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

Oscar Cunningham 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.

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References
  1. Oscar Cunningham (January 20, 2018). Re: Largest and oldest methuselah ever found! (discussion thread) at the ConwayLife.com forums
  2. Oscar Cunningham (January 20, 2018). Re: Largest and oldest methuselah ever found! (discussion thread) at the ConwayLife.com forums
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