A Simple Search Problem

05/17/2021
by   Marshall Buck, et al.
0

A simple problem is studied in which there are N boxes and a prize known to be in one of the boxes. Furthermore, the probability that the prize is in any box is given. It is desired to find the prize with minimal expected work, where it takes one unit of work to open a box and look inside. The paper establishes bounds on the minimal work in terms of the p=1/2 Hölder norm of the probability density and in terms of the entropy of the probability density. We also introduce the notion of "Cartesian product" of problems, and determine the asymptotic behavior of the minimal work for the nth power of a problem. (This article is a newly typeset version of an internal publication written in 1984. The second author passed away on November 12, 2020, and his estate has approved the submission of this paper.)

READ FULL TEXT

page 1

page 2

page 3

page 4

research
02/18/2019

Generation of dynamical S-boxes via lag time chaotic series for cryptosystems

In this work, we present an algorithm for the design of n× n-bits substi...
research
01/02/2021

A space-indexed formulation of packing boxes into a larger box

Current integer programming solvers fail to decide whether 12 unit cubes...
research
06/18/2020

On the Design of Chaos-Based S-boxes

Substitution boxes (S-boxes) are critical nonlinear elements to achieve ...
research
07/21/2022

Optimal Algorithms for Free Order Multiple-Choice Secretary

Suppose we are given integer k ≤ n and n boxes labeled 1,…, n by an adve...
research
04/23/2018

Rendition: Reclaiming what a black box takes away

The premise of our work is deceptively familiar: A black box f(·) has al...
research
09/19/2019

A note on minimal art galleries

We will consider some extensions of the polygonal art gallery problem. I...
research
03/06/2023

The calculation of the probability density of a strictly stable law at large X

The article is devoted to the problem of calculating the probability den...

Please sign up or login with your details

Forgot password? Click here to reset