Related papers: Limits of Mallows trees
We study search trees with 2-way comparisons (2WCST's), which involve separate less-than and equal-to tests in their nodes, each test having two possible outcomes, yes and no. These trees have a much subtler structure than standard search…
Given a rooted tree and a ranking of its leaves, what is the minimum number of inversions of the leaves that can be attained by ordering the tree? This variation of the problem of counting inversions in arrays originated in mathematical…
We establish limit theorems that describe the asymptotic local and global geometric behaviour of random enriched trees considered up to symmetry. We apply these general results to random unlabelled weighted rooted graphs and uniform random…
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…
Geometry of networks endowed with a causal structure is discussed using the conventional framework of equilibrium statistical mechanics. The popular growing network models appear as particular causal models. We focus on a class of tree…
The last decade brought a significant increase in the amount of data and a variety of new inference methods for reconstructing the detailed evolutionary history of various cancers. This brings the need of designing efficient procedures for…
Computing the rotation distance between two binary trees with $n$ internal nodes efficiently (in $poly(n)$ time) is a long standing open question in the study of height balancing in tree data structures. In this paper, we initiate the study…
We present a complete classification of the deterministic distributed time complexity for a family of graph problems: binary labeling problems in trees. These are locally checkable problems that can be encoded with an alphabet of size two…
Measuring the complexity of tree structures can be beneficial in areas that use tree data structures for storage, communication, and processing purposes. This complexity can then be used to compress tree data structures to their…
The Robinson-Foulds (RF) metric is arguably the most widely used measure of phylogenetic tree similarity, despite its well-known shortcomings: For example, moving a single taxon in a tree can result in a tree that has maximum distance to…
Tree-based networks are a class of phylogenetic networks that attempt to formally capture what is meant by "tree-like" evolution. A given non-tree-based phylogenetic network, however, might appear to be very close to being tree-based, or…
Linear codes are widely studied in coding theory as they have nice applications in distributed storage, combinatorics, lattices, cryptography and so on. Constructing linear codes with desirable properties is an interesting research topic.…
Any Boolean function corresponds with a complete full binary decision tree. This tree can in turn be represented in a maximally compact form as a direct acyclic graph where common subtrees are factored and shared, keeping only one copy of…
Semidirected networks have received interest in evolutionary biology as the appropriate generalization of unrooted trees to networks, in which some but not all edges are directed. Yet these networks lack proper theoretical study. We define…
Motivated by applications to low-rank matrix completion, we give a combinatorial characterization of the independent sets in the algebraic matroid associated to the collection of $m\times n$ rank-2 matrices and $n\times n$ skew-symmetric…
We study the statistics of the Mallows measure on permutations in the limit pioneered by Starr (2009). Our main result is the local central limit theorem for its height function. We also re-derive versions of the law of large numbers and…
Algorithms for learning decision trees often include heuristic local-search operations such as (1) adjusting the threshold of a cut or (2) also exchanging the feature of that cut. We study minimizing the number of classification errors by…
Minimal spanning trees on infinite vertex sets are investigated. A criterion for minimality of a spanning tree having a finite length is obtained, which generalizes the corresponding classical result for finite sets. It is given an analytic…
We provide an $\Omega(n\log n) $ lower bound and an $O(n^2)$ upper bound for the smallest size of rooted binary trees (a.k.a. phylogenetic tree shapes), which are universal for rooted binary trees with $n$ leaves, i.e., contain all of them…
Decision trees are powerful tools for classification and regression that attract many researchers working in the burgeoning area of machine learning. One advantage of decision trees over other methods is their interpretability, which is…