Related papers: The Euler Path to Static Level-Ancestors
Matrix scaling is a simple to state, yet widely applicable linear-algebraic problem: the goal is to scale the rows and columns of a given non-negative matrix such that the rescaled matrix has prescribed row and column sums. Motivated by…
The explosion in workload complexity and the recent slow-down in Moore's law scaling call for new approaches towards efficient computing. Researchers are now beginning to use recent advances in machine learning in software optimizations,…
Automated theorem proving has long been a key task of artificial intelligence. Proofs form the bedrock of rigorous scientific inquiry. Many tools for both partially and fully automating their derivations have been developed over the last…
The AHU-algorithm solves the computationally difficult graph isomorphism problem for rooted trees, and does so with a linear time complexity. Although the AHU-algorithm has remained state of the art for almost 50 years, it has been…
Given two rooted, labeled trees $P$ and $T$ the tree path subsequence problem is to determine which paths in $P$ are subsequences of which paths in $T$. Here a path begins at the root and ends at a leaf. In this paper we propose this…
We propose an Euler particle transport (EPT) approach for generative learning. The proposed approach is motivated by the problem of finding an optimal transport map from a reference distribution to a target distribution characterized by the…
We develop a general embedding method based on the Friedman-Pippenger tree embedding technique (1987) and its algorithmic version, essentially due to Aggarwal et al. (1996), enhanced with a roll-back idea allowing to sequentially retrace…
Given an undirected graph, the k-vertex cut problem (k-VCP) asks for a minimum-cost set of vertices whose removal yields at least k connected components in the resulting graph. The k-VCP is an important problem in network optimization, with…
Subset-Sum and k-SAT are two of the most extensively studied problems in computer science, and conjectures about their hardness are among the cornerstones of fine-grained complexity. One of the most intriguing open problems in this area is…
We examine the amount of preprocessing needed for answering certain on-line queries as fast as possible. We start with the following basic problem. Suppose we are given a semigroup $(S,\circ )$. Let $s_1 ,\ldots, s_n$ be elements of $S$. We…
Invex programs are a special kind of non-convex problems which attain global minima at every stationary point. While classical first-order gradient descent methods can solve them, they converge very slowly. In this paper, we propose new…
Given an undirected graph $G=(V,E)$ with positive edge lengths and two vertices $s$ and $t$, the next-to-shortest path problem is to find an $st$-path which length is minimum amongst all $st$-paths strictly longer than the shortest path…
Solving linear systems is often the computational bottleneck in real-life problems. Iterative solvers are the only option due to the complexity of direct algorithms or because the system matrix is not explicitly known. Here, we develop a…
We study the design of fixed-parameter algorithms for problems already known to be solvable in polynomial time. The main motivation is to get more efficient algorithms for problems with unattractive polynomial running times. Here, we focus…
We propose an algorithm for deep learning on networks and graphs. It relies on the notion that many graph algorithms, such as PageRank, Weisfeiler-Lehman, or Message Passing can be expressed as iterative vertex updates. Unlike previous…
We consider an ordinal tree $T$ on $n$ nodes, with each node assigned a $d$-dimensional weight vector $\pnt{w} \in \{1,2,\ldots,n\}^d,$ where $d \in \mathbb{N}$ is a constant. We study path queries as generalizations of well-known…
Avraham et al. [AFK+15] presented an alternative approach to parametric search, called \emph{bifurcation}, that performs faster under certain circumstances. Intuitively, when the underlying decider execution can be rolled back cheaply and…
Linear programming has been practically solved mainly by simplex and interior point methods. Compared with the weakly polynomial complexity obtained by the interior point methods, the existence of strongly polynomial bounds for the length…
Let R be the polynomial ring in r variables over a field k, with maximal ideal M and let V denote a vector subspace of the space of degree-j homogeneous elements of R. We study three related algebras determined by V. The first is the…
We derive an equivalent form of Halpern's fixed-point iteration scheme for solving a co-coercive equation (also called a root-finding problem), which can be viewed as a Nesterov's accelerated interpretation. We show that one method is…