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The Theory of NP-Completeness

The Theory of NP-Completeness

The Theory of NP-Completeness. Cook ’ s Theorem (1971). Prof. Cook Toronto U. Receiving Turing Award (1982) Discussing difficult problems: worst case lower bound seems to be in the order of an exponential function NP-complete ( NPC ) Problems.

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686 views • 47 slides
How to prove that a problem is NPC

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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491 views • 28 slides
Case Studies: Bin Packing & The Traveling Salesman Problem

Case Studies: Bin Packing & The Traveling Salesman Problem

Case Studies: Bin Packing & The Traveling Salesman Problem. David S. Johnson AT&T Labs – Research. Applications. Packing commercials into station breaks Packing files onto floppy disks (CDs, DVDs, etc.) Packing MP3 songs onto CDs Packing IP packets into frames, SONET time slots, etc.

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469 views • 25 slides
Odds and Ends

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 .

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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174 views • 8 slides
CS 221 – May 24

CS 221 – May 24

CS 221 – May 24. What is it good for? Many trials or iterations needed for maximum precision Large input Intractable problems Please note: H2 due 5pm today Q2 at start of Tuesday H3 due next Wednesday. Redistricting. Redraw congressional district boundaries every 10 years.

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149 views • 6 slides

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