Enumerating or counting combinatorial objects in graphs is a fundamental data mining task. We consider the problem of assessing the number of Eulerian trails in directed graphs, which is formalized as follows: Given a directed graph \(G=(V,E)\) , with \(|V|=n\) nodes and \(|E|=m\) edges, and an integer \( z \) , assess whether the number \(\#ET(G)\) of Eulerian trails of \( G \) is at least \( z \) . This problem underlies many applications in domains ranging from data privacy to computational biology, data compression, and transportation networks. Practitioners currently address this problem by applying the famous BEST theorem, which, in fact, counts \(\#ET(G)\) instead of just assessing whether \(\#ET(G)\geq z\) . Unfortunately, this solution takes \(\mathcal{O}(n^{\omega})\) arithmetic operations, where \(\omega < 2.373\) denotes the matrix multiplication exponent . Since in most real-world graphs, the number \( m \) of edges is comparable to the number \( n \) of nodes, and \( z \) is moderate in practice, the algorithmic challenge is: Can we solve the problem faster for certain values of \( m \) and \( z \) ? We want to design a combinatorial algorithm for assessing whether \(\#ET(G)\geq z\) , which does not resort to the BEST theorem and has a predictably bounded cost as a function of \( m \) and \( z \) . We address this challenge as follows. We first introduce a general algorithmic scheme for assessing (and enumerating) Eulerian trails. We then introduce a novel tree data structure to reduce the number of iterations in this general scheme. Finally, we complement the above with further combinatorial insight leading to an algorithm with a worst-case bound of \(\mathcal{O}(m\cdot\min\{z,\#ET(G)\})\) time. Our experiments using six benchmark datasets with multi-million edges from different domains show that our implementations are up to two orders of magnitude faster than the BEST theorem, perform much fewer than \(mz\) iterations and scale near-linearly with \( m \) in most cases. Our experiments further show that our implementations bring substantial efficiency benefits in a data privacy application which employs the BEST theorem for the assessment.

Applications in domains ranging from bioinformatics to advertising feature strings (sequences of letters over some alphabet) that come with numerical scores (utilities). The utilities quantify the importance, interest, profit, or risk of the letters occurring at every position of a string. For instance, DNA fragments generated by sequencing machines come with a confidence score per position. Motivated by the ever-increasing rate of generating such data, as well as by their importance in several domains, we introduce Useful String Indexing (USI), a natural generalization of the classic String Indexing problem. Given a string$S$(the text) of length$n$, USI asks for preprocessing$S$into a compact data structure supporting the following queries efficiently: given a shorter string$P$(the pattern), return the global utility$U(P)$of$P$in$S$, where$U$is a function that maps any string$P$to a utility score based on the utilities of the letters of every occurrence of$P$in$S$. Our work also makes the following contributions: (1) We propose a novel and efficient data structure for USI based on finding the top-$K$frequent substrings of$S$. (2) We propose a linear-space data structure that can be used to mine the top-$K$frequent substrings of$S$or to tune the parameters of the USI data structure. (3) We propose a novel space-efficient algorithm for estimating the set of the top-$K$frequent substrings of$S$, thus improving the construction space of the data structure for USI. (4) We show that popular space-efficient top-$K$frequent item mining strategies employed by state-of-the-art algorithms do not smoothly translate from items to substrings. (5) Using billion-letter datasets, we experimentally demonstrate that: (i) our top-$K$frequent substring mining algorithms are accurate and scalable, unlike two state-of-the-art methods; and (ii) our USI data structures are up to 15 times faster in querying than 4 nontrivial baselines while occupying the same space with them.

A string is often provided with numerical scores (utilities) which quantify the importance, interest, profit, or risk of the letters occurring at every position of the string. For example, every DNA fragment produced by modern sequencing machines comes with a confidence score per position. Motivated by the abundance of strings with utilities, we introduce Utility-oriented String Mining (USM), a natural generalization of the classic frequent substring mining problem. Given a string S of length n and a threshold 𝒱, USM asks for every string R whose utility U (R) is at least 𝒱, where U is a function that maps R to a utility score based on the utilities of all letters of every occurrence of R in S. In addition, our work makes the following contributions: (1) We identify a class 𝕌 of utility functions for which USM admits an 𝒪 (n2)-time algorithm. (2) We prove that no listing algorithm solves the USM problem in subquadratic time for every utility function, or even for every function in 𝕌. (3) We propose an 𝒪 (n log n)-time algorithm that solves USM for a class of monotone functions from 𝕌. (4) We design another 𝒪 (n log n)-time algorithm for the same problem that is comparable in runtime but offers drastic space savings in practice when, in addition, a lower bound on the length of the output strings is provided as input. (5) We demonstrate experimentally using publicly available, billion-letter datasets that our algorithms are many times more efficient, in terms of runtime and/or space, compared to an Apriori-like baseline which employs advanced string processing tools.

