directed hypergraphs algorithms and applications - Free

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A hard instance with a weakly superior function: gap Remember: g (h Z, t) = w X,t + min (g(h Z, x1), g(h Z, x2), …, g(h Z, xn))
In the previous example we have the following sequence of steps: Extract-min (Q) = a 3 g(a 3) = 6 Extract-min (Q) = a 2 g(a 2) = 7 Extract-min (Q) = a 1 g(a 1) = 8 Extract-min (Q) = a 0 g(a 0) = 9 Enqueue (c 0) g(c 0) = 10 Extract-min (Q) = c 0 Enqueue (c 1) g(c 1) = 11 Extract-min (Q) = c 1 Enqueue (b 1) g(b 1) = 12 Extract-min (Q) = b 1 Now a new link (a 1 b 1, c 0) is created <strong>and</strong> c 0 has to be enqueued again with g(c 0) =9 <strong>and</strong> so on: g(c 0) =8, g(c 0) =7, etc.
Page 1 and 2: DIRECTED HYPERGRAPHS ALGORITHMS AND
Page 3 and 4: Shortest Hyperpath Problems The fol
Page 5 and 6: Measuring hyperpaths On directed hy
Page 7 and 8: Left Hyperpath Gap=3 Rank=4 Gap and
Page 9 and 10: An example of the folded an unfolde
Page 11 and 12: Example. In the most intuitive case
Page 13 and 14: Threshold: t = (0, max, max) t (∅
Page 15 and 16: The most general formulation of (si
Page 17 and 18: Generalization: Bellman-Ford equati
Page 19 and 20: Functional directed hypergraph H F
Page 21 and 22: Minimization of superior context fr
Page 23 and 24: Weakly superior functions (WSUP): g
Page 25 and 26: In the following we will see how (a
Page 27 and 28: Algorithm 1 - Let H = be a directe
Page 29: Algorithm 1 can be applied to minim
Page 33 and 34: Note that in this case convergence
Page 35 and 36: Algorithm 2 computes all shortest d
Page 37: Essential references • Ausiello,

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