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Neighborhood algorithms may take a considerable percentage of computer time in discrete element methods (DEM). While the sort-and-sweep algorithm is ideal in some ways, as it only deal with particles whose relative positions change in one…
The decision tree is one of the most fundamental programming abstractions. A commonly used type of decision tree is the alphabetic binary tree, which uses (without loss of generality) ``less than'' versus ''greater than or equal to'' tests…
Recently, considerable effort has been put into developing fast algorithms to reconstruct a rooted phylogenetic network that explains two rooted phylogenetic trees and has a minimum number of hybridization vertices. With the standard…
The Gomory-Hu tree, or a cut tree, is a classic data structure that stores minimum $s$-$t$ cuts of an undirected weighted graph for all pairs of nodes $(s,t)$. We propose a new approach for computing the cut tree based on a reduction to the…
Rotation distance between rooted binary trees measures the number of simple operations it takes to transform one tree into another. There are no known polynomial-time algorithms for computing rotation distance. We give an efficient,…
We consider the tree consensus problem, an important problem in bioinformatics. Given a rooted tree $t$ and another tree $T$, one would like to incorporate compatible information from $T$ to $t$. This problem is a subproblem in the tree…
Randomized experiments have been critical tools of decision making for decades. However, subjects can show significant heterogeneity in response to treatments in many important applications. Therefore it is not enough to simply know which…
Reachability analysis is a powerful tool when it comes to capturing the behaviour, thus verifying the safety, of autonomous systems. However, general-purpose methods, such as Hamilton-Jacobi approaches, suffer from the curse of…
The metric space of phylogenetic trees defined by Billera, Holmes, and Vogtmann, which we refer to as BHV space, provides a natural geometric setting for describing collections of trees on the same set of taxa. However, it is sometimes…
In this paper, we introduce a new representation for ordered trees, the weight sequence representation. We then use this to construct new representations for both rooted trees and free trees, namely the canonical weight sequence…
We study learning-augmented binary search trees (BSTs) via Treaps with carefully designed priorities. The result is a simple search tree in which the depth of each item $x$ is determined by its predicted weight $w_x$. Specifically, each…
Survival analysis studies and predicts the time of death, or other singular unrepeated events, based on historical data, while the true time of death for some instances is unknown. Survival trees enable the discovery of complex nonlinear…
We study the complexity of finding communication trees with the lowest possible completion time for rooted, irregular gather and scatter collective communication operations in fully connected, $k$-ported communication networks under a…
The Maximum Agreement Forest (Maf) problem is a well-studied problem in evolutionary biology, which asks for a largest common subforest of a given collection of phylogenetic trees with identical leaf label-set. However, the previous work…
Similarity-based Hierarchical Clustering (HC) is a classical unsupervised machine learning algorithm that has traditionally been solved with heuristic algorithms like Average-Linkage. Recently, Dasgupta reframed HC as a discrete…
In this article we compare the known dynamical polynomial time algorithm for the game-over attack strategy, to that of the brute force approach; of checking all the ordered rooted subtrees of a given tree that represents a given computer…
Higher-order unification has been shown to be undecidable. Miller discovered the pattern fragment and subsequently showed that higher-order pattern unification is decidable and has most general unifiers. We extend the algorithm to…
Decision trees and randomized forests are widely used in computer vision and machine learning. Standard algorithms for decision tree induction optimize the split functions one node at a time according to some splitting criteria. This greedy…
We give an algorithm for finding the arboricity of a weighted, undirected graph, defined as the minimum number of spanning forests that cover all edges of the graph, in $\sqrt{n} m^{1+o(1)}$ time. This improves on the previous best bound of…
In an era where artificial intelligence and machine learning algorithms increasingly impact human life, it is crucial to develop models that account for potential discrimination in their predictions. This paper tackles this problem by…