Planar Object Tracking in the Wild: A Benchmark

Planar object tracking is an actively studied problem in vision-based robotic applications. While several benchmarks have been constructed for evaluating state-of-the-art algorithms, there is a lack of video sequences captured in the wild rather than in constrained laboratory environment. In this paper, we present a carefully designed planar object tracking benchmark containing 210 videos of 30 planar objects sampled in the natural environment. In particular, for each object, we shoot seven videos involving various challenging factors, namely scale change, rotation, perspective distortion, motion blur, occlusion, out-of-view, and unconstrained. The ground truth is carefully annotated semi-manually to ensure the quality. Moreover, eleven state-of-the-art algorithms are evaluated on the benchmark using two evaluation metrics, with detailed analysis provided for the evaluation results. We expect the proposed benchmark to benefit future studies on planar object tracking.Comment: Accepted by ICRA 201

On the asymptotic and practical complexity of solving bivariate systems over the reals

This paper is concerned with exact real solving of well-constrained, bivariate polynomial systems. The main problem is to isolate all common real roots in rational rectangles, and to determine their intersection multiplicities. We present three algorithms and analyze their asymptotic bit complexity, obtaining a bound of \sOB(N^{14}) for the purely projection-based method, and \sOB(N^{12}) for two subresultant-based methods: this notation ignores polylogarithmic factors, where $N$ bounds the degree and the bitsize of the polynomials. The previous record bound was \sOB(N^{14}). Our main tool is signed subresultant sequences. We exploit recent advances on the complexity of univariate root isolation, and extend them to sign evaluation of bivariate polynomials over two algebraic numbers, and real root counting for polynomials over an extension field. Our algorithms apply to the problem of simultaneous inequalities; they also compute the topology of real plane algebraic curves in \sOB(N^{12}), whereas the previous bound was \sOB(N^{14}). All algorithms have been implemented in MAPLE, in conjunction with numeric filtering. We compare them against FGB/RS, system solvers from SYNAPS, and MAPLE libraries INSULATE and TOP, which compute curve topology. Our software is among the most robust, and its runtimes are comparable, or within a small constant factor, with respect to the C/C++ libraries. Key words: real solving, polynomial systems, complexity, MAPLE softwareComment: 17 pages, 4 algorithms, 1 table, and 1 figure with 2 sub-figure

A Generic Approach to Searching for Jacobians

We consider the problem of finding cryptographically suitable Jacobians. By applying a probabilistic generic algorithm to compute the zeta functions of low genus curves drawn from an arbitrary family, we can search for Jacobians containing a large subgroup of prime order. For a suitable distribution of curves, the complexity is subexponential in genus 2, and O(N^{1/12}) in genus 3. We give examples of genus 2 and genus 3 hyperelliptic curves over prime fields with group orders over 180 bits in size, improving previous results. Our approach is particularly effective over low-degree extension fields, where in genus 2 we find Jacobians over F_{p^2) and trace zero varieties over F_{p^3} with near-prime orders up to 372 bits in size. For p = 2^{61}-1, the average time to find a group with 244-bit near-prime order is under an hour on a PC.Comment: 22 pages, to appear in Mathematics of Computatio

Privacy-Preserving Genetic Relatedness Test

An increasing number of individuals are turning to Direct-To-Consumer (DTC) genetic testing to learn about their predisposition to diseases, traits, and/or ancestry. DTC companies like 23andme and Ancestry.com have started to offer popular and affordable ancestry and genealogy tests, with services allowing users to find unknown relatives and long-distant cousins. Naturally, access and possible dissemination of genetic data prompts serious privacy concerns, thus motivating the need to design efficient primitives supporting private genetic tests. In this paper, we present an effective protocol for privacy-preserving genetic relatedness test (PPGRT), enabling a cloud server to run relatedness tests on input an encrypted genetic database and a test facility's encrypted genetic sample. We reduce the test to a data matching problem and perform it, privately, using searchable encryption. Finally, a performance evaluation of hamming distance based PP-GRT attests to the practicality of our proposals.Comment: A preliminary version of this paper appears in the Proceedings of the 3rd International Workshop on Genome Privacy and Security (GenoPri'16