Data sanitization and frequent pattern mining are two well-studied topics in data mining. Our work initiates a study on the fundamental relation between data sanitization and frequent pattern mining in the context of sequential (string) data. Current methods for string sanitization hide confidential patterns. This, however, may lead to spurious patterns that harm the utility of frequent pattern mining. The main computational problem is to minimize this harm. Our contribution here is as follows. First, we present several hardness results, for different variants of this problem, essentially showing that these variants cannot be solved or even be approximated in polynomial time. Second, we propose integer linear programming formulations for these variants and algorithms to solve them, which work in polynomial time under realistic assumptions on the input parameters. We complement the integer linear programming algorithms with a greedy heuristic. Third, we present an extensive experimental study, using both synthetic and real-world datasets, that demonstrates the effectiveness and efficiency of our methods. Beyond sanitization, the process of missing value replacement may also lead to spurious patterns. Interestingly, our results apply in this context as well.

String data are often disseminated to support applications such as location-based service provision or DNA sequence analysis. This dissemination, however, may expose sensitive patterns that model confidential knowledge (e.g., trips to mental health clinics from a string representing a user’s location history). In this article, we consider the problem of sanitizing a string by concealing the occurrences of sensitive patterns, while maintaining data utility, in two settings that are relevant to many common string processing tasks. In the first setting, we aim to generate the minimal-length string that preserves the order of appearance and frequency of all non-sensitive patterns. Such a string allows accurately performing tasks based on the sequential nature and pattern frequencies of the string. To construct such a string, we propose a time-optimal algorithm, TFS-ALGO. We also propose another time-optimal algorithm, PFS-ALGO, which preserves a partial order of appearance of non-sensitive patterns but produces a much shorter string that can be analyzed more efficiently. The strings produced by either of these algorithms are constructed by concatenating non-sensitive parts of the input string. However, it is possible to detect the sensitive patterns by “reversing” the concatenation operations. In response, we propose a heuristic, MCSR-ALGO, which replaces letters in the strings output by the algorithms with carefully selected letters, so that sensitive patterns are not reinstated, implausible patterns are not introduced, and occurrences of spurious patterns are prevented. In the second setting, we aim to generate a string that is at minimal edit distance from the original string, in addition to preserving the order of appearance and frequency of all non-sensitive patterns. To construct such a string, we propose an algorithm, ETFS-ALGO, based on solving specific instances of approximate regular expression matching. We implemented our sanitization approach that applies TFS-ALGO, PFS-ALGO, and then MCSR-ALGO, and experimentally show that it is effective and efficient. We also show that TFS-ALGO is nearly as effective at minimizing the edit distance as ETFS-ALGO, while being substantially more efficient than ETFS-ALGO.

We initiate a study on the fundamental relation between data sanitization (i.e., the process of hiding confidential information in a given dataset) and frequent pattern mining, in the context of sequential (string) data. Current methods for string sanitization hide confidential patterns introducing, however, a number of spurious patterns that may harm the utility of frequent pattern mining. The main computational problem is to minimize this harm. Our contribution here is twofold. First, we present several hardness results, for different variants of this problem, essentially showing that these variants cannot be solved or even be approximated in polynomial time. Second, we propose integer linear programming formulations for these variants and algorithms to solve them, which work in polynomial time under certain realistic assumptions on the problem parameters.

Stroke is the second single highest cause of death in Europe. The low reliability of animal models in replicating the human disease is one of the most serious problems in the field of medical and pharmaceutical research about stroke. The standard models for the study of ischemic stroke are often poorly predictive as they simulate only partially the human disease. This work aims at investigating animal models with diseases typically associated with the onset of stroke in human patients.