directed hypergraphs algorithms and applications - Free

In the example a major role is played by two facts:
1) a node can become reachable from a new source set during
the computation and therefore it has to be repeatedly visited
during shortest path computation
2) the measure is based on weakly superior functions and
therefore the value of the measure can decrease after a cycle
has been visited; this cannot happen with superior functions
As a consequence the approach of Algorithm 1 would incur
into cost
O(|N| log |N| + W |H |)
where W = # of values of domain (possible values of measure)