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Pursuit–evasion (variants of which are referred to as cops and robbers and graph searching) is a family of problems in mathematics and computer science in which one group attempts to track down members of another group in an environment.
In graph theory, the shortest path problem is the problem of finding a path between two vertices (or nodes) in a graph such that the sum of the weights of its constituent edges is minimized. [1] The problem of finding the shortest path between two intersections on a road map may be modeled as a special case of the shortest path problem in graphs, where the vertices correspond to intersections ...
Mathematically, turn by turn navigation is based on the shortest path problem within graph theory, which examines how to identify the path that best meets some criteria (shortest, cheapest, fastest, etc.) between two points in a large network.
The generalized travelling salesman problem, also known as the "travelling politician problem", deals with "states" that have (one or more) "cities", and the salesman must visit exactly one city from each state. One application is encountered in ordering a solution to the cutting stock problem in order to minimize knife changes.
Secretary problem. The secretary problem demonstrates a scenario involving optimal stopping theory [ 1 ][ 2 ] that is studied extensively in the fields of applied probability, statistics, and decision theory. It is also known as the marriage problem, the sultan's dowry problem, the fussy suitor problem, the googol game, and the best choice problem.
In mathematics, graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of vertices (also called nodes or points) which are connected by edges (also called arcs, links or lines).
For example, in the case of a wheeled robot, a simple kinematic car model (also known as Dubins' car) for the systems is: where is the car's position, is the heading, the car is moving at a constant speed , and the turn rate control is bounded.
Graph partition into subgraphs of specific types (triangles, isomorphic subgraphs, Hamiltonian subgraphs, forests, perfect matchings) are known NP-complete. Partition into cliques is the same problem as coloring the complement of the given graph.
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