Engineering Top-Down Weight-Balanced Trees

Weight-balanced trees are a popular form of self-balancing binary search trees. Their popularity is due to desirable guarantees, for example regarding the required work to balance annotated trees. While usual weight-balanced trees perform their balancing operations in a bottom-up fashion after a modification to the tree is completed, there exists a top-down variant which performs these balancing operations during descend. This variant has so far received only little attention. We provide an in-depth analysis and engineering of these top-down weight-balanced trees, demonstrating their superior performance. We also gaining insights into how the balancing parameters necessary for a weight-balanced tree should be chosen - with the surprising observation that it is often beneficial to choose parameters which are not feasible in the sense of the correctness proofs for the rebalancing algorithm.Comment: Accepted for publication at ALENEX 202

Rank, select and access in grammar-compressed strings

Given a string $S$ of length $N$ on a fixed alphabet of $\sigma$ symbols, a grammar compressor produces a context-free grammar $G$ of size $n$ that generates $S$ and only $S$. In this paper we describe data structures to support the following operations on a grammar-compressed string: \mbox{rank}_c(S,i) (return the number of occurrences of symbol $c$ before position $i$ in $S$); \mbox{select}_c(S,i) (return the position of the $i$th occurrence of $c$ in $S$); and \mbox{access}(S,i,j) (return substring $S[i,j]$). For rank and select we describe data structures of size $O(n\sigma\log N)$ bits that support the two operations in $O(\log N)$ time. We propose another structure that uses $O(n\sigma\log (N/n)(\log N)^{1+\epsilon})$ bits and that supports the two queries in $O(\log N/\log\log N)$, where $\epsilon>0$ is an arbitrary constant. To our knowledge, we are the first to study the asymptotic complexity of rank and select in the grammar-compressed setting, and we provide a hardness result showing that significantly improving the bounds we achieve would imply a major breakthrough on a hard graph-theoretical problem. Our main result for access is a method that requires $O(n\log N)$ bits of space and $O(\log N+m/\log_\sigma N)$ time to extract $m=j-i+1$ consecutive symbols from $S$. Alternatively, we can achieve $O(\log N/\log\log N+m/\log_\sigma N)$ query time using $O(n\log (N/n)(\log N)^{1+\epsilon})$ bits of space. This matches a lower bound stated by Verbin and Yu for strings where $N$ is polynomially related to $n$.Comment: 16 page

Customer churn prediction in telecom using machine learning and social network analysis in big data platform

Customer churn is a major problem and one of the most important concerns for large companies. Due to the direct effect on the revenues of the companies, especially in the telecom field, companies are seeking to develop means to predict potential customer to churn. Therefore, finding factors that increase customer churn is important to take necessary actions to reduce this churn. The main contribution of our work is to develop a churn prediction model which assists telecom operators to predict customers who are most likely subject to churn. The model developed in this work uses machine learning techniques on big data platform and builds a new way of features' engineering and selection. In order to measure the performance of the model, the Area Under Curve (AUC) standard measure is adopted, and the AUC value obtained is 93.3%. Another main contribution is to use customer social network in the prediction model by extracting Social Network Analysis (SNA) features. The use of SNA enhanced the performance of the model from 84 to 93.3% against AUC standard. The model was prepared and tested through Spark environment by working on a large dataset created by transforming big raw data provided by SyriaTel telecom company. The dataset contained all customers' information over 9 months, and was used to train, test, and evaluate the system at SyriaTel. The model experimented four algorithms: Decision Tree, Random Forest, Gradient Boosted Machine Tree "GBM" and Extreme Gradient Boosting "XGBOOST". However, the best results were obtained by applying XGBOOST algorithm. This algorithm was used for classification in this churn predictive model.Comment: 24 pages, 14 figures. PDF https://rdcu.be/budK