NP-Complete problems NP-Complete problems - Ace

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✬✩A Formal Language framework: ReducibilityEvery decision problem has a corresponding language = themaximal set of input strings that produce “yes” answers.Let L A ,L B ⊆ {0,1} ∗ be the languages corresponding to the twodecision <strong>problems</strong> A and B, respectively.Definition: L A is polynomial-time reducible to L B (writtenL A ≤ p L B ) if:• there exists a poly-time computable functionf: {0,1} ∗ → {0,1} ∗• such that for all α ∈ {0,1} ∗α ∈ L A if and only if f(α) ∈ L B .CS404/504✫Design and Analysis of Algorithms: Lecture 26Computer Science6✪
✬✩Implication of A ≤ p B• f is called a reduction function and the poly-timealgorithm F that computes f is called a reductionalgorithm.• We can use B to solve A:– Providing an answer to whether f(α) ∈ L B directlyprovides the answer to whether α ∈ L A . Hence:• Solving A is no “harder” than solving B.CS404/504✫Design and Analysis of Algorithms: Lecture 26Computer Science7✪
Page 1 and 2: ✬✩NP-Complete problemsNP-comple
Page 3 and 4: ✬✩From P to NPC• However, the
Page 5: ✬✩Polynomial reductionsCS404/50
Page 9 and 10: ✬✩NP-hard and NP-Complete• De
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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