Related papers: A High Quartets Distance Construction

We address the maximum size of binary codes and binary constant weight codes with few distances. Previous works established a number of bounds for these quantities as well as the exact values for a range of small code lengths. As our main…

Let $T$ be a random tree taken uniformly at random from the family of labelled trees on $n$ vertices. In this note, we provide bounds for $c(n)$, the number of sub-trees of $T$ that hold asymptotically almost surely. With computer support…

Plane increasing trees are rooted labeled trees embedded into the plane such that the sequence of labels is increasing on any branch starting at the root. Relaxed binary trees are a subclass of unlabeled directed acyclic graphs. We…

Due to hybridization events in evolution, studying two different genes of a set of species may yield two related but different phylogenetic trees for the set of species. In this case, we want to measure the dissimilarity of the two trees.…

This paper considers the enumeration of trees avoiding a contiguous pattern. We provide an algorithm for computing the generating function that counts n-leaf binary trees avoiding a given binary tree pattern t. Equipped with this counting…

Edit distance between trees is a natural generalization of the classical edit distance between strings, in which the allowed elementary operations are contraction, uncontraction and relabeling of an edge. Demaine et al. [ACM Trans. on…

Trees are useful entities allowing to model data structures and hierarchical relationships in networked decision systems ubiquitously. An ordered tree is a rooted tree where the order of the subtrees (children) of a node is significant. In…

Alternative novel measures of the distance between any two partitions of a n-set are proposed and compared, together with a main existing one, namely 'partition-distance' D(.,.). The comparison achieves by checking their restriction to…

We give a simple formula for the number of hypertrees with $k$ hyperedges of given sizes and $n+1$ labelled vertices with prescribed degrees. A slight generalization of this formula counts labelled bipartite trees with prescribed degrees in…

Between the leaves and the nodes of a complete binary tree, a separate parent-child-sister hierarchy is employed independent of the parent-child-sister hierarchy used for the rest of the tree. Two different versions of such a local…

Phylogenetic trees are frequently used to model evolution. Such trees are typically reconstructed from data like DNA, RNA, or protein alignments using methods based on criteria like maximum parsimony (amongst others). Maximum parsimony has…

This paper tightens the best known analysis of Hein's 1989 algorithm to infer the topology of a weighted tree based on the lengths of paths between its leaves. It shows that the number of length queries required for a degree-$k$ tree of $n$…

Uniform cost-distance Steiner trees minimize the sum of the total length and weighted path lengths from a dedicated root to the other terminals. They are applied when the tree is intended for signal transmission, e.g. in chip design or…

A fundamental problem in network science is the normalization of the topological or physical distance between vertices, that requires understanding the range of variation of the unnormalized distances. Here we investigate the limits of the…

Tree edit distance is a well-studied measure of dissimilarity between rooted trees with node labels. It can be computed in $O(n^3)$ time [Demaine, Mozes, Rossman, and Weimann, ICALP 2007], and fine-grained hardness results suggest that the…

We give a combinatorial proof of a recent result of B\'ona by constructing a bijection from the set of all neighbors of leaves of increasing trees of size $n$ to the set of derangements of length $n$.

The path-difference metric is one of the oldest distances for the comparison of fully resolved phylogenetic trees, but its statistical properties are still quite unknown. In this paper we compute the mean value of the square of the…

Pairwise ordered tree alignment are combinatorial objects that appear in RNA secondary structure comparison. However, the usual representation of tree alignments as supertrees is ambiguous, i.e. two distinct supertrees may induce identical…

Recursive partitioning is the core of several statistical methods including CART, random forest, and boosted trees. Despite the popularity of tree based methods, to date, there did not exist methods for combining multiple trees into a…

Alphabetic codes and binary search trees are combinatorial structures that abstract search procedures in ordered sets endowed with probability distributions. In this paper, we design new linear-time algorithms to construct alphabetic codes,…