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Travelling Salesman, by director Timothy Lanzone, is the story of four mathematicians hired by the U.S. government to solve the most elusive problem in computer-science history: P vs. NP. [ 77] Solutions to the problem are used by mathematician Robert A. Bosch in a subgenre called TSP art.
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. 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 ...
Turn-by-turn navigation is a feature of some satellite navigation devices where directions for a selected route are continually presented to the user in the form of spoken or visual instructions. [1] The system keeps the user up-to-date about the best route to the destination, and is often updated according to changing factors such as traffic ...
Robot in a wooden maze. A maze-solving algorithm is an automated method for solving a maze.The random mouse, wall follower, Pledge, and Trémaux's algorithms are designed to be used inside the maze by a traveler with no prior knowledge of the maze, whereas the dead-end filling and shortest path algorithms are designed to be used by a person or computer program that can see the whole maze at once.
A scale-free network is a network whose degree distribution follows a power law, at least asymptotically. That is, the fraction P ( k) of nodes in the network having k connections to other nodes goes for large values of k as. where is a parameter whose value is typically in the range (wherein the second moment ( scale parameter) of is infinite ...
Turán's theorem states that the Turán graph has the largest number of edges among all Kr+1 -free n -vertex graphs. Turán's theorem, and the Turán graphs giving its extreme case, were first described and studied by Hungarian mathematician Pál Turán in 1941. [1] The special case of the theorem for triangle-free graphs is known as Mantel's ...
Path (graph theory) A three-dimensional hypercube graph showing a Hamiltonian path in red, and a longest induced path in bold black. In graph theory, a path in a graph is a finite or infinite sequence of edges which joins a sequence of vertices which, by most definitions, are all distinct (and since the vertices are distinct, so are the edges).
Algebraic graph theory is a branch of mathematics in which algebraic methods are applied to problems about graphs. This is in contrast to geometric, combinatoric, or algorithmic approaches. There are three main branches of algebraic graph theory, involving the use of linear algebra, the use of group theory, and the study of graph invariants .