Publication

On finding another room-partitioning of the vertices

2010
Conference Papers

Abstract

Let T be a triangulated surface given by the list of vertex-triples of its triangles, called rooms. A room-partitioning of T is a subset R of the rooms such that each vertex of T is in exactly one room in R. We prove that if T has a room-partitioning R, then there is another room-partitioning of T which is different from R. The proof is a simple algorithm which walks from room to room, which however we show to be exponential by constructing a sequence of (planar) instances, where the algorithm walks from room to room an exponential number of times relative to the number of rooms in the instance. We unify the above theorem with Nash’s theorem stating that a 2-person game has an equilibrium, by proving a combinatorially simple common generalization.

Official source

https://infoscience.epfl.ch/entities/publication/506ca199-75b9-44a0-96f9-f0c441701fab

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2010
Conference Papers

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/506ca199-75b9-44a0-96f9-f0c441701fab

About this result

Related concepts (24)

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First-person shooter (FPS) is a sub-genre of shooter video games centered on gun and other weapon-based combat in a first-person perspective, with the player experiencing the action through the eyes of a protagonist or antagonist which is armed, and then controlling the player character in a three-dimensional space. The genre shares common traits with other shooter games, and in turn falls under the action game genre. Since the genre's inception, advanced 3D and pseudo-3D graphics have challenged hardware development, and multiplayer gaming has been integral.

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On finding another room-partitioning of the vertices

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