### Efficient Algorithms for Shortest Paths in Sparse NetworksEfficient Algorithms for Shortest Paths in Sparse Networks

Access Restriction
Subscribed

 Author Johnson, Donald B. Source ACM Digital Library Content type Text Publisher Association for Computing Machinery (ACM) File Format PDF Copyright Year ©1977 Language English
 Subject Domain (in DDC) Computer science, information & general works ♦ Data processing & computer science Abstract Algorithms for finding shortest paths are presented which are faster than algorithms previously known on networks which are relatively sparse in arcs. Known results which the results of this paper extend are surveyed briefly and analyzed. A new implementation for priority queues is employed, and a class of “arc set partition” algorithms is introduced. For the single source problem on networks with nonnegative arcs a running time of $\textit{O}(min(\textit{n}1+1/\textit{k}$ + $\textit{e},$ $\textit{n}$ + $\textit{e})$ log $\textit{n}))$ is achieved, where there are $\textit{n}$ nodes and $\textit{e}$ arcs, and $\textit{k}$ is a fixed integer satisfying $\textit{k}$ > 0. This bound is $\textit{O}(\textit{e})$ on dense networks. For the single source and all pairs problem on unrestricted networks the running time is $\textit{O}(min(\textit{n}2+1/\textit{k}$ + $\textit{ne},$ $\textit{n}2$ log $\textit{n}$ + $\textit{ne}$ log $\textit{n}).$ ISSN 00045411 Age Range 18 to 22 years ♦ above 22 year Educational Use Research Education Level UG and PG Learning Resource Type Article Publisher Date 1977-01-01 Publisher Place New York e-ISSN 1557735X Journal Journal of the ACM (JACM) Volume Number 24 Issue Number 1 Page Count 13 Starting Page 1 Ending Page 13

#### Open content in new tab

Source: ACM Digital Library