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In a recent paper Avis, Bremner, Tiwary and Watanabe gave a method for constructing linear programs (LPs) based on algorithms written in a simple programming language called Sparks. If an algorithm produces the solution $x$ to a problem in…
Assembly planning is a fundamental problem in robotics and automation, which involves designing a sequence of motions to bring the separate constituent parts of a product into their final placement in the product. Assembly planning is…
Combinatorics, like computer science, often has to deal with large objects of unspecified (or unusable) structure. One powerful way to deal with such an arbitrary object is to decompose it into more usable components. In particular, it has…
This article presents a general solution to the problem of computational complexity. First, it gives a historical introduction to the problem since the revival of the foundational problems of mathematics at the end of the 19th century.…
In this paper we tackle the problem of automatically designing concurrent data structure operations given a sequential data structure specification and knowledge about concurrent behavior. Designing concurrent code is a non-trivial task…
While the capacity, feasibility and methods to obtain codes for network coding problems are well studied, the decoding procedure and complexity have not garnered much attention. In this work, we pose the decoding problem at a sink node in a…
Simulating quantum circuits using classical computers lets us analyse the inner workings of quantum algorithms. The most complete type of simulation, strong simulation, is believed to be generally inefficient. Nevertheless, several…
Cover's function counting theorem is a milestone in the theory of artificial neural networks. It provides an answer to the fundamental question of determining how many binary assignments (dichotomies) of $p$ points in $n$ dimensions can be…
We define a notion of network capacity region of networks that generalizes the notion of network capacity defined by Cannons et al. and prove its notable properties such as closedness, boundedness and convexity when the finite field is…
I describe my path to unconventionality in my exploration of theoretical and applied aspects of computation towards revealing the algorithmic and reprogrammable properties and capabilities of the world, in particular related to applications…
We tackle the problem of automatically designing concurrent data structure operations given a sequential data structure specification and knowledge about concurrent behavior. Designing concurrent code is a non-trivial task even in simplest…
Variable projection solves structured optimization problems by completely minimizing over a subset of the variables while iterating over the remaining variables. Over the last 30 years, the technique has been widely used, with empirical and…
SSP reductions are a type of polynomial reductions that also preserve the solutions of the instances. This means there is a mapping from each solution in the original instance to one in the reduced instance, allowing direct deduction of an…
A semidefinite program (SDP) is a particular kind of convex optimization problem with applications in operations research, combinatorial optimization, quantum information science, and beyond. In this work, we propose variational quantum…
Guiding the design of neural networks is of great importance to save enormous resources consumed on empirical decisions of architectural parameters. This paper constructs shallow sigmoid-type neural networks that achieve 100% accuracy in…
Machine Learning with deep neural networks has transformed computational approaches to scientific and engineering problems. Central to many of these advancements are precisely tuned neural architectures that are tailored to the domains in…
Data-driven algorithm design is a paradigm that uses statistical and machine learning techniques to select from a class of algorithms for a computational problem an algorithm that has the best expected performance with respect to some…
We present a neural architecture that takes as input a 2D or 3D shape and outputs a program that generates the shape. The instructions in our program are based on constructive solid geometry principles, i.e., a set of boolean operations on…
We study a new formulation of the team-formation problem, where the goal is to form teams to work on a given set of tasks requiring different skills. Deviating from the classic problem setting where one is asking to cover all skills of each…
We study planted problems---finding hidden structures in random noisy inputs---through the lens of the sum-of-squares semidefinite programming hierarchy (SoS). This family of powerful semidefinite programs has recently yielded many new…