Related papers: Optimal Tuning of Two-Dimensional Keyboards
We introduce the natural notion of a matching frame in a $2$-dimensional string. A matching frame in a $2$-dimensional $n\times m$ string $M$, is a rectangle such that the strings written on the horizontal sides of the rectangle are…
We present here a variational method for maximizing the bandgap in a one-dimensional system where the potential is subject to given constraints. Two specific examples are studied in detail. In the first, we show that if the potential is…
We introduce an algorithm which can be directly used to feasible and optimum search in linear programming. Starting from an initial point the algorithm iteratively moves a point in a direction to resolve the violated constraints. At the…
High-dimensional simulation optimization is notoriously challenging. We propose a new sampling algorithm that converges to a global optimal solution and suffers minimally from the curse of dimensionality. The algorithm consists of two…
Alignments, i.e., position-wise comparisons of two or more strings or ordered lists are of utmost practical importance in computational biology and a host of other fields, including historical linguistics and emerging areas of research in…
Recently, we presented a new Two-Bar Charts Packing Problem (2-BCPP), in which it is necessary to pack two-bar charts (2-BCs) in a unit-height strip of minimum length. The problem is a generalization of the Bin Packing Problem and 2-D…
This paper completely solves the controllability problems of two-dimensional multi-input discrete-time bilinear systems with and without drift. Necessary and sufficient conditions for controllability, which cover the existing results, are…
We derive a new lower bound for the bandwidth of a graph that is based on a new lower bound for the minimum cut problem. Our new semidefinite programming relaxation of the minimum cut problem is obtained by strengthening the known…
Low-harmonic formulas for closed relativistic strings are given. General parametrizations are presented for the addition of second- and third-harmonic waves to the fundamental wave. The method of determination of the parametrizations is…
Column-sparse packing problems arise in several contexts in both deterministic and stochastic discrete optimization. We present two unifying ideas, (non-uniform) attenuation and multiple-chance algorithms, to obtain improved approximation…
This paper presents a novel convex optimization-based method for finding the globally optimal solutions of a class of mixed-integer non-convex optimal control problems. We consider problems with non-convex constraints that restrict the…
We discuss two classes of exact (in $\a'$) string solutions described by conformal sigma models. They can be viewed as two possibilities of constructing a conformal model out of the non-conformal one based on the metric of a $D$-dimensional…
The problem of biclustering consists of the simultaneous clustering of rows and columns of a matrix such that each of the submatrices induced by a pair of row and column clusters is as uniform as possible. In this paper we approximate the…
Approximation algorithms for classical constraint satisfaction problems are one of the main research areas in theoretical computer science. Here we define a natural approximation version of the QMA-complete local Hamiltonian problem and…
The Closest String Problem is an NP-complete problem which appears more commonly in bioinformatics and coding theory. Less surprisingly, classical approaches have been pursued with two prominent algorithms being the genetic algorithm and…
Finding a \emph{single} best solution is the most common objective in combinatorial optimization problems. However, such a single solution may not be applicable to real-world problems as objective functions and constraints are only…
We study augmenting a plane Euclidean network with a segment, called a shortcut, to minimize the largest distance between any two points along the edges of the resulting network. Problems of this type have received considerable attention…
Quadratic constrained quadratic programming problems often occur in various fields such as engineering practice, management science, and network communication. This article mainly studies a non convex quadratic programming problem with…
The mathematics of musical intervals and scales has been extensively studied. Vastly simplified, our ears seem to prefer intervals whose frequency ratios have small numerator and denominator, such as 2:1 (octave), 3:2 (perfect fifth), 4:3…
When computing bounds, spatial branch-and-bound algorithms often linearly outer approximate convex relaxations for non-convex expressions in order to capitalize on the efficiency and robustness of linear programming solvers. Considering…