On orientations and shortest paths

Rafael Hassin*, Nimrod Megiddo

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


An orientation of an undirected graph is a choice of direction for each of its edges. An orientation is called ideal with respect to a given set of pairs of vertices if it does not increase the shortest-path distances between the members of any of the pairs. A polynomial-time algorithm is given for constructing an ideal orientation with respect to two given pairs and any positive edge-lengths, or else recognizing that no such orientation exists. Moreover, we show that this problem is in the class NC. For a general number of pairs the problem is proven NP-complete even with unit edge-lengths.

Original languageEnglish
Pages (from-to)589-602
Number of pages14
JournalLinear Algebra and Its Applications
Issue numberC
StatePublished - 1989


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