“Short-Dot”: Computing Large Linear Transforms Distributedly Using Coded Short Dot Products

Short-Dot: Computing Large Linear Transforms Distributedly Using Coded Short Dot Products

Faced with saturation of Moore’s law and increasing size and dimension of data, system designers have increasingly resorted to parallel and distributed computing to reduce computation time of machine-learning algorithms. However, distributed computing is often bottle necked by a small fraction of slow processors called “stragglers” that reduce the speed of computation because the fusion node ha...

On Computing Short Products

A polynomial consisting of only the low degree monomials of the (full) product of two univariate polynomials f and g is called a short product of f and g. A global algorithm, independent of the actual multiplication algorithm used, to compute short products is proposed. Its performance for several multiplication algorithms is studied. Also several applications of short products are pointed out.

Towards multi-state based computing using quantum-dot cellular automata

In this article we present an extended quantum-dot cellular automaton (QCA) cell. The extension is mainly focused on the enlargement of the range of possible states of a single QCA cell. In a QCA cell the electrons, owing to electrostatic repulsion, align along one of the two diagonal configurations that correspond to their maximal spatial separation. This gives the QCA cell the ability to enco...

Spin-Based Quantum Dot Quantum Computing

Short Tours through Large Linear Forests

A tour in a graph is a connected walk that visits every vertex at least once, and returns to the starting vertex. Vishnoi (2012) proved that every connected d-regular graph with n vertices has a tour of length at most (1 + o(1))n, where the o(1) term (slowly) tends to 0 as d grows. His proof is based on van-derWarden’s conjecture (proved independently by Egorychev (1981) and by Falikman (1981))...