Related papers: On vertex covers, matchings and random trees

In spatial networks vertices are arranged in some space and edges may cross. When arranging vertices in a 1-dimensional lattice edges may cross when drawn above the vertex sequence as it happens in linguistic and biological networks. Here…

In this paper, we provide finite sample results to assess the consistency of Generalized Pareto regression trees, as tools to perform extreme value regression. The results that we provide are obtained from concentration inequalities, and…

We consider the Vertex Cover problem in intersection graphs of axis-parallel rectangles on the plane. We present two algorithms: The first is an EPTAS for non-crossing rectangle families, rectangle families $\calR$ where $R_1 \setminus R_2$…

We consider the problem of graph matchability in non-identically distributed networks. In a general class of edge-independent networks, we demonstrate that graph matchability can be lost with high probability when matching the networks…

We propose a principled method for autoencoding with random forests. Our strategy builds on foundational results from nonparametric statistics and spectral graph theory to learn a low-dimensional embedding of the model that optimally…

Coloring is a notoriously hard problem, and even more so in the online setting, where each arriving vertex has to be colored immediately and irrevocably. Already on trees, which are trivially two-colorable, it is impossible to achieve…

This work considers a number of optimization problems and reductive relations between them. The two main problems we are interested in are the \emph{Optimal Decision Tree} and \emph{Set Cover}. We study these two fundamental tasks under…

Tree covering is a technique for decomposing a tree into smaller-sized trees with desirable properties, and has been employed in various succinct data structures. However, significant hurdles stand in the way of a practical implementation…

In this paper, we consider the average size of independent edge sets, also called matchings, in a graph. We characterize the extremal graphs for the average size of matchings in general graphs and trees. In addition, we obtain inequalities…

Tree-based phylogenetic networks, which may be roughly defined as leaf-labeled networks built by adding arcs only between the original tree edges, have elegant properties for modeling evolutionary histories. We answer an open question of…

Increasingly, biologists are constructing evolutionary trees on large numbers of overlapping sets of taxa, and then combining them into a `supertree' that classifies all the taxa. In this paper, we ask how much coverage of the total set of…

Typical performance of approximation algorithms is studied for randomized minimum vertex cover problems. A wide class of random graph ensembles characterized by an arbitrary degree distribution is discussed with some theoretical frameworks.…

In this paper, we consider the problems of enumerating minimal vertex covers and minimal dominating sets with capacity and/or connectivity constraints. We develop polynomial-delay enumeration algorithms for these problems on bounded-degree…

We consider large uniform random trees where we fix for each vertex its degree and height. We prove, under natural conditions of convergence for the profile, that those trees properly renormalized converge. To this end, we study the paths…

This article explores a new type of optimal covering of a complete graph by small cliques of different sizes, namely the minimum covering with minimum excess. In particular, the minimum size of a covering by triples and quadruples with…

It is a classical result that an unrooted tree $T$ having positive real-valued edge lengths and no vertices of degree two can be reconstructed from the induced distance between each pair of leaves. Moreover, if each non-leaf vertex of $T$…

Background: Tree reconciliation problems have long been studied in phylogenetics. A particular variant of the reconciliation problem for a gene tree T and a species tree S assumes that for each interior vertex x of T it is known whether x…

In mathematical phylogenetics, evolutionary relationships are often represented by trees and networks. The latter are typically used whenever the relationships cannot be adequately described by a tree, which happens when so-called…

We investigate algorithms to find the first vertex in large trees generated by either the uniform attachment or preferential attachment model. We require the algorithm to output a set of $K$ vertices, such that, with probability at least…

The relationship between two important problems in tree pattern matching, the largest common subtree and the smallest common supertree problems, is established by means of simple constructions, which allow one to obtain a largest common…