A faster algorithm for the single source shortest path problem with few distinct positive lengths

Authors:
James B. Orlin;Kamesh Madduri;K. Subramani;M. Williamson
Affiliations:
Sloan School of Management, MIT, Cambridge, MA, USA;Computational Research Division, Lawrence Berkeley Laboratory, Berkeley, CA, USA;LDCSEE, West Virginia University, Morgantown, WV, USA;LDCSEE, West Virginia University, Morgantown, WV, USA
Venue:
Journal of Discrete Algorithms
Year:
2010

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Abstract

In this paper, we propose an efficient method for implementing Dijkstra's algorithm for the Single Source Shortest Path Problem (SSSPP) in a graph whose edges have positive length, and where there are few distinct edge lengths. The SSSPP is one of the most widely studied problems in theoretical computer science and operations research. On a graph with n vertices, m edges and K distinct edge lengths, our algorithm runs in O(m) time if nK=