NP-Complete problems NP-Complete problems - Ace

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✬✩Implication of A ≤ p BLemma 34.3 If L 1 ≤ p L 2 and L 2 ∈ P, then L 1 ∈ P.• Proof:– Let A 2 be a poly-time algorithm that decides L 2 .– Let F be a poly-time reduction algorithm that does thereduction.– We construct a poly-time algorithm A 1 that decides L 1 .CS404/504✫Design and Analysis of Algorithms: Lecture 26Computer Science8✪
✬✩NP-hard and NP-Complete• Definition: L is NP-hard if ∀ L’ ∈ NP, L’ ≤ p L.• Definition: L is NP-Complete if:1) L ∈ NP.2) L ∈ NP-hard.A very likely possibility:CS404/504✫Design and Analysis of Algorithms: Lecture 26Computer Science9✪
Page 1 and 2: ✬✩NP-Complete problemsNP-comple
Page 3 and 4: ✬✩From P to NPC• However, the
Page 5 and 6: ✬✩Polynomial reductionsCS404/50
Page 7: ✬✩Implication of A ≤ p B• f
Page 11 and 12: ✬✩CKT-SAT problemDecision probl
Page 13 and 14: ✬✩Alternative definition of NP-
Page 15 and 16: ✬✩Another NPC problem: SATFormu
Page 17 and 18: ✬✩SAT: Poly-time reductionThe r
Page 19: ✬✩SAT: Poly-time reduction• E

NP-Complete problems NP-Complete problems - Ace

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