slides

Dijkstra Algorithm
• Dijkstra does not require acyclicity
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instead of topological order, we use best-first order
but this requires superiority of the semiring
Let K =(A, ⊕, ⊗, 0, 1) be a semiring, and ≤ a partial ordering over A.
We say K is superior if for all a, b ∈ A
d(u)
• basically, combination always gets worse
• or, no negative edge in a graph
w(e)
a ≤ a ⊗ b, b ≤ a ⊗ b.
d(u) ⊗ w(e)
({0, 1}, ∨, ∧, 0, 1)
([0, 1], max, ×, 0, 1)
(R + ∪{+∞}, min, +, +∞, 0)
(R ∪{+∞}, min, +, +∞, 0)
Liang Huang
18
Dynamic Programming