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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.
NP-complete special cases include the edge dominating set problem, i.e., the dominating set problem in line graphs. NP-complete variants include the connected dominating set problem and the maximum leaf spanning tree problem. [3]: ND2. Feedback vertex set [2][3]: GT7. Feedback arc set [2][3]: GT8.
A function f: R → R is bijective if and only if its graph meets every horizontal and vertical line exactly once. If X is a set, then the bijective functions from X to itself, together with the operation of functional composition (∘), form a group , the symmetric group of X , which is denoted variously by S( X ), S X , or X !
Shortest path problem. Shortest path (A, C, E, D, F) between vertices A and F in the weighted directed graph. 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]
A signal-flow graph or signal-flowgraph (SFG), invented by Claude Shannon, [1] but often called a Mason graph after Samuel Jefferson Mason who coined the term, [2] is a specialized flow graph, a directed graph in which nodes represent system variables, and branches (edges, arcs, or arrows) represent functional connections between pairs of nodes.
Exponential growth is the inverse of logarithmic growth. Not all cases of growth at an always increasing rate are instances of exponential growth. For example the function grows at an ever increasing rate, but is very remote from growing exponentially. For example, when it grows at 3 times its size, but when it grows at 30% of its size.
R (programming language) R is a programming language for statistical computing and data visualization. It has been adopted in the fields of data mining, bioinformatics, and data analysis. [9] The core R language is augmented by a large number of extension packages, containing reusable code, documentation, and sample data.
The Turán graph T(n,r) is an example of an extremal graph. It has the maximum possible number of edges for a graph on n vertices without (r + 1)-cliques. This is T(13,4). Extremal graph theory is a branch of combinatorics, itself an area of mathematics, that lies at the intersection of extremal combinatorics and graph theory. In essence ...