Complexity_2

Complexity_2 - {1, , 3t} such that for i=1, , t? 2 4 b a b...

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University Dortmund Faculty of Electrical Engineering Computer Engineering Institute Scheduling Problems and Solutions Uwe Schwiegelshohn CEI University Dortmund Summer Term 2004
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Problem Classification Deterministic scheduling problems polynomial NP – hard time solution NP-hard strongly ordinary sense NP-hard pseudo polynomial solution
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Partition Given positive integers a 1,…, a t and , do there exist two disjoint subsets S1 and S2 such that for i=1,2? = = t j j a b 1 2 1 = i S j j b a Partition is NP-hard in the ordinary sense.
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3-Partition Given positive integers a 1,…, a 3t, b with , j = 1,… , 3t, and do there exist t pairwise disjoint three element subsets Si 
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Unformatted text preview: {1, , 3t} such that for i=1, , t? 2 4 b a b j < < = i S j j b a 3-Partition is strongly NP-hard. tb a t j j = = 3 1 Proof of NP-Hardness A scheduling problem is NP-hard in the ordinary sense if partition (or a similar problem) can be reduced to this problem with a polynomial time algorithm and there is an algorithm with pseudo polynomial time complexity that solves the scheduling problem. A scheduling problem is strongly NP-hard if 3-partition (or a similar problem) can be reduced to this problem with a polynomial time algorithm....
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Complexity_2 - {1, , 3t} such that for i=1, , t? 2 4 b a b...

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