Related papers: Ultra-Sparse Near-Additive Emulators
We consider the problem of constructing fast and small parallel prefix adders for non-uniform input arrival times. This problem arises whenever the adder is embedded into a more complex circuit, e. g. a multiplier. Most previous results are…
We design fast deterministic algorithms for distance computation in the congested clique model. Our key contributions include: -- A $(2+\epsilon)$-approximation for all-pairs shortest paths in $O(\log^2{n} / \epsilon)$ rounds on unweighted…
Given an edge-weighted graph $G$ and $\epsilon>0$, a $(1+\epsilon)$-spanner is a spanning subgraph $G'$ whose shortest path distances approximate those of $G$ within a $(1+\epsilon)$ factor. If $G$ is from certain minor-closed graph…
Let $(V,\delta)$ be a finite metric space, where $V$ is a set of $n$ points and $\delta$ is a distance function defined for these points. Assume that $(V,\delta)$ has a constant doubling dimension $d$ and assume that each point $p\in V$ has…
To our knowledge, there are only two known algorithms for constructing sparse and light spanners for general graphs. One of them is the greedy algorithm of Alth$\ddot{o}$fer et al. \cite{ADDJS93}, analyzed by Chandra et al. in SoCG'92. The…
Automatically designing fast and space-efficient digital circuits is challenging because circuits are discrete, must exactly implement the desired logic, and are costly to simulate. We address these challenges with CircuitVAE, a search…
We study the unsplittable flow on a path problem (UFP) where we are given a path with non-negative edge capacities and tasks, which are characterized by a subpath, a demand, and a profit. The goal is to find the most profitable subset of…
In this paper, we design sub-linear space streaming algorithms for estimating three fundamental parameters -- maximum independent set, minimum dominating set and maximum matching -- on sparse graph classes, i.e., graphs which satisfy…
Structural network embedding is a crucial step in enabling effective downstream tasks for complex systems that aims to project a network into a lower-dimensional space while preserving similarities among nodes. We introduce a simple and…
We use deep sparsely connected neural networks to measure the complexity of a function class in $L^2(\mathbb R^d)$ by restricting connectivity and memory requirement for storing the neural networks. We also introduce representation system -…
The blow-up lemma states that a system of super-regular pairs contains all bounded degree spanning graphs as subgraphs that embed into a corresponding system of complete pairs. This lemma has far-reaching applications in extremal…
We consider the fundamental problem of estimating the mean of a vector $y=X\beta+z$, where $X$ is an $n\times p$ design matrix in which one can have far more variables than observations, and $z$ is a stochastic error term--the so-called…
In this paper, we revisit the classic approximate All-Pairs Shortest Paths (APSP) problem in undirected graphs. For unweighted graphs, we provide an algorithm for $2$-approximate APSP in $\tilde O(n^{2.5-r}+n^{\omega(r)})$ time, for any…
In this paper, we propose a new framework for designing fast parallel algorithms for fundamental statistical subset selection tasks that include feature selection and experimental design. Such tasks are known to be weakly submodular and are…
Distributed optimization algorithms are frequently faced with solving sub-problems on disjoint connected parts of a network. Unfortunately, the diameter of these parts can be significantly larger than the diameter of the underlying network,…
Computer models are used as replacements for physical experiments in a large variety of applications. Nevertheless, direct use of the computer model for the ultimate scientific objective is often limited by the complexity and cost of the…
Spiking Neural Networks (SNNs) and transformers represent two powerful paradigms in neural computation, known for their low power consumption and ability to capture feature dependencies, respectively. However, transformer architectures…
Approximate computing is an emerging paradigm to improve the power and performance efficiency of error-resilient applications. As adders are one of the key components in almost all processing systems, a significant amount of research has…
We show that every locally sparse graph contains a linearly sized expanding subgraph. For constants $c_1>c_2>1$, $0<\alpha<1$, a graph $G$ on $n$ vertices is called a $(c_1,c_2,\alpha)$-graph if it has at least $c_1n$ edges, but every…
A temporal graph is an undirected graph $G=(V,E)$ along with a function that assigns a time-label to each edge in $E$. A path in $G$ with non-decreasing time-labels is called temporal path and the distance from $u$ to $v$ is the minimum…