directed hypergraphs algorithms and applications - Free

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Exercises Prove that the following problems are NP-hard: • hyperpath with minimum size • hyperpath with minimum source area • hyperpath with minimum number of source sets
Essential references • Ausiello, D’Atri, Sacca’, Minimal representation of directed hypergraphs, SIAM on Comp., 1986 • Ausiello, Italiano, Online algorithms for polynomially solvable satisfiability problems, J. of Logic Prog., 1991 • Gallo, Longo, Nguyen, Pallottino, Directed hypergraphs and applications, Discrete Applied Math., 1993 • Ramalingam, Reps, An incremental algorithm for a generalization of the shortest path problem, J. of Algorithms, 1996 • Esparza, Kiefer, Luttenberger, Solving monotone polynomial equations, 5° IFIP Conf. on Theor. Comp. Sc., 2008 • Ausiello, Italiano, Laura, Nanni, Sarracco, Classification and traversal algorithmic techniques for optimization problems on directed hyperpaths, Tech. Rep. DIS, Sapienza University of Rome 2011
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 and 30: Algorithm 1 can be applied to minim
Page 31 and 32: In the previous example we have the
Page 33 and 34: Note that in this case convergence
Page 35: Algorithm 2 computes all shortest d

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