directed hypergraphs algorithms and applications - Free

More documents

Recommendations

Info

Related formulations • Minimization of superior context-free grammars (Knuth 1977) • Minimization of additive weighting functions (Nguyen, Pallottino 1988) • Monotone systems of polynomial equations (Esparza et al. 2008)
Minimization of superior context free grammars Productions: θ : Y → g θ (X 1, …, X n) n≥ 0 Y, X 1, …, X n ∈ V N ; g θ , (, ), , ∈ V T where ∀θ g θ is monotone non decreasing in each variable and ∀θ g θ (x 1, …, x n) ≥ max{ x i | i = 1, …, n} (superior functions: e.g. max (x, y), (x + y) etc. ) Language: L(Y) = { α | α ∈ V T* and Y ⇒ α} (e.g. = max ( (3 +1), (4 + max(2, 3)))) Val (α ) ∈ ℜ + Problem: Given a superior context free grammar and given the axiom Y find α in L(Y) such that Val (α) is minimum.
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: Functional directed hypergraph H F
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 and 36: Algorithm 2 computes all shortest d
Page 37: Essential references • Ausiello,

directed hypergraphs algorithms and applications - Free

Create successful ePaper yourself

Delete template?

Save as template?