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The ubiquitous Variable-Byte encoding is one of the fastest compressed representation for integer sequences. However, its compression ratio is usually not competitive with other more sophisticated encoders, especially when the integers to…
The problem of optimization of the array size for modern discrete Fourier transform libraries is considered and reformulated as an integer linear programming problem. Acceleration of finding an optimal solution using standard freely…
Inverse optimization, determining parameters of an optimization problem that render a given solution optimal, has received increasing attention in recent years. While significant inverse optimization literature exists for convex…
In order to generate prime implicants for a given cube (minterm), most of minimization methods increase the dimension of this cube by removing one literal from it at a time. But there are two problems of exponential complexity. One of them…
Best Fit is a well known online algorithm for the bin packing problem, where a collection of one-dimensional items has to be packed into a minimum number of unit-sized bins. In a seminal work, Kenyon [SODA 1996] introduced the (asymptotic)…
Quantum state tomography is an indispensable but costly part of many quantum experiments. Typically, it requires measurements to be carried in a number of different settings on a fixed experimental setup. The collected data is often…
In order to anticipate rare and impactful events, we propose to quantify the worst-case risk under distributional ambiguity using a recent development in kernel methods -- the kernel mean embedding. Specifically, we formulate the…
This study investigates the misclassification excess risk bound in the context of 1-bit matrix completion, a significant problem in machine learning involving the recovery of an unknown matrix from a limited subset of its entries. Matrix…
Random embedding has been applied with empirical success to large-scale black-box optimization problems with low effective dimensions. This paper proposes the EmbeddedHunter algorithm, which incorporates the technique in a hierarchical…
Recent advances in mathematical programming have made Mixed Integer Optimization a competitive alternative to popular regularization methods for selecting features in regression problems. The approach exhibits unquestionable foundational…
This paper reformulates the problem of finding a longest common increasing subsequence of the two given input sequences in a very succinct way. An extremely simple linear space algorithm based on the new formula can find a longest common…
Today's PCs can directly manipulate numbers not longer than 64 bits because the size of the CPU registers and the data-path are limited. Consequently, arithmetic operations such as addition, can only be performed on numbers of that length.…
This paper considers an optimization problem for a dynamical system whose evolution depends on a collection of binary decision variables. We develop scalable approximation algorithms with provable suboptimality bounds to provide…
We establish the optimal nonergodic sublinear convergence rate of the proximal point algorithm for maximal monotone inclusion problems. First, the optimal bound is formulated by the performance estimation framework, resulting in an infinite…
What is the higher-dimensional analog of a permutation? If we think of a permutation as given by a permutation matrix, then the following definition suggests itself: A d-dimensional permutation of order n is an [n]^(d+1) array of zeros and…
We study the classical problem of characterizing the channel capacity and its achieving distribution in a generic fashion. We derive a simple relation between three parameters: the input-output function, the input cost function and the…
A well studied special case of bin packing is the 3-partition problem, where n items of size > 1/4 have to be packed in a minimum number of bins of capacity one. The famous Karmarkar-Karp algorithm transforms a fractional solution of a…
Correcting insertions/deletions as well as substitution errors simultaneously plays an important role in DNA-based storage systems as well as in classical communications. This paper deals with the fundamental task of constructing codes that…
We propose new estimates for the frontier of a set of points. They are defined as kernel estimates covering all the points and whose associated support is of smallest surface. The estimates are written as linear combinatio- ns of kernel…
We consider redundant binary joint digital expansions of integer vectors. The redundancy is used to minimize the Hamming weight, i.e., the number of nonzero digit vectors. This leads to efficient linear combination algorithms in abelian…