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Alternatively, If A is an adjacency matrix for the graph, modified to have nonzero entries on its main diagonal, then the nonzero entries of A k give the adjacency matrix of the k th power of the graph, [14] from which it follows that constructing k th powers may be performed in an amount of time that is within a logarithmic factor of the time ...
G(V, E): weighted directed graph, with set of vertices V and set of directed edges E, w(u, v): cost of directed edge from node u to node v (costs are non-negative). Links that do not satisfy constraints on the shortest path are removed from the graph s: the source node; t: the destination node; K: the number of shortest paths to find; p u: a ...
In graph theory, Yen's algorithm computes single-source K-shortest loopless paths for a graph with non-negative edge cost. [1] The algorithm was published by Jin Y. Yen in 1971 and employs any shortest path algorithm to find the best path, then proceeds to find K − 1 deviations of the best path.
(For a graph with n vertices and r terminals, they use t = n − r − 1 added vertices per tree.) Then, they ask for the k -minimum spanning tree in this augmented graph with k = rt . The only way to include this many vertices in a k -spanning tree is to use at least one vertex from each added tree, for there are not enough vertices remaining ...
The main difference between modular decomposition and power graph analysis is the emphasis of power graph analysis in decomposing graphs not only using modules of nodes but also modules of edges (cliques, bicliques). Indeed, power graph analysis can be seen as a loss-less simultaneous clustering of both nodes and edges.
In algebraic number theory the n-th power residue symbol (for an integer n > 2) is a generalization of the (quadratic) Legendre symbol to n-th powers. These symbols are used in the statement and proof of cubic , quartic , Eisenstein , and related higher [ 1 ] reciprocity laws .
Series of Books in the Mathematical Sciences (1st ed.). New York: W. H. Freeman and Company. ISBN 9780716710455. MR 0519066. OCLC 247570676.. This book is a classic, developing the theory, then cataloguing many NP-Complete problems. Cook, S.A. (1971). "The complexity of theorem proving procedures".
In computer science, quickselect is a selection algorithm to find the kth smallest element in an unordered list, also known as the kth order statistic.Like the related quicksort sorting algorithm, it was developed by Tony Hoare, and thus is also known as Hoare's selection algorithm. [1]