Simple and Efficient Fully-Functional Succinct Trees

The fully-functional succinct tree representation of Navarro and Sadakane (ACM Transactions on Algorithms, 2014) supports a large number of operations in constant time using $2n+o(n)$ bits. However, the full idea is hard to implement. Only a simplified version with $O(\log n)$ operation time has been implemented and shown to be practical and competitive. We describe a new variant of the original idea that is much simpler to implement and has worst-case time $O(\log\log n)$ for the operations. An implementation based on this version is experimentally shown to be superior to existing implementations

Partial match queries in relaxed K-dt trees

The study of partial match queries on random hierarchical multidimensional data structures dates back to Ph. Flajolet and C. Puech’s 1986 seminal paper on partial match retrieval. It was not until recently that fixed (as opposed to random) partial match queries were studied for random relaxed K-d trees, random standard K-d trees, and random 2-dimensional quad trees. Based on those results it seemed natural to classify the general form of the cost of fixed partial match queries into two families: that of either random hierarchical structures or perfectly balanced structures, as conjectured by Duch, Lau and Martínez (On the Cost of Fixed Partial Queries in K-d trees Algorithmica, 75(4):684–723, 2016). Here we show that the conjecture just mentioned does not hold by introducing relaxed K-dt trees and providing the average-case analysis for random partial match queries as well as some advances on the average-case analysis for fixed partial match queries on them. In fact this cost –for fixed partial match queries– does not follow the conjectured forms.Peer ReviewedPostprint (author's final draft

Runtime Optimizations for Prediction with Tree-Based Models

Tree-based models have proven to be an effective solution for web ranking as well as other problems in diverse domains. This paper focuses on optimizing the runtime performance of applying such models to make predictions, given an already-trained model. Although exceedingly simple conceptually, most implementations of tree-based models do not efficiently utilize modern superscalar processor architectures. By laying out data structures in memory in a more cache-conscious fashion, removing branches from the execution flow using a technique called predication, and micro-batching predictions using a technique called vectorization, we are able to better exploit modern processor architectures and significantly improve the speed of tree-based models over hard-coded if-else blocks. Our work contributes to the exploration of architecture-conscious runtime implementations of machine learning algorithms