 
Summary: On the Exponent of the All Pairs Shortest Path Problem
Noga Alon
Department of Mathematics
Sackler Faculty of Exact Sciences
TelAviv University
Zvi Galil
Department of Computer Science
Sackler Faculty of Exact Sciences
TelAviv University and Columbia University
Oded Margalit
Department of Computer Science
Sackler Faculty of Exact Sciences
TelAviv University
Abstract
The upper bound on the exponent, , of matrix multiplication over a ring that was three
in 1968 has decreased several times and since 1986 it has been 2.376. On the other hand, the
exponent of the algorithms known for the all pairs shortest path problem has stayed at three all
these years even for the very special case of directed graphs with uniform edge lengths. In this
paper we give an algorithm of time O n
log3
