At least one centimetre for each millimetre.

“At least one” caching

We consider a variant of the caching problem, where each request is a set of pages of a fixed size, instead of a single page. In order to serve such a request, we require at least one of those pages to be present in the cache. Each page is assumed to have unit size and unit cost for getting loaded into the cache. We prove lower bounds on the competitive ratio for this problem in both the determ...

Finding at Least One Point in Each Connected Component of a Real Algebraic Set Defined by a Single Equation

Deciding efficiently the emptiness of a real algebraic set defined by a single equation is a fundamental problem of computational real algebraic geometry. We propose an algorithm for this test. We find, when the algebraic set is non empty, at least one point on each semialgebraically connected component. The problem is reduced to deciding the existence of real critical points of the distance fu...

Properness Defects of Projections and Computation of at Least One Point in Each Connected Component of a Real Algebraic Set

Computing at least one point in each connected component of a real algebraic set is a basic subroutine to decide emptiness of semialgebraic sets, which is a fundamental algorithmic problem in effective real algebraic geometry. In this article, we propose a new algorithm for the former task, which avoids a hypothesis of properness required in many of the previous methods. We show how studying th...

NLP Found Helpful (at least for one Text Categorization Task)

The Prevalence of at Least One-Time Substance Abuse among Kerman Pre-university Male Students

Background: Substance abuse is one of the main health problems in Iran and awareness about its spread and procedure of spread in the society, particularly the susceptible society of students, is very important with regard to the population pyramid of Iran. Methods: This study was performed by cross-sectional method. The sampling size was 610 male students in pre-university grade by a probabilis...