An Optimization Problem Related to the Computation of the Epsilon-entropy of an Ellipsoid in a Hamming Space

نویسندگان

  • Ilya Dumer
  • Mark Semenovich Pinsker
  • Vyacheslav V. Prelov
چکیده

The problem of optimizing (finding the maximin of) the difference between the entropy functions of two n-dimensional vectors under special restrictions on their components is solved. This optimum gives the main term of the asymptotics for the ε-entropy of an ellipsoid in a Hamming space as the dimension of the space grows.

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Epsilon-entropy of an Ellipsoid in a Hamming Space

i=1 aix 2 i ≤ r). The main goal of this paper is to investigate the asymptotic behavior of the ε-entropy of an ellipsoid Ea(r) as n→ ∞. Recall that the ε-entropy Hε(A) of a set A is defined as the logarithm of the minimal number of points of an ε-net covering the set A, i.e., Hε(A) = logmin |Mε|, (1.2) where the minimum is taken over all sets Mε such that Mε = {y ∈ E 2 | ∀x ∈ A ∃y ∈Mε : d(x, y)...

متن کامل

On the inverse maximum perfect matching problem under the bottleneck-type Hamming distance

Given an undirected network G(V,A,c) and a perfect matching M of G, the inverse maximum perfect matching problem consists of modifying minimally the elements of c so that M becomes a maximum perfect matching with respect to the modified vector. In this article, we consider the inverse problem when the modifications are measured by the weighted bottleneck-type Hamming distance. We propose an alg...

متن کامل

An Optimization Model for Epidemic Mitigation and Some Theoretical and Applied Generalizations

In this paper, we present a binary-linear optimization model to prevent the spread of an infectious disease in a community. The model is based on the remotion of some connections in a contact network in order to separate infected nodes from the others. By using this model we nd an exact optimal solution and determine not only the minimum number of deleted links but also their exact positions. T...

متن کامل

Fr{'e}chet and Hausdorff Queries on $x$-Monotone Trajectories

vspace{0.2cm}In this paper, we design a data structure for the following problem. Let $pi$ be an $x$-monotone trajectory with $n$ vertices in the plane and $epsilon >0$. We show how to preprocess $pi$ and $epsilon$ into a data structure such that for any horizontal query segment $Q$ in the plane, one can quickly determine the minimal continuous fraction of $pi$ whose Fr{'e}chet and Hausdo...

متن کامل

An Evolutionary Algorithm Based on a Hybrid Multi-Attribute Decision Making Method for the Multi-Mode Multi-Skilled Resource-constrained Project Scheduling Problem

This paper addresses the multi-mode multi-skilled resource-constrained project scheduling problem. Activities of real world projects often require more than one skill to be accomplished. Besides, in many real-world situations, the resources are multi-skilled workforces. In presence of multi-skilled resources, it is required to determine the combination of workforces assigned to each activity. H...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

عنوان ژورنال:
  • Probl. Inf. Transm.

دوره 38  شماره 

صفحات  -

تاریخ انتشار 2002