A shortest-path algorithm with expected time O(n2 log n log* n)

We present an algorithm which finds the shortest distance between all pairs of points in a non-negatively weighted directed graph in the average time stated in the title. This algorithm, an extension of Spira's solution [Sp], executes in the stated time over quite general classes of probability distributions on graphs.

[1]  Leslie G. Valiant,et al.  Fast probabilistic algorithms for hamiltonian circuits and matchings , 1977, STOC '77.

[2]  Edsger W. Dijkstra,et al.  A note on two problems in connexion with graphs , 1959, Numerische Mathematik.

[3]  Donald E. Knuth,et al.  Big Omicron and big Omega and big Theta , 1976, SIGA.

[4]  Jin Y. Yen,et al.  Finding the Lengths of All Shortest paths in N -Node Nonnegative-Distance Complete Networks Using 12N3 Additions and N3 Comparisons , 1972, JACM.

[5]  G. Dantzig.  On the Shortest Route Through a Network , 1960 .

[6]  Alfred V. Aho,et al.  The Design and Analysis of Computer Algorithms , 1974 .

[7]  Philip M. Spira,et al.  A New Algorithm for Finding all Shortest Paths in a Graph of Positive Arcs in Average Time 0(n2 log2n) , 1973, SIAM J. Comput..

[8]  Michael L. Fredman,et al.  New Bounds on the Complexity of the Shortest Path Problem , 1976, SIAM J. Comput..

[9]  John S. Carson,et al.  A Note on Spira's Algorithm for the All-Pairs Shortest-Path Problem , 1977, SIAM J. Comput..

[10]  Alon Itai,et al.  Finding a minimum circuit in a graph , 1977, STOC '77.

[11]  Feller William,et al.  An Introduction To Probability Theory And Its Applications , 1950 .

[12]  Claus-Peter Schnorr,et al.  An Algorithm for Transitive Closure with Linear Expected Time , 1978, SIAM J. Comput..

[13]  Michael L. Fredman,et al.  On the decision tree complexity of the shortest path problems , 1975, 16th Annual Symposium on Foundations of Computer Science (sfcs 1975).