# Minimum covering polyplet

A **minimum covering polyplet** (**MCP**) of a pattern is a polyplet (i.e. orthogonally/diagonally connected pattern) of minimal population covering said pattern.^{[1]} The **minimum covering polyplet size** (**MCPS**) of a pattern is the size of a minimum covering polyplet^{[1]}; unlike the minimum covering polyplet itself, this is a single, well-defined number.

## Computation

Finding a minimum covering polyplet for a given pattern is an instance of the Steiner tree problem,^{[1]} which is NP-hard; however, finding a minimum covering polyplet for a given small pattern is often easy in practice.

## Uses

Macbi proposed using the minimum covering polyplet size to gauge the size of a methuselah, as it penalizes both population and bounding box.^{[2]} The resulting metric is L/MCPS.

## References

- ↑
^{1.0}^{1.1}^{1.2}Macbi. Re: Largest and oldest methuselah ever found! (discussion thread) at the ConwayLife.com forums - ↑ Macbi. Re: Largest and oldest methuselah ever found! (discussion thread) at the ConwayLife.com forums