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Motivated by an application in computational topology, we consider a novel variant of the problem of efficiently maintaining dynamic rooted trees. This variant requires merging two paths in a single operation. In contrast to the standard…
The parallel ordering of large graphs is a difficult problem, because on the one hand minimum degree algorithms do not parallelize well, and on the other hand the obtainment of high quality orderings with the nested dissection algorithm…
The study of optimal decision trees has gained increasing attention in recent years; however, despite substantial progress, it still suffers from two major challenges: First, trees constructed by existing optimal decision tree (ODT)…
To turn environmentally derived metabarcoding data into community matrices for ecological analysis, sequences must first be clustered into operational taxonomic units (OTUs). This task is particularly complex for data including large…
Let $G=(V,E)$ be an undirected multi-graph on $n=|V|$ vertices and $S\subseteq V$ be a Steiner set. Steiner cut is a fundamental concept; moreover, global cut $(|S|=n)$, as well as (s,t)-cut $(|S|=2)$, is just a special case of Steiner cut.…
IoT Big Data requires new machine learning methods able to scale to large size of data arriving at high speed. Decision trees are popular machine learning models since they are very effective, yet easy to interpret and visualize. In the…
Link-cut trees have been introduced by D.D. Sleator and R.E. Tarjan (Journal of Computer and System Sciences, 1983) with the aim of efficiently maintaining a forest of vertex-disjoint dynamic rooted trees under cut and link operations.…
We present a novel framework for dynamic cut aggregation in L-shaped algorithms. The aim is to improve the parallel performance of distributed L-shaped algorithms through reduced communication latency and load imbalance. We show how…
Given a directed graph $G$ and a pair of nodes $s$ and $t$, an $s$-$t$ bridge of $G$ is an edge whose removal breaks all $s$-$t$ paths of $G$. Similarly, an $s$-$t$ articulation point of $G$ is a node whose removal breaks all $s$-$t$ paths…
The tree edit distance problem is a natural generalization of the classic string edit distance problem. Given two ordered, edge-labeled trees $T_1$ and $T_2$, the edit distance between $T_1$ and $T_2$ is defined as the minimum total cost of…
We study the Requirement Cut problem, a generalization of numerous classical graph partitioning problems including Multicut, Multiway Cut, $k$-Cut, and Steiner Multicut among others. Given a graph with edge costs, terminal groups $(S_1,…
This work presents a data-driven reduced-order modeling framework to accelerate the computations of $N$-body dynamical systems and their pair-wise interactions. The proposed framework differs from traditional acceleration methods, like the…
We give a deterministic algorithm for finding the minimum (weight) cut of an undirected graph on $n$ vertices and $m$ edges using $\text{polylog}(n)$ calls to any maximum flow subroutine. Using the current best deterministic maximum flow…
Gravitational $N$-body simulations calculate numerous interactions between particles. The tree algorithm reduces these calculations by constructing a hierarchical oct-tree structure and approximating gravitational forces on particles. Over…
We study (s,t)-cuts of second minimum capacity and present the following algorithmic and graph-theoretic results. 1. Vazirani and Yannakakis [ICALP 1992] designed the first algorithm for computing an (s,t)-cut of second minimum capacity…
A flow graph $G=(V,E,s)$ is a directed graph with a distinguished start vertex $s$. The dominator tree $D$ of $G$ is a tree rooted at $s$, such that a vertex $v$ is an ancestor of a vertex $w$ if and only if all paths from $s$ to $w$…
Structured pruning is an effective approach for compressing large pre-trained neural networks without significantly affecting their performance. However, most current structured pruning methods do not provide any performance guarantees, and…
Optimal transport (OT) is a powerful framework to compare probability measures, a fundamental task in many statistical and machine learning problems. Substantial advances have been made in designing OT variants which are either…
We present a new universal source code for distributions of unlabeled binary and ordinal trees that achieves optimal compression to within lower order terms for all tree sources covered by existing universal codes. At the same time, it…
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…