TR-2012-20

Shortest paths in mixed graphs

Zoltán Király



Abstract

Finding shortest paths in mixed graphs is NP-hard even when the weighting is conservative. We give an FPT algorithm for this problem, where the parameter k is the number of "negative trees". We may always assume that the undirected edges have negative weight, and in a conservative weighting they form some trees -- these trees are called the negative trees. Our algorithm extends to mixed graphs with conservative weighting, where in each strongly connected component there are at most k negative trees. Necessarily we can also detect whether the weighting is conservative or not. If it is not conservative we give a strongly polynomial algorithm for the shortest exact (and bounded) walk problems, where we are looking the shortest walk from s to t consisting of exactly (at most) K edges.


Bibtex entry:

@techreport{egres-12-20,
AUTHOR = {Kir{\'a}ly, Zolt{\'a}n},
TITLE = {Shortest paths in mixed graphs},
NOTE= {{\tt www.cs.elte.hu/egres}},
INSTITUTION = {Egerv{\'a}ry Research Group, Budapest},
YEAR = {2012},
NUMBER = {TR-2012-20}
}


Last modification: 5.6.2018. Please email your comments to Tamás Király!