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Building on the blueprint from Goemans and Williamson (1995) for the Max-Cut problem, we construct a polynomial-time approximation algorithm for orthogonally constrained quadratic optimization problems. First, we derive a semidefinite…
Detecting the dimensionality of graphs is a central topic in machine learning. While the problem has been tackled empirically as well as theoretically, existing methods have several drawbacks. On the one hand, empirical tools are…
Complex orthogonal designs (CODs) play a crucial role in the construction of space-time block codes. Their real analog, real orthogonal designs (or equivalently, sum of squares composition formula) have a long history. Adams et al. (2011)…
Local algorithms on graphs are algorithms that run in parallel on the nodes of a graph to compute some global structural feature of the graph. Such algorithms use only local information available at nodes to determine local aspects of the…
Without unrealistic continuity and smoothness assumptions on a distributional density of one dimensional dataset, constructing an authentic possibly-gapped histogram becomes rather complex. The candidate ensemble is described via a…
Constrained coding is a fundamental field in coding theory that tackles efficient communication through constrained channels. While channels with fixed constraints have a general optimal solution, there is increasing demand for parametric…
There has been recent interest in the study of shortest self-orthogonal embeddings of binary linear codes, since many such codes are optimal self-orthogonal codes. Several authors have studied the length of a shortest self-orthogonal…
Graded posets frequently arise throughout combinatorics, where it is natural to try to count the number of elements of a fixed rank. These counting problems are often $\#\textbf{P}$-complete, so we consider approximation algorithms for…
We consider the problem of switching off unwanted interactions in a given multi-partite Hamiltonian. This is known to be an important primitive in quantum information processing and several schemes have been presented in the literature to…
In the problem of minimal perfect hashing, we are given a size $k$ subset $\mathcal{A}$ of a universe of keys $[n] = \{1,2, \cdots, n\}$, for which we wish to construct a hash function $h: [n] \to [k]$ such that $h(\cdot)$ maps…
Augmented designs are typically used in early-stage breeding programs to compare single replicates of test entries by combining them with replicated check varieties. One or two dimensional incomplete blocking can be incorporated in the…
The prior independent framework for algorithm design considers how well an algorithm that does not know the distribution of its inputs approximates the expected performance of the optimal algorithm for this distribution. This paper gives a…
Hadamard matrices, orthogonal designs and amicable orthogonal designs have a number of applications in coding theory, cryptography, wireless network communication and so on. Product designs were introduced by Robinson in order to construct…
Motivated by the study of a variant of sunflowers, Alon and Holzman recently introduced focal-free hypergraphs. In this paper, we show that there is an interesting connection between the maximum size of focal-free hypergraphs and the…
We connect the study of pseudodeterministic algorithms to two major open problems about the structural complexity of $\mathsf{BPTIME}$: proving hierarchy theorems and showing the existence of complete problems. Our main contributions can be…
Constructing ensembles of circuits which efficiently approximate the Haar measure over various groups is a long-standing and fundamental problem in quantum information theory. Recently it was shown that one can obtain approximate designs…
Orthogonal Monte Carlo (OMC) is a very effective sampling algorithm imposing structural geometric conditions (orthogonality) on samples for variance reduction. Due to its simplicity and superior performance as compared to its Quasi Monte…
Parareal is a well-studied algorithm for numerically integrating systems of time-dependent differential equations by parallelising the temporal domain. Given approximate initial values at each temporal sub-interval, the algorithm locates a…
We provide a robust and general algorithm for computing distribution functions associated to induced orthogonal polynomial measures. We leverage several tools for orthogonal polynomials to provide a spectrally-accurate method for a broad…
The double-direction orthogonalization algorithm is applied to construct sequences of polynomials, which are orthogonal over the interval [0,1]with the weighting function 1. Functional and recurrent relations are derived for the sequences…