Editing 173: Movie Seating

{{comic
| number    = 173
| date      = October 20, 2006
| title     = Movie Seating
| image     = movie_seating.png
| titletext = It's like the traveling salesman problem, but the endpoints are different and you can't ask your friends for help because they're sitting three seats down.
}}

==Explanation==
At the time of writing in most movie theaters in the US, {{w|Movie theater#Pricing and admission|seats were not reserved}}. That is, tickets were sold by screening without seat assignment, so an entering patron can take any vacant seat. Therefore, a group of incoming patrons may walk in a column and take a section of consecutive seats in a row, each person taking one next to the person in front of them. The order of these people is thus determined by the order in which they walk into the theater, which is in most cases random. After this comic was published, some theaters around the U.S. began to sell movie tickets with reserved seats, both online and when purchased at the theater. When you buy your ticket, you also specify which seat you would like to sit in. Therefore, if you buy multiple tickets, you can select seats that are adjacent to each other.

Cueball is upset at the way he and his friends have sat down at the movie theater. Part of the problem is that two people who are apparently in a relationship do not sit together. He therefore tries to use a {{w|social graph}} to calculate the best way for him and his seven friends to sit in a row, while taking into account all of the social connections among them. In {{w|mathematics}}, this type of problem is called {{w|combinatorial optimisation}}. The most popular example, the {{w|Traveling salesman problem|traveling salesman problem}}, is referenced in the title text, as well as in comics [[287]] and [[399]].

The title text shows that another part of the problem is that Cueball's friends, who could have helped him calculate a solution, are each sitting three seats away from him, and so he cannot ask them for help.

===Solutions===
[[User:Squidy9002]] wrote a program to find the best option through brute force, ignoring the one-way crush. According to their program, the best order is: 8, 5, 7, 4, 3, 6, 2, 1.

Two other hypothetical solutions for the specific problem proposed in the comic are here:

[[File:173_Solutions.jpg|1000px]]

==Transcript==
:At the movies, I get frustrated when we file into our row haphazardly, ignoring the computationally difficulty problem of seating people together for maximum enjoyment.
:[Map of relationships between 8 people.]
:[Legend:] 
::Single line: friends.
::Double line: in a relationship.
::Arrow: one-way crush.
::Dashed line: acquaintances
:[The eight friends sit in a row in a dark cinema. Cueball and one other are between two lovers.]
:Cueball: Guys! This is not socially optimal!

==Trivia==
In ''[[xkcd: volume 0]]'', Randall says that this was his "passive-aggressive way of asking my friends to let me plan seating."

{{comic discussion}}

[[Category:Comics featuring Cueball]]
[[Category:Comics featuring Megan]]
[[Category:Comics featuring Hairy]]
[[Category:Math]]
[[Category:Programming]]
[[Category:Comics with inverted brightness]]
[[Category:Multiple Cueballs]]