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We present improved learning-augmented algorithms for finding an approximate minimum spanning tree (MST) for points in an arbitrary metric space. Our work follows a recent framework called metric forest completion (MFC), where the learned…
Kondo et al. (DS 2014) proposed methods for computing distances between unordered rooted trees by transforming an instance of the distance computing problem into an instance of the integer programming problem. They showed that the tree edit…
We present a tree structure algorithm for optimal control problems with state constraints. We prove a convergence result for a discrete time approximation of the value function based on a novel formulation of the constrained problem. Then…
The contributions of the paper span theoretical and implementational results. First, we prove that Kd-trees can be extended to spaces in which the distance is measured with an arbitrary Bregman divergence. Perhaps surprisingly, this shows…
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…
In this paper, we present a contraction-guided adaptive partitioning algorithm for improving interval-valued robust reachable set estimates in a nonlinear feedback loop with a neural network controller and disturbances. Based on an estimate…
We study the problem of finding a temporal hybridization network for a set of phylogenetic trees that minimizes the number of reticulations. First, we introduce an FPT algorithm for this problem on an arbitrary set of $m$ binary trees with…
The similarity of two polygonal curves can be measured using the Fr\'echet distance. We introduce the notion of a more robust Fr\'echet distance, where one is allowed to shortcut between vertices of one of the curves. This is a natural…
In many interesting cases the reconstruction of a correct phylogeny is blurred by high mutation rates and/or horizontal transfer events. As a consequence a divergence arises between the true evolutionary distances and the differences…
It is well-understood that different algorithms, training processes, and corpora produce different word embeddings. However, less is known about the relation between different embedding spaces, i.e. how far different sets of embeddings…
In the Steiner Forest problem, we are given a graph with edge lengths, and a collection of demand pairs; the goal is to find a subgraph of least total length such that each demand pair is connected in this subgraph. For over twenty years,…
Nearest neighbor (kNN) methods have been gaining popularity in recent years in light of advances in hardware and efficiency of algorithms. There is a plethora of methods to choose from today, each with their own advantages and…
Comparing and computing distances between phylogenetic trees are important biological problems, especially for models where edge lengths play an important role. The geodesic distance measure between two phylogenetic trees with edge lengths…
Approximate nearest neighbor algorithms are used to speed up nearest neighbor search in a wide array of applications. However, current indexing methods feature several hyperparameters that need to be tuned to reach an acceptable…
Starting with a similarity function between objects, it is possible to define a distance metric on pairs of objects, and more generally on probability distributions over them. These distance metrics have a deep basis in functional analysis,…
We present a comprehensive classical and parameterized complexity analysis of decision tree pruning operations, extending recent research on the complexity of learning small decision trees. Thereby, we offer new insights into the…
Given a set $P$ of terminals in the plane and a partition of $P$ into $k$ subsets $P_1, ..., P_k$, a two-level rectilinear Steiner tree consists of a rectilinear Steiner tree $T_i$ connecting the terminals in each set $P_i$ ($i=1,...,k$)…
Computing optimal transport distances such as the earth mover's distance is a fundamental problem in machine learning, statistics, and computer vision. Despite the recent introduction of several algorithms with good empirical performance,…
In phylogenetic networks, it is desirable to estimate edge lengths in substitutions per site or calendar time. Yet, there is a lack of scalable methods that provide such estimates. Here we consider the problem of obtaining edge length…
Tree structures appear in many fields of the life sciences, including phylogenetics, developmental biology and nucleic acid structures. Trees can be used to represent RNA secondary structures, which directly relate to the function of…