The Art Gallery Problem – Helping Heist Movies and D&D Campaigns Alike

Sure, George Clooney is a good-looking man but did he consider the art gallery problem in Ocean’s 11? …No seriously, I have no idea. I’ve never seen the movie. 🙁

I was curious about graph theory and what prominent topics are involved in it. Perhaps one of the most interesting and practical problem I found in the Wikipedia entry for graph theory is the art gallery problem (also see here).

To sum it up: The problem asks us to consider how many security guards we’d need to carefully monitor an art gallery. This depends on many variables such as the size and shape of the art gallery.

Marianne Freiberger for Plus Magazine, summarizes the mathematician S. Fisk’s answer to this conundrum as:

..[Y]ou never need more than n/3 guards (so that’s 9/3 = 3 guards in the example in the figure). That’s true for any simple polygon with n vertices, no matter how complicated and irregular it looks.”

Which is pretty amazing.

So next time you’re watching your favorite heist movie or thinking about starting a heist campaign in D&D, consider the art gallery problem!

2 Replies to “The Art Gallery Problem – Helping Heist Movies and D&D Campaigns Alike”

  1. I always did wonder how they figured out how many guards are needed to be hired but I didn’t realize it used this method. I thought that when you tied in D&D to the art problem was very interesting. It makes me wonder how many other scenarios in life we could use the art gallery problem. I also found another article talking about the art gallery problem that goes much more into detail about different examples depending on room sizes, it can get very complex as well when the room are abnormal.

    1. Thanks for the comment, Cam! interesting link and I noticed from some of the links I posted that the level of complexity can get really up there. Sure don’t envy the planners on that one!

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