Graph Theory Based Methods
A maze can be generated by starting with a predetermined arrangement of cells (most commonly a rectangular grid but other arrangements are possible) with wall sites between them. This predetermined arrangement can be considered as a connected graph with the edges representing possible wall sites and the nodes representing cells. The purpose of the maze generation algorithm can then be considered to be making a subgraph where it is challenging to find a route between two particular nodes.
If the subgraph is not connected, then there are regions of the graph that are wasted because they do not contribute to the search space. If the graph contains loops, then there may be multiple paths between the chosen nodes. Because of this, maze generation is often approached as generating a random spanning tree. Loops which can confound naive maze solvers may be introduced by adding random edges to the result during the course of the algorithm.
Read more about this topic: Maze Generation Algorithm
Famous quotes containing the words graph, theory, based and/or methods:
“In this Journal, my pen is a delicate needle point, tracing out a graph of temperament so as to show its daily fluctuations: grave and gay, up and down, lamentation and revelry, self-love and self-disgust. You get here all my thoughts and opinions, always irresponsible and often contradictory or mutually exclusive, all my moods and vapours, all the varying reactions to environment of this jelly which is I.”
—W.N.P. Barbellion (1889–1919)
“Many people have an oversimplified picture of bonding that could be called the “epoxy” theory of relationships...if you don’t get properly “glued” to your babies at exactly the right time, which only occurs very soon after birth, then you will have missed your chance.”
—Pamela Patrick Novotny (20th century)
“I want relations which are not purely personal, based on purely personal qualities; but relations based upon some unanimous accord in truth or belief, and a harmony of purpose, rather than of personality. I am weary of personality.... Let us be easy and impersonal, not forever fingering over our own souls, and the souls of our acquaintances, but trying to create a new life, a new common life, a new complete tree of life from the roots that are within us.”
—D.H. (David Herbert)
“The ancient bitter opposition to improved methods [of production] on the ancient theory that it more than temporarily deprives men of employment ... has no place in the gospel of American progress.”
—Herbert Hoover (1874–1964)