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The Minimum Path Cover (MPC) problem consists of finding a minimum-cardinality set of node-disjoint paths that cover all nodes in a given graph. We explore a variant of the MPC problem on acyclic digraphs (DAGs) where, given a subset of…
Given a set of pairwise disjoint polygonal obstacles in the plane, finding an obstacle-avoiding Euclidean shortest path between two points is a classical problem in computational geometry and has been studied extensively. Previously,…
Score-based methods for learning Bayesain networks(BN) aim to maximizing the global score functions. However, if local variables have direct and indirect dependence simultaneously, the global optimization on score functions misses edges…
We give an algorithmic and lower-bound framework that facilitates the construction of subexponential algorithms and matching conditional complexity bounds. It can be applied to intersection graphs of similarly-sized fat objects, yielding…
Universal methods for optimization are designed to achieve theoretically optimal convergence rates without any prior knowledge of the problem's regularity parameters or the accurarcy of the gradient oracle employed by the optimizer. In this…
In a series of papers, Avraham, Filtser, Kaplan, Katz, and Sharir (SoCG'14), Kaplan, Katz, Saban, and Sharir (ESA'23), and Katz, Saban, and Sharir (ESA'24) studied a class of geometric optimization problems -- including reverse shortest…
In this paper, we study batch parallel algorithms for the dynamic connectivity problem, a fundamental problem that has received considerable attention in the sequential setting. The most well known sequential algorithm for dynamic…
We study the problem of clustering networks whose nodes have imputed or physical positions in a single dimension, for example prestige hierarchies or the similarity dimension of hyperbolic embeddings. Existing algorithms, such as the…
The densest subgraph problem, introduced in the 80s by Picard and Queyranne as well as Goldberg, is a classic problem in combinatorial optimization with a wide range of applications. The lowest outdegree orientation problem is known to be…
Scheduling computational tasks represented by directed acyclic graphs (DAGs) is challenging because of its complexity. Conventional scheduling algorithms rely heavily on simple heuristics such as shortest job first (SJF) and critical path…
The Subgraph Isomorphism problem is of considerable importance in computer science. We examine the problem when the pattern graph H is of bounded treewidth, as occurs in a variety of applications. This problem has a well-known algorithm via…
One of the most accurate methods for solving the time-dependent Schr\"{o}dinger equation uses a combination of the dynamic Fourier method with the split-operator algorithm on a tensor-product grid. To reduce the number of required grid…
We consider the fundamental problems of determining the rooted and global edge and vertex connectivities (and computing the corresponding cuts) in directed graphs. For rooted (and hence also global) edge connectivity with small integer…
Directed acyclic graphs (DAGs) are directed graphs in which there is no path from a vertex to itself. DAGs are an omnipresent data structure in computer science and the problem of counting the DAGs of given number of vertices and to sample…
Estimating the structure of directed acyclic graphs (DAGs, also known as Bayesian networks) is a challenging problem since the search space of DAGs is combinatorial and scales superexponentially with the number of nodes. Existing approaches…
We propose a mathematical formalism for discrete multi-scale dynamical systems induced by maps which parallels the established geometric singular perturbation theory for continuous-time fast-slow systems. We identify limiting maps…
A discrete Bayesian network is a directed acyclic graph (DAG) consisting of categorical variables. Two popular approaches for DBN modeling include classification and nonparametric methods. However, both methods often require a large number…
In this paper we present the first deterministic polynomial time algorithm for determining the existence of a Hamiltonian cycle and finding a Hamiltonian cycle in general graphs. Our algorithm can also solve the Hamiltonian path problem in…
We report a scalable hybrid quantum-classical machine learning framework to build Bayesian networks (BN) that captures the conditional dependence and causal relationships of random variables. The generation of a BN consists of finding a…
Given an $n$-vertex $m$-edge graph $G$ with non negative edge-weights, the girth of $G$ is the weight of a shortest cycle in $G$. For any graph $G$ with polynomially bounded integer weights, we present a deterministic algorithm that…