Rainbow minmax gap

Rainbow minmax gap is a problem in combinatorial optimization.

Definitions
There is a set P of n colored points on the real line.

A subset Q of P is called a rainbow set if it contains at most a single point of each color; it is called a complete rainbow set if it contains exactly one point of each color.

The max gap of a set of points Q is the largest difference between consecutive points of Q.

Rainbow minmax gap is the problem of finding a complete rainbow set Q, such that max-gap(Q) is as small as possible.

Solutions
The problem is NP-hard. There is a 2-factor approximation algorithm.