Related papers: Monadic Datalog Containment on Trees
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…
We show how a collection of Euler-tour trees for a forest on $n$ vertices can be stored in $2 n + o (n)$ bits such that simple queries take constant time, more complex queries take logarithmic time and updates take polylogarithmic amortized…
Many discrete mathematics problems in phylogenetics are defined in terms of the relative labeling of pairs of leaf-labeled trees. These relative labelings are naturally formalized as tanglegrams, which have previously been an object of…
Regular tree grammars and regular path expressions constitute core constructs widely used in programming languages and type systems. Nevertheless, there has been little research so far on reasoning frameworks for path expressions where node…
Embeddings of graphs into distributions of trees that preserve distances in expectation are a cornerstone of many optimization algorithms. Unfortunately, online or dynamic algorithms which use these embeddings seem inherently randomized and…
Motivated by an application in computational topology, we consider a novel variant of the problem of efficiently maintaining dynamic rooted trees. This variant requires merging two paths in a single operation. In contrast to the standard…
We introduce a tree-based formulation for the minimum-cost multi-commodity flow problem that addresses large-scale instances. The method decomposes the source-based model by representing flows as convex combinations of trees rooted at…
Tree-child networks are a recently-described class of directed acyclic graphs that have risen to prominence in phylogenetics (the study of evolutionary trees and networks). Although these networks have a number of attractive mathematical…
Graham and Sloane proposed in 1980 a conjecture stating that every tree has a harmonious labelling, a graph labelling closely related to additive base. Very limited results on this conjecture are known. In this paper, we proposed a…
The problem of comparing trees representing the evolutionary histories of cancerous tumors has turned out to be crucial, since there is a variety of different methods which typically infer multiple possible trees. A departure from the…
In a temporal forest each edge has an associated set of time labels that specify the time instants in which the edges are available. A temporal path from vertex $u$ to vertex $v$ in the forest is a selection of a label for each edge in the…
Combinatorial trees can be used to represent genealogies of asexual individuals. These individuals can be endowed with birth and death times, to obtain a so-called `chronological tree'. In this work, we are interested in the continuum…
Extreme classification problems are multiclass and multilabel classification problems where the number of outputs is so large that straightforward strategies are neither statistically nor computationally viable. One strategy for dealing…
Reinforcement learning techniques achieved human-level performance in several tasks in the last decade. However, in recent years, the need for interpretability emerged: we want to be able to understand how a system works and the reasons…
We give a representation for labeled ordered trees that supports labeled queries such as finding the i-th ancestor of a node with a given label. Our representation is succinct, namely the redundancy is small-o of the optimal space for…
For an undirected graph G, we consider the following problems: given a fixed graph H, can we partition the vertices of G into two non-empty sets A and B such that neither the induced graph G[A] nor G[B] contain H (i) as a subgraph? (ii) as…
Random forests and, more generally, (decision\nobreakdash-)tree ensembles are widely used methods for classification and regression. Recent algorithmic advances allow to compute decision trees that are optimal for various measures such as…
Classically, planning tasks are studied as a two-step process: plan creation and plan execution. In situations where plan creation is slow (for example, due to expensive information access or complex constraints), a natural speed-up tactic…
Augmentation makes search trees tremendously more versatile, allowing them to support efficient aggregation queries, order-statistic queries, and range queries in addition to insertion, deletion, and lookup. In this paper, we present the…
We consider the top tree compression scheme introduced by Bille et al. [ICALP 2013] and construct an infinite family of trees on $n$ nodes labeled from an alphabet of size $\sigma$, for which the size of the top DAG is…