相关论文: The Influence of Dimensions on the Complexity of C…

In this paper, we revisit the problem of indexing multi-dimensional data in memory for the efficient support of multi-dimensional range queries and nearest neighbor queries. This is a classic problem in main-memory databases, where there is…

We revisit binary decision trees from the perspective of partitions of the data. We introduce the notion of partitioning function, and we relate it to the growth function and to the VC dimension. We consider three types of features:…

Inferring a decision tree from a given dataset is one of the classic problems in machine learning. This problem consists of buildings, from a labelled dataset, a tree such that each node corresponds to a class and a path between the tree…

Decision trees are renowned for their ability to achieve high predictive performance while remaining interpretable, especially on tabular data. Traditionally, they are constructed through recursive algorithms, where they partition the data…

A resolving set $S$ of a graph $G$ is a subset of its vertices such that no two vertices of $G$ have the same distance vector to $S$. The Metric Dimension problem asks for a resolving set of minimum size, and in its decision form, a…

The palindromic tree (a.k.a. eertree) for a string $S$ of length $n$ is a tree-like data structure that represents the set of all distinct palindromic substrings of $S$, using $O(n)$ space [Rubinchik and Shur, 2018]. It is known that, when…

Given a set S of n \geq d points in general position in R^d, a random hyperplane split is obtained by sampling d points uniformly at random without replacement from S and splitting based on their affine hull. A random hyperplane search tree…

In the first paper (part I) of this series of two, we introduce four novel definitions of the ODT problems: three for size-constrained trees and one for depth-constrained trees. These definitions are stated unambiguously through executable…

The problem of constructing optimal factoring automata arises in the context of unification factoring for the efficient execution of logic programs. Given an ordered set of $n$ strings of length $m$, the problem is to construct a trie-like…

Label tree-based algorithms are widely used to tackle multi-class and multi-label problems with a large number of labels. We focus on a particular subclass of these algorithms that use probabilistic classifiers in the tree nodes. Examples…

Data-driven algorithm design is a paradigm that uses statistical and machine learning techniques to select from a class of algorithms for a computational problem an algorithm that has the best expected performance with respect to some…

This paper deals with computation trees over an arbitrary structure consisting of a set along with collections of functions and predicates that are defined on it. It is devoted to the comparative analysis of three parameters of problems…

Optimal motion planning involves obstacles avoidance where path planning is the key to success in optimal motion planning. Due to the computational demands, most of the path planning algorithms can not be employed for real-time based…

Random dimensionality reduction is a versatile tool for speeding up algorithms for high-dimensional problems. We study its application to two clustering problems: the facility location problem, and the single-linkage hierarchical clustering…

In many situations, the choice of an adequate similarity measure or metric on the feature space dramatically determines the performance of machine learning methods. Building automatically such measures is the specific purpose of…

Decision trees are highly interpretable models for solving classification problems in machine learning (ML). The standard ML algorithms for training decision trees are fast but generate suboptimal trees in terms of accuracy. Other discrete…

Random Forests are one of the most popular classifiers in machine learning. The larger they are, the more precise is the outcome of their predictions. However, this comes at a cost: their running time for classification grows linearly with…

Real-life machine learning problems exhibit distributional shifts in the data from one time to another or from one place to another. This behavior is beyond the scope of the traditional empirical risk minimization paradigm, which assumes…

Despite the latest prevailing success of deep neural networks (DNNs), several concerns have been raised against their usage, including the lack of intepretability the gap between DNNs and other well-established machine learning models, and…

In this paper, we study three algorithmic problems involving computation trees: the optimization, solvability, and satisfiability problems. The solvability problem is concerned with recognizing computation trees that solve problems. The…