One goal of shortest path algorithm

One goal of shortest path algorithms is to find the lengths of all possible shortest
paths in a weighted graph at the same time. For instance, given a road network
with all lengths of roads listed, we would like to make a list of shortest distances
between any two cities, not just the length from Detroit to Philadelphia or even
from Detroit to all cities. In this section we discuss an algorithm to compute
those lengths, developed recently by Arlinghaus, Arlinghaus, and Nystuen [1].
A program, never published previously, by which the computations were done
for that research, is included.
The algorithm constructed here is based on a new way to compute powers
of matrices, which we will call the Hedetniemi matrix sum. This sum was
suggested to Nystuen at the University of Michigan by S. Hedetniemi, who was
then a graduate student in mathematics. Hedetniemi later completed

ผลลัพธ์ (อังกฤษ) 2:

Goal is one of Shortest path algorithms of all possible lengths to Find the Shortest
Paths in a weighted graph at the Same time. For instance, Given a Road Network
with lengths of all roads listed, we would like to Make a list of Shortest distances
between any Two Cities, not just the Length from Detroit to Philadelphia or even
from Detroit to all Cities. In this section we Discuss an algorithm to Compute
those lengths, developed recently by Arlinghaus, Arlinghaus, and Nystuen [1].
A Program, Never Published previously, by which the computations were done
for that Research, is included.
The algorithm constructed here is. based on a New Way to Compute powers
of matrices, which we Hedetniemi Will Call the Matrix Sum. Sum this was
at the University of Michigan SUGGESTED to Nystuen by S. Hedetniemi, Who was
then a student Graduate in Mathematics. Hedetniemi later completed