Thresholded Covering Algorithms for Robust and Max-Min Optimization

The general problem of robust optimization is this: one of several possible scenarios will appear tomorrow, but things are more expensive tomorrow than they are today. What should you anticipatorily buy today, so that the worst-case cost (summed over both days) is minimized? Feige et al. and Khandekar et al. considered the k-robust model where the possible outcomes tomorrow are given by all demand-subsets of size k, and gave algorithms for the set cover problem, and the Steiner tree and facility location problems in this model, respectively. In this paper, we give the following simple and intuitive template for k-robust problems: "having built some anticipatory solution, if there exists a single demand whose augmentation cost is larger than some threshold, augment the anticipatory solution to cover this demand as well, and repeat". In this paper we show that this template gives us improved approximation algorithms for k-robust Steiner tree and set cover, and the first approximation algorithms for k-robust Steiner forest, minimum-cut and multicut. All our approximation ratios (except for multicut) are almost best possible. As a by-product of our techniques, we also get algorithms for max-min problems of the form: "given a covering problem instance, which k of the elements are costliest to cover?".Comment: 24 page

Snail Homing and Mating Search Algorithm: A Novel Bio-Inspired Metaheuristic Algorithm

In this paper, a novel Snail Homing and Mating Search (SHMS) algorithm is proposed. It is inspired from the biological behaviour of the snails. Snails continuously travels to find food and a mate, leaving behind a trail of mucus that serves as a guide for their return. Snails tend to navigate by following the available trails on the ground and responding to cues from nearby shelter homes. The proposed SHMS algorithm is investigated by solving several unimodal and multimodal functions. The solutions are validated using standard statistical tests such as two-sided and pairwise signed rank Wilcoxon test and Friedman rank test. The solution obtained from the SHMS algorithm exhibited superior robustness as well as search space exploration capabilities within the less computational cost. The real-world application of SHMS algorithm is successfully demonstrated in the engineering design domain by solving three cases of design and economic optimization shell and tube heat exchanger problem. The objective function value and other statistical results obtained using SHMS algorithm are compared with other well-known metaheuristic algorithms.Comment: 46 Pages, 11 Figures, 24 Table

Energy saving in fixed wireless broadband networks

International audienceIn this paper, we present a mathematical formulation for saving energy in fixed broadband wireless networks by selectively turning off idle communication devices in low-demand scenarios. This problem relies on a fixed-charge capacitated network design (FCCND), which is very hard to optimize. We then propose heuristic algorithms to produce feasible solutions in a short time.Dans cet article, nous proposons une modélisation en programme linéaire en nombres entiers pour le problème de minimiser la consommation d'énergie dans les réseaux de collecte à faisceaux hertziens en éteignant une partie des équipements lorsque le trafic est bas. Ce problème repose sur un problème de dimensionnement de réseaux dont les arcs ont une capacité fixe, qui est très difficile à résoudre. Nous proposons un algorithme heuristique fournissant rapidement des solutions réalisables

Noncommutativity in a Time-Dependent Background

We compute a time-dependent noncommutativity parameter in a model with a time-dependent background, a space-time metric of the plane wave type supported by a Neveu-Schwarz two-form potential. This model is an open string version of the WZW model based on a non-semi-simple group previously studied by Nappi and Witten. The background we study is not conformally invariant. We consider a light-cone action for the sigma-model, compute the worldsheet propagator, and use it to derive a time-dependent noncommutativity parameter.Comment: 12 pages; v3: statement corrected and references adde

Brownian Motion and Polymer Statistics on Certain Curved Manifolds

We have calculated the probability distribution function G(R,L|R',0) of the end-to-end vector R-R' and the mean-square end-to-end distance (R-R')^2 of a Gaussian polymer chain embedded on a sphere S^(D-1) in D dimensions and on a cylinder, a cone and a curved torus in 3-D. We showed that: surface curvature induces a geometrical localization area; at short length the polymer is locally "flat" and (R-R')^2 = L l in all cases; at large scales, (R-R')^2 is constant for the sphere, it is linear in L for the cylinder and reaches different constant values for the torus. The cone vertex induces (function of opening angle and R') contraction of the chain for all lengths. Explicit crossover formulas are derived.Comment: 9 pages, 4 figures, RevTex, uses amssymb.sty and multicol.sty, to appear in Phys. Rev

Heisenberg-picture approach to the exact quantum motion of a time-dependent forced harmonic oscillator

In the Heisenberg picture, the generalized invariant and exact quantum motions are found for a time-dependent forced harmonic oscillator. We find the eigenstate and the coherent state of the invariant and show that the dispersions of these quantum states do not depend on the external force. Our formalism is applied to several interesting cases.Comment: 15 pages, two eps files, to appear in Phys. Rev. A 53 (6) (1996

Visualizing and exploring patterns of large mutational events with SigProfilerMatrixGenerator

BACKGROUND: All cancers harbor somatic mutations in their genomes. In principle, mutations affecting between one and fifty base pairs are generally classified as small mutational events. Conversely, large mutational events affect more than fifty base pairs, and, in most cases, they encompass copy-number and structural variants affecting many thousands of base pairs. Prior studies have demonstrated that examining patterns of somatic mutations can be leveraged to provide both biological and clinical insights, thus, resulting in an extensive repertoire of tools for evaluating small mutational events. Recently, classification schemas for examining large-scale mutational events have emerged and shown their utility across the spectrum of human cancers. However, there has been no computationally efficient bioinformatics tool that allows visualizing and exploring these large-scale mutational events. RESULTS: Here, we present a new version of SigProfilerMatrixGenerator that now delivers integrated capabilities for examining large mutational events. The tool provides support for examining copy-number variants and structural variants under two previously developed classification schemas and it supports data from numerous algorithms and data modalities. SigProfilerMatrixGenerator is written in Python with an R wrapper package provided for users that prefer working in an R environment. CONCLUSIONS: The new version of SigProfilerMatrixGenerator provides the first standardized bioinformatics tool for optimized exploration and visualization of two previously developed classification schemas for copy number and structural variants. The tool is freely available at https://github.com/AlexandrovLab/SigProfilerMatrixGenerator with an extensive documentation at https://osf.io/s93d5/wiki/home/