{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Complexity_2

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

This preview shows pages 1–5. Sign up to view the full content.

University Dortmund Faculty of Electrical Engineering Computer Engineering Institute Scheduling Problems and Solutions Uwe Schwiegelshohn CEI University Dortmund Summer Term 2004

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Problem Classification Deterministic scheduling problems polynomial NP – hard time solution NP-hard strongly ordinary sense NP-hard pseudo polynomial solution
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.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
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 
This is the end of the preview. Sign up to access the rest of the document.

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....
View Full Document

• Spring '10
• JohnFowler
• Computational complexity theory, polynomial time algorithm, CEI University Dortmund, positive integers a1, University Dortmund

{[ snackBarMessage ]}