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Secretary problem. Graphs of probabilities of getting the best candidate (red circles) from n applications, and k / n (blue crosses) where k is the sample size. 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 ...
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 ...
A drawing of a graph. 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 ).
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 ...
Pursuit–evasion. 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. Early work on problems of this type modeled the environment geometrically. [1]
A graph with edges colored to illustrate a closed walk, H–A–B–A–H, in green; a circuit which is a closed walk in which all edges are distinct, B–D–E–F–D–C–B, in blue; and a cycle which is a closed walk in which all vertices are distinct, H–D–G–H, in red. In graph theory, a cycle in a graph is a non-empty trail in which ...
In graph theory, a branch of mathematics, the handshaking lemma is the statement that, in every finite undirected graph, the number of vertices that touch an odd number of edges is even. For example, if there is a party of people who shake hands, the number of people who shake an odd number of other people's hands is even. [ 1]
In the area of graph theory in mathematics, a signed graph is a graph in which each edge has a positive or negative sign. A signed graph is balanced if the product of edge signs around every cycle is positive. The name "signed graph" and the notion of balance appeared first in a mathematical paper of Frank Harary in 1953. [1]