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Coded distributed matrix multiplication (CDMM) schemes, such as MatDot codes, seek efficient ways to distribute matrix multiplication task(s) to a set of $N$ distributed servers so that the answers returned from any $R$ servers are…
Locally recoverable codes are widely used in distributed and cloud storage systems. The objective of this paper is to present a construction of near MDS codes with oval polynomials and then determine the locality of the codes. It turns out…
We consider the problem of evaluating distinct multivariate polynomials over several massive datasets in a distributed computing system with a single master node and multiple worker nodes. We focus on the general case when each multivariate…
We consider the problem of secure distributed matrix multiplication (SDMM) in which a user wishes to compute the product of two matrices with the assistance of honest but curious servers. We construct polynomial codes for SDMM by studying a…
In this paper we study various approaches for exploiting symmetries in polynomial optimization problems within the framework of semi definite programming relaxations. Our special focus is on constrained problems especially when the…
Gradient coding schemes effectively mitigate full stragglers in distributed learning by introducing identical redundancy in coded local partial derivatives corresponding to all model parameters. However, they are no longer effective for…
The inverse of a large matrix can often be accurately approximated by a polynomial of degree significantly lower than the order of the matrix. The iteration polynomial generated by a run of the GMRES algorithm is a good candidate, and its…
Multidimensional Retiming is one of the most important optimization techniques to improve timing parameters of nested loops. It consists in exploring the iterative and recursive structures of loops to redistribute computation nodes on cycle…
In this paper, we extend the work of (Abbondati et al., 2024) on decoding simultaneous rational number codes by addressing two important scenarios: multiplicities and the presence of bad primes (divisors of denominators). First, we…
We introduce a class of bosonic quantum error-correcting codes, termed \emph{extended binomial codes}, which generalize the structure of one-mode binomial codes by incorporating ideas from high-rate qubit stabilizer codes. These codes are…
Multi-party computation (MPC) is promising for designing privacy-preserving machine learning algorithms at edge networks. An emerging approach is coded-MPC (CMPC), which advocates the use of coded computation to improve the performance of…
The maximum common subtree isomorphism problem asks for the largest possible isomorphism between subtrees of two given input trees. This problem is a natural restriction of the maximum common subgraph problem, which is ${\sf NP}$-hard in…
Diversity coding is a network restoration technique which offers near-hitless restoration, while other state-of-the art techniques are significantly slower. Furthermore, the extra spare capacity requirement of diversity coding is…
Coded multicasting has been shown to be a promis- ing approach to significantly improve the caching performance of content delivery networks with multiple caches downstream of a common multicast link. However, achievable schemes proposed to…
Many problems of systems control theory boil down to solving polynomial equations, polynomial inequalities or polyomial differential equations. Recent advances in convex optimization and real algebraic geometry can be combined to generate…
The EM (Expectation-Maximization) algorithm is regarded as an MM (Majorization-Minimization) algorithm for maximum likelihood estimation of statistical models. Expanding this view, this paper demonstrates that by choosing an appropriate…
We introduce a novel approach to reduce the computational effort of solving mixed-integer convex chance constrained programs through the scenario approach. Instead of reducing the number of required scenarios, we directly minimize the…
Specialized function gradient computing hardware could greatly improve the performance of state-of-the-art optimization algorithms, e.g., based on gradient descent or conjugate gradient methods that are at the core of control, machine…
The purpose of this note is to survey a methodology to solve systems of polynomial equations and inequalities. The techniques we discuss use the algebra of multivariate polynomials with coefficients over a field to create large-scale linear…
For interior-point algorithms in linear programming, it is well-known that the selection of the centering parameter is crucial for proving polynomility in theory and for efficiency in practice. However, the selection of the centering…