A Faster All-Pairs Shortest Path Algorithm for Real-Weighted Sparse Graphs
We present a faster all-pairs shortest paths algorithm for arbitrary real-weighted directed graphs. The algorithm works in the fundamental comparison- addition model and runs in O(mn+n 2 log log n) time, where m and n are the number of edges & vertices, respectively. This is strictly faster than Johnson’s algorithm (for arbitrary edge-weights) and Dijkstra’s algorithm (for positive edge-weights) when m = o(n log n) and matches the running time of Hagerup’s APSP algorithm, which assumes integer edge-weights and a more powerful model of computation.
KeywordsShort Path Edge Length Short Path Problem Short Path Algorithm Normalize Edge Length
Unable to display preview. Download preview PDF.
- [CLR90]T. Cormen, C. Leiserson, R. Rivest. Intro. to Algorithms. MIT Press, 1990.Google Scholar
- [G85]H. N. Gabow. A scaling algorithm for weighted matching on general graphs. In Proc. FOCS 1985, 90–99.Google Scholar
- [Hag00]T. Hagerup. Improved shortest paths on the word RAM. In Proc. ICALP 2000, LNCS volume 1853, 61–72.Google Scholar
- [Pet02]S. Pettie. A faster all-pairs shortest path algorithm for real-weighted sparse graphs. UTCS Technical Report CS-TR-02-13, February, 2002.Google Scholar
- [Pet02b]S. Pettie. On the comparison-addition complexity of all-pairs shortest paths. UTCS Technical Report CS-TR-02-21, April, 2002.Google Scholar
- [PRS02]S. Pettie, V. Ramachandran, S. Sridhar. Experimental evaluation of a new shortest path algorithm. Proceedings of ALENEX 2002.Google Scholar
- [PR02]S. Pettie, V. Ramachandran. Computing shortest paths with comparisons and additions. Proceedings of SODA 2002, 267–276.Google Scholar
- [Z01]U. Zwick. Exact and approximate distances in graphs-A survey. Updated version at http://www.cs.tau.ac.il/zwick/, Proc. of 9th ESA (2001), 33–48.