'Partition problem' diaporamas de présentation

The Theory of NP-Completeness

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How to prove that a problem is NPC

How to prove that a problem is NPC. Cook. Cook showed the first NPC problem: SAT Cook received Turing Award in 1982. Karp. R. Karp showed several NPC problems, such as 3-STA, node (vertex) cover, and Hamiltonian cycle, etc. Karp received Turing Award in 1985.

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Case Studies: Bin Packing & The Traveling Salesman Problem

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Odds and Ends

Odds and Ends. HP ? p HC (again) Turing reductions Strong NP-completeness versus Weak NP-completeness Vertex Cover to Hamiltonian Cycle. Example: HP ? p HC. Hamiltonian Path Input: Undirected Graph G = (V,E) Y/N Question: Does G contain a Hamiltonian Path? Hamiltonian Cycle

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Example 4 : Show that the Square Packing (SP) Problem is NP-complete .

Example 4 : Show that the Square Packing (SP) Problem is NP-complete . Motivation : truck loading, processor allocation problem in a partitionable mesh connected system, the design of VLSI chips and etc. Square Packing Problem

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