Related papers: Efficient Circuit Simulation in MapReduce
The rapid advancement of embedded multicore and many-core systems has revolutionized computing, enabling the development of high-performance, energy-efficient solutions for a wide range of applications. As models scale up in size, data…
Recently, studying fundamental graph problems in the \emph{Massively Parallel Computation (MPC) framework, inspired by the MapReduce paradigm, has gained a lot of attention. An assumption common to a vast majority of approaches is to allow…
We present a novel characterization of the mapping of multiple parallelism forms (e.g. data and model parallelism) onto hierarchical accelerator systems that is hierarchy-aware and greatly reduces the space of software-to-hardware mapping.…
The problem of exactly summing n floating-point numbers is a fundamental problem that has many applications in large-scale simulations and computational geometry. Unfortunately, due to the round-off error in standard floating-point…
The shrinking of transistor geometries as well as the increasing complexity of integrated circuits, significantly aggravate nonlinear design behavior. This demands accurate and fast circuit simulation to meet the design quality and…
In this paper, we investigate three fundamental problems in the Massively Parallel Computation (MPC) model: (i) grid graph connectivity, (ii) approximate Euclidean Minimum Spanning Tree (EMST), and (iii) approximate DBSCAN. Our first result…
We present a novel automated technique for parallelizing quantum circuits via forward and backward translation to measurement-based quantum computing patterns and analyze the trade off in terms of depth and space complexity. As a result we…
Motivated by recent progress on symmetry breaking problems such as maximal independent set (MIS) and maximal matching in the low-memory Massively Parallel Computation (MPC) model (e.g., Behnezhad et al.~PODC 2019; Ghaffari-Uitto SODA 2019),…
Power circuits have been introduced in 2012 by Myasnikov, Ushakov and Won as a data structure for non-elementarily compressed integers supporting the arithmetic operations addition and $(x,y) \mapsto x\cdot 2^y$. The same authors applied…
The problem of solving a system of polynomial equations is one of the most fundamental problems in applied mathematics. Among them, the problem of solving a system of binomial equations form a important subclass for which specialized…
We analyse the power of graph neural networks (GNNs) in terms of Boolean circuit complexity and descriptive complexity. We prove that the graph queries that can be computed by a polynomial-size bounded-depth family of GNNs are exactly those…
Circuits are fundamental objects in linear programming and oriented matroid theory, representing the elementary difference vectors of a polyhedron between points in its affine space. A recent concept introduced by Ekbatani, Natura, and…
Quantum computations are typically compiled into a circuit of basic quantum gates. Just like for classical circuits, a quantum compiler should optimize the quantum circuit, e.g. by minimizing the number of required gates. Optimizing quantum…
A main open question in contemporary AI research is quantifying the forms of reasoning neural networks can perform when perfectly trained. This paper answers this by interpreting reasoning tasks as circuit emulation, where the gates define…
We propose a novel quantum algorithm for solving linear optimization problems by quantum-mechanical simulation of the central path. While interior point methods follow the central path with an iterative algorithm that works with successive…
Distributed optimization is an essential paradigm to solve large-scale optimization problems in modern applications where big-data and high-dimensionality creates a computational bottleneck. Distributed optimization algorithms that exhibit…
The operations used for neural network computation map favorably onto simple analog circuits, which outshine their digital counterparts in terms of compactness and efficiency. Nevertheless, such implementations have been largely supplanted…
Given a large graph G = (V,E) with millions of nodes and edges, how do we compute its connected components efficiently? Recent work addresses this problem in map-reduce, where a fundamental trade-off exists between the number of map-reduce…
Data structures that allow efficient distance estimation (distance oracles, distance sketches, etc.) have been extensively studied, and are particularly well studied in centralized models and classical distributed models such as CONGEST. We…
Faced with continuously increasing scale of data, original back-propagation neural network based machine learning algorithm presents two non-trivial challenges: huge amount of data makes it difficult to maintain both efficiency and…