Related papers: On the locality of the Pr\"ufer code
Phylogenetic trees are leaf-labelled trees used to model the evolution of species. Here we explore the practical impact of kernelization (i.e. data reduction) on the NP-hard problem of computing the TBR distance between two unrooted binary…
The rank modulation scheme has been proposed for efficient writing and storing data in non-volatile memory storage. Error-correction in the rank modulation scheme is done by considering permutation codes. In this paper we consider codes in…
We investigate \Delta_n, the distance between randomly selected pairs of nodes among n keys in a random trie, which is a kind of digital tree. Analytical techniques, such as the Mellin transform and an excursion between poissonization and…
The unordered tree edit distance is a natural metric to compute distances between trees without intrinsic child order, such as representations of chemical molecules. While the unordered tree edit distance is MAX SNP-hard in principle, it is…
Temporal sequences of terrains arise in various application areas. To analyze them efficiently, one generally needs a suitable abstraction of the data as well as a method to compare and match them over time. In this paper we consider merge…
T-Duality is a poorly understood symmetry of the space-time fields of string theory that interchanges long and short distances. It is best understood in the context of toroidal compactification where, loosely speaking, radii of the torus…
We show that the Schaeffer's tree for an infinite quadrangulation only changes locally when changing the root of the quadrangulation. This follows from one property of distances in the infinite uniform random quadrangulation.
Given two messages - as linear sequences of letters, it is immediate to determine whether one can be transformed into the other by simple substitution cipher of the letters. On the other hand, if the letters are carried as labels on nodes…
We consider partitions of a point set into two parts, and the lengths of the minimum spanning trees of the original set and of the two parts. If $w(P)$ denotes the length of a minimum spanning tree of $P$, we show that every set $P$ of $n…
Merge trees are fundamental structures in topological data analysis. Interleaving distance is a widely accepted metric for comparing merge trees, with applications in visualization and scientific computing. While a greedy algorithm exists…
Metric learning has the aim to improve classification accuracy by learning a distance measure which brings data points from the same class closer together and pushes data points from different classes further apart. Recent research has…
This paper considers structure learning from data with $n$ samples of $p$ variables, assuming that the structure is a forest, using the Chow-Liu algorithm. Specifically, for incomplete data, we construct two model selection algorithms that…
In this article we investigate the Uniform Spanning Forest ($\mathsf{USF}$) in the nearest-neighbour integer lattice $\mathbf{Z}^{d+1} = \mathbf{Z}\times \mathbf{Z}^d$ with an assignment of conductances that makes the underlying (Network)…
A locally testable code (LTC) is an error-correcting code that has a property-tester. The tester reads $q$ bits that are randomly chosen, and rejects words with probability proportional to their distance from the code. The parameter $q$ is…
A degree sequence is a sequence ${\bf s}=(N_i,i\geq 0)$ of non-negative integers satisfying $1+\sum_i iN_i=\sum_i N_i<\infty$. We are interested in the uniform distribution $\mathbb{P}_{{\bf s}}$ on rooted plane trees whose degree sequence…
We introduce the following natural generalization of trace reconstruction, parameterized by a deletion probability $\delta \in (0,1)$ and length $n$: There is a length $n$ string of probabilities, $S=p_1,\ldots,p_n,$ and each "trace" is…
A projective Reed-Muller (PRM) code, obtained by modifying a (classical) Reed-Muller code with respect to a projective space, is a doubly extended Reed-Solomon code when the dimension of the related projective space is equal to 1. The…
We study a natural analogue of Ulam's problem for random rooted trees distributed according to a Plancherel-type measure. This probability measure is closely related to the classical Plancherel measure on integer partitions. For a…
Many natural language processing (NLP) applications require the computation of similarities between pairs of syntactic or semantic trees. Many researchers have used tree edit distance for this task, but this technique suffers from the…
The problem of comparing probability distributions is at the heart of many tasks in statistics and machine learning. Established comparison methods treat the standard setting that the distributions are supported in the same space. Recently,…