Publication

Piercing quasi-rectangles-On a problem of Danzer and Rogers

János Pach, Gábor Tardos
2012
Journal Articles

Abstract

It is an old problem of Danzer and Rogers to decide whether it is possible to arrange 0(1/epsilon) points in the unit square so that every rectangle of area epsilon > 0 within the unit square contains at least one of them. We show that the answer to this question is in the negative if we slightly relax the notion of rectangles, as follows.

Official source

https://infoscience.epfl.ch/entities/publication/ee0bc082-7b73-4dc1-abad-4738cb9ddc2c

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János Pach, Gábor Tardos
2012
Journal Articles

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/ee0bc082-7b73-4dc1-abad-4738cb9ddc2c

About this result

Related concepts (8)

Knapsack problem

The knapsack problem is the following problem in combinatorial optimization: Given a set of items, each with a weight and a value, determine which items to include in the collection so that the total weight is less than or equal to a given limit and the total value is as large as possible. It derives its name from the problem faced by someone who is constrained by a fixed-size knapsack and must fill it with the most valuable items.

Decision problem

In computability theory and computational complexity theory, a decision problem is a computational problem that can be posed as a yes–no question of the input values. An example of a decision problem is deciding by means of an algorithm whether a given natural number is prime. Another is the problem "given two numbers x and y, does x evenly divide y?". The answer is either 'yes' or 'no' depending upon the values of x and y. A method for solving a decision problem, given in the form of an algorithm, is called a decision procedure for that problem.

Problem solving

Problem solving is the process of achieving a goal by overcoming obstacles, a frequent part of most activities. Problems in need of solutions range from simple personal tasks (e.g. how to turn on an appliance) to complex issues in business and technical fields. The former is an example of simple problem solving (SPS) addressing one issue, whereas the latter is complex problem solving (CPS) with multiple interrelated obstacles.

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