Related papers: Tree congruence: quantifying similarity between de…
Circular-arc graphs are intersection graphs of arcs on the circle. The aim of our work is to present a polynomial time algorithm testing whether two circular-arc graphs are isomorphic. To accomplish our task we construct decomposition…
Motivated from the study of eccentricity, center, and sum of eccentricities in graphs and trees, we introduce several new distance-based global and local functions based on the smallest distance from a vertex to some leaf (called the…
Tree-width is an invaluable tool for computational problems on graphs. But often one would like to compute on other kinds of objects (e.g. decorated graphs or even algebraic structures) where there is no known tree-width analogue. Here we…
Measuring the importance of nodes in a network with a centrality measure is a core task in any network application. There are many measures available and it is speculated that many encode similar information. We give an explicit non-linear…
Comprehensive evaluation of machine learning models is the key to make sure that they perform as robustly and consistently as desired. In order to summarize the experimental results and pick a winner, Critical Difference (CD) diagrams are…
High-dimensional compositional covariates, often derived from count data, are subject to measurement error and are frequently analyzed after aggregation along a prespecified tree to improve interpretability in applications such as…
The similarity of graph structures, such as Meaning Representations (MRs), is often assessed via structural matching algorithms, such as Smatch (Cai and Knight, 2013). However, Smatch involves a combinatorial problem that suffers from…
The problem of realizing finite metric spaces in terms of weighted graphs has many applications. For example, the mathematical and computational properties of metrics that can be realized by trees have been well-studied and such research…
Centrality measures are widely used to assign importance to graph-structured data. Recently, understanding the principles of such measures has attracted a lot of attention. Given that measures are diverse, this research has usually focused…
Topological data analysis is an approach to study shape of a data set by means of topology. Its main object of study is the persistence diagram, which represents the topological features of the data set at different spatial resolutions.…
We investigated testing the likelihood of a phylogenetic tree by comparison to its subtree pruning and regrafting (SPR) neighbors, with or without re-optimizing branch lengths. This is inspired by aspects of Bayesian significance tests, and…
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…
This paper offers a new authentication algorithm based on image matching of nano-resolution visual identifiers with tree-shaped patterns. The algorithm includes image-to-tree conversion by greedy extraction of the fractal pattern skeleton…
In the $L_0$ Fitting Tree Metrics problem, we are given all pairwise distances among the elements of a set $V$ and our output is a tree metric on $V$. The goal is to minimize the number of pairwise distance disagreements between the input…
Algorithms for decentralized optimization and learning rely on local optimization steps coupled with combination steps over a graph. Recent works have demonstrated that using a time-varying sequence of matrices that achieves finite-time…
In this paper we study functions on the interval that have the same persistent homology. By introducing an equivalence relation modeled after topological conjugacy, which we call graph-equivalence, a precise enumeration of functions with…
Tree shape statistics, particularly measures of tree (im)balance, play an important role in the analysis of the shape of phylogenetic trees. With applications ranging from testing evolutionary models to studying the impact of fertility…
We revisit the use of probabilistic values, which include the well-known Shapley and Banzhaf values, to rank features for explaining the local predicted values of decision trees. The quality of feature rankings is typically assessed with…
Sparse shortcuttings of trees -- equivalently, sparse 1-spanners for tree metrics with bounded hop-diameter -- have been studied extensively (under different names and settings), since the pioneering works of [Yao82, Cha87, AS87, BTS94],…
In this work we define a metric structure to compare functions defined on different merge trees. The metric introduced possesses some stability properties, which we illustrate within a standard topological data analysis (TDA) framework, and…