Parallel asynchronous label-correcting methods for shortest paths

We develop parallel asynchronous implementations of some known and some new label-correcting methods for finding a shortest path from a single origin to all the other nodes of a directed graph. We compare these implementations on a shared-memory multiprocessor, the Alliant FX/80, using several types of randomly generated problems. Excellent (sometimes superlinear) speedup is achieved with some of the methods, and it is found that the asynchronous versions of these methods are substantially faster than their synchronous counterparts.

[1]  U. Pape,et al.  Implementation and efficiency of Moore-algorithms for the shortest route problem , 1974, Math. Program..

[2]  Darwin Klingman,et al.  NETGEN: A Program for Generating Large Scale Capacitated Assignment, Transportation, and Minimum Cost Flow Network Problems , 1974 .

[3]  Dimitri P. Bertsekas,et al.  Data Networks , 1986 .

[4]  G. Gallo,et al.  SHORTEST PATH METHODS: A UNIFYING APPROACH , 1986 .

[5]  Giorgio Gallo,et al.  Shortest path algorithms , 1988 .

[6]  M. Bartholomew-Biggs,et al.  Some effective methods for unconstrained optimization based on the solution of systems of ordinary differential equations , 1989 .

[7]  John N. Tsitsiklis,et al.  Parallel and distributed computation , 1989 .

[8]  Dimitri P. Bertsekas,et al.  Linear network optimization - algorithms and codes , 1991 .

[9]  Dimitri P. Bertsekas,et al.  An Auction Algorithm for Shortest Paths , 1991, SIAM J. Optim..

[10]  Dimitri P. Bertsekas,et al.  Parallel synchronous and asynchronous implementations of the auction algorithm , 1991, Parallel Comput..

[11]  Dimitri P. Bertsekas,et al.  Data networks (2nd ed.) , 1992 .

[12]  Jeffery L. Kennington,et al.  The one-to-one shortest-path problem: An empirical analysis with the two-tree Dijkstra algorithm , 1993, Comput. Optim. Appl..

[13]  Dimitri P. Bertsekas,et al.  A simple and fast label correcting algorithm for shortest paths , 1993, Networks.

[14]  Jesper Larsson Träff.  Precis: Distributed Shortest Path Algorithms , 1993, PARLE.

[15]  Dimitri P. Bertsekas,et al.  Parallel Shortest Path Auction Algorithms , 1994, Parallel Comput..

[16]  Dimitri P. Bertsekas,et al.  Polynomial auction algorithms for shortest paths , 1995, Comput. Optim. Appl..

[17]  J. Walrand,et al.  Distributed Dynamic Programming , 2022 .