A transitive closure algorithm
TLDR
An algorithm is given for computing the transitive closure of a directed graph in a time no greater than a1N1n+a2n2 for largen and the method uses aboutn2+n bits and 5n words of storage.Abstract:
An algorithm is given for computing the transitive closure of a directed graph in a time no greater thana1N1n+a2n2 for largen wherea1 anda2 are constants depending on the computer used to execute the algorithm,n is the number of nodes in the graph andN1 is the number of arcs (not counting those arcs which are part of a cycle and not counting those arcs which can be removed without changing the transitive closure). For graphs where each arc is selected at random with probabilityp, the average time to compute the transitive closure is no greater than min{a1pn3+a2n2, 1/2a1n2p−2+a2n2} for largen. The algorithm will compute the transitive closure of an undirected graph in a time no greater thana2n2 for largen. The method uses aboutn2+n bits and 5n words of storage (where each word can holdn+2 values).read more
Citations
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References
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Book
The Art of Computer Programming
TL;DR: The arrangement of this invention provides a strong vibration free hold-down mechanism while avoiding a large pressure drop to the flow of coolant fluid.
Journal ArticleDOI
A Theorem on Boolean Matrices
TL;DR: It is proved the validity of an algorithm whose running time goes up slightly faster than the square of d, the running times of which increase-other things being equal-as the cube of d.
Journal ArticleDOI
Topological sorting of large networks
TL;DR: The approach to the problem presented here centers upon the use of multiple adaptive matched filters that classify normalized signals that compare between machine and human performance.
Journal ArticleDOI
EULER: a generalization of ALGOL, and its formal definition: Part II
Niklaus Wirth,Helmut Weber +1 more
TL;DR: In this section the algorithmic language EULER is described first informally and then formally by its syntax and semantics, creating a language which is simpler and yet more flexible than ALGOL 60.
Journal ArticleDOI
An algorithm for computing all paths in a graph
TL;DR: An algorithm for computing B is given which is especially suitable if the number of arcs in G is relatively small compared to thenumber of nodes, and which is probably most economical to Warshall.