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  1. ; ; ; ; (, Schloss Dagstuhl – Leibniz-Zentrum für Informatik)
    Mestre, Julián; Wirth, Anthony (Ed.)
    We consider the classical single-source shortest path problem in directed weighted graphs. D. Eppstein proved recently an Ω(n³) lower bound for oblivious algorithms that use relaxation operations to update the tentative distances from the source vertex. We generalize this result by extending this Ω(n³) lower bound to adaptive algorithms that, in addition to relaxations, can perform queries involving some simple types of linear inequalities between edge weights and tentative distances. Our model captures as a special case the operations on tentative distances used by Dijkstra’s algorithm. 
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