相关论文: Representability of forests via generalized subtou…

Geometric modeling by constraints leads to large systems of algebraic equations. This paper studies bipartite graphs underlaid by systems of equations. It shows how these graphs make possible to polynomially decompose these systems into…

Given a tree $T$, its path polytope is the convex hull of the edge indicator vectors for the paths between any two distinct leaves in $T$. These polytopes arise naturally in polyhedral geometry and applications, such as phylogenetics,…

Answering connectivity queries in real algebraic sets is a fundamental problem in effective real algebraic geometry that finds many applications in e.g. robotics where motion planning issues are topical. This computational problem is…

Deep Learning models enjoy considerable success in Natural Language Processing. While deep architectures produce useful representations that lead to improvements in various tasks, they are often difficult to interpret. This makes the…

We study graph estimation and density estimation in high dimensions, using a family of density estimators based on forest structured undirected graphical models. For density estimation, we do not assume the true distribution corresponds to…

Ensemble models (bagging and gradient-boosting) of relational decision trees have proved to be one of the most effective learning methods in the area of probabilistic logic models (PLMs). While effective, they lose one of the most important…

Decision Trees have remained a popular machine learning method for tabular datasets, mainly due to their interpretability. However, they lack the expressiveness needed to handle highly nonlinear or unstructured datasets. Motivated by recent…

Trees can accelerate queries that search or aggregate values over large collections. They achieve this by storing metadata that enables quick pruning (or inclusion) of subtrees when predicates on that metadata can prove that none (or all)…

Wavelet trees are widely used in the representation of sequences, permutations, text collections, binary relations, discrete points, and other succinct data structures. We show, however, that this still falls short of exploiting all of the…

The generalized maximum-entropy sampling problem (GMESP) is to select an order-$s$ principal submatrix from an order-$n$ covariance matrix, to maximize the product of its $t$ greatest eigenvalues, $0<t\leq s <n$. Introduced more than 25…

We consider a special case of the generalized minimum spanning tree problem (GMST) and the generalized travelling salesman problem (GTSP) where we are given a set of points inside the integer grid (in Euclidean plane) where each grid cell…

Decompositions of networks are useful not only for structural exploration. They also have implications and use in analysis and computational solution of processes (such as the Ising model, percolation, SIR model) running on a given network.…

In several domains, data objects can be decomposed into sets of simpler objects. It is then natural to represent each object as the set of its components or parts. Many conventional machine learning algorithms are unable to process this…

In the context of algorithm theory, various studies have been conducted on spanning trees with desirable properties. In this paper, we consider the \textsc{Minimum Cover Spanning Tree} problem (MCST for short). Given a graph $G$ and a…

We present a general bijective approach to planar hypermaps with two main results. First we obtain unified bijections for all classes of maps or hypermaps defined by face-degree constraints and girth constraints. To any such class we…

We study approaches for the exact solution of the \NP--hard minimum spanning tree problem under conflict constraints. Given a graph $G(V,E)$ and a set $C \subset E \times E$ of conflicting edge pairs, the problem consists of finding a…

Boosted trees is a dominant ML model, exhibiting high accuracy. However, boosted trees are hardly intelligible, and this is a problem whenever they are used in safety-critical applications. Indeed, in such a context, rigorous explanations…

We introduce the notion of quota trees in directed graphs. Given a nonnegative integer ``quota'' for each vertex of a directed multigraph $G$, a quota tree is an immersed rooted tree which hits each vertex of $G$ the prescribed number of…

Bi-level optimisation problems have gained increasing interest in the field of combinatorial optimisation in recent years. With this paper, we start the runtime analysis of evolutionary algorithms for bi-level optimisation problems. We…

Given a graph $G=(V,E)$, the minimum branch vertices problem consists in finding a spanning tree $T=(V,E')$ of $G$ minimizing the number of vertices with degree greater than two. We consider a simple combinatorial lower bound for the…