SlideShare a Scribd company logo

lecture 30

•Download as PPT, PDF•
•
S
sajinsc

The document reviews concepts related to NP-completeness, including reductions between problems. It provides examples of reducing the directed Hamiltonian cycle problem to the undirected version. It also reduces 3-SAT to the clique problem by transforming a Boolean formula to a graph, then further reduces clique to vertex cover. Hundreds of problems have been shown to be NP-complete through relatively simple reductions like these that leverage previous results.

EducationTechnology
1 of 24
CS 332: Algorithms NP Completeness Continued: Reductions
Review: P and NP ,[object Object],[object Object],[object Object]
Review: P and NP ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Review: NP-Complete ,[object Object],[object Object],[object Object],[object Object]
Review: NP-Complete ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Review: Proving Problems NP-Complete ,[object Object],[object Object]
Review: Directed  Undirected Ham. Cycle ,[object Object],[object Object],[object Object],[object Object]
Review: Directed  Undirected Ham. Cycle ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Review: Hamiltonian Cycle  TSP ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Review: Hamiltonian Cycle  TSP ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
The SAT Problem ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Conjunctive Normal Form ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
The 3-CNF Problem ,[object Object],[object Object],[object Object],[object Object]
3-CNF  Clique ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
3-CNF  Clique ,[object Object],[object Object]
3-CNF  Clique ,[object Object],[object Object],[object Object],[object Object],[object Object]
3-CNF  Clique ,[object Object],[object Object],[object Object],[object Object],[object Object]
Clique  Vertex Cover ,[object Object],[object Object],[object Object],[object Object]
Clique  Vertex Cover ,[object Object],[object Object],[object Object],[object Object],[object Object]
Clique  Vertex Cover ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Clique  Vertex Cover ,[object Object],[object Object],[object Object],[object Object],[object Object]
General Comments ,[object Object],[object Object],[object Object]
Other NP-Complete Problems ,[object Object],[object Object],[object Object],[object Object],[object Object]
The End

Recommended

Topological Sort
Topological SortTopological Sort
Topological SortDr Sandeep Kumar Poonia
 
Np complete
Np completeNp complete
Np completeDr. C.V. Suresh Babu
 
SINGLE-SOURCE SHORTEST PATHS
SINGLE-SOURCE SHORTEST PATHS SINGLE-SOURCE SHORTEST PATHS
SINGLE-SOURCE SHORTEST PATHS Md. Shafiuzzaman Hira
 
Shortest path algorithms
Shortest path algorithmsShortest path algorithms
Shortest path algorithmsAmit Kumar Rathi
 
Automata theory
Automata theoryAutomata theory
Automata theoryPardeep Vats
 
Knapsack problem algorithm, greedy algorithm
Knapsack problem algorithm, greedy algorithmKnapsack problem algorithm, greedy algorithm
Knapsack problem algorithm, greedy algorithmHoneyChintal
 
Optimal binary search tree dynamic programming
Optimal binary search tree dynamic programmingOptimal binary search tree dynamic programming
Optimal binary search tree dynamic programmingP. Subathra Kishore, KAMARAJ College of Engineering and Technology, Madurai
 
Optimal binary search tree
Optimal binary search treeOptimal binary search tree
Optimal binary search treeKavya P
 

Recommended

Topological Sort
Topological SortTopological Sort
Topological SortDr Sandeep Kumar Poonia
 
Np complete
Np completeNp complete
Np completeDr. C.V. Suresh Babu
 
SINGLE-SOURCE SHORTEST PATHS
SINGLE-SOURCE SHORTEST PATHS SINGLE-SOURCE SHORTEST PATHS
SINGLE-SOURCE SHORTEST PATHS Md. Shafiuzzaman Hira
 
Shortest path algorithms
Shortest path algorithmsShortest path algorithms
Shortest path algorithmsAmit Kumar Rathi
 
Automata theory
Automata theoryAutomata theory
Automata theoryPardeep Vats
 
Knapsack problem algorithm, greedy algorithm
Knapsack problem algorithm, greedy algorithmKnapsack problem algorithm, greedy algorithm
Knapsack problem algorithm, greedy algorithmHoneyChintal
 
Optimal binary search tree dynamic programming
Optimal binary search tree dynamic programmingOptimal binary search tree dynamic programming
Optimal binary search tree dynamic programmingP. Subathra Kishore, KAMARAJ College of Engineering and Technology, Madurai
 
Optimal binary search tree
Optimal binary search treeOptimal binary search tree
Optimal binary search treeKavya P
 
Graph coloring using backtracking
Graph coloring using backtrackingGraph coloring using backtracking
Graph coloring using backtrackingshashidharPapishetty
 
Fractional knapsack class 13
Fractional knapsack class 13Fractional knapsack class 13
Fractional knapsack class 13Kumar
 
Backtracking
BacktrackingBacktracking
Backtrackingsubhradeep mitra
 
01 Knapsack using Dynamic Programming
01 Knapsack using Dynamic Programming01 Knapsack using Dynamic Programming
01 Knapsack using Dynamic ProgrammingFenil Shah
 
Ford Fulkerson Algorithm
Ford Fulkerson AlgorithmFord Fulkerson Algorithm
Ford Fulkerson AlgorithmAdarsh Rotte
 
Graph theory
Graph theoryGraph theory
Graph theoryJeane Paguio
 
Np completeness
Np completenessNp completeness
Np completenessRajendran
 
Trees and graphs
Trees and graphsTrees and graphs
Trees and graphsLokesh Singrol
 
Network flow problems
Network flow problemsNetwork flow problems
Network flow problemsDr Sandeep Kumar Poonia
 
Dynamic Programming-Knapsack Problem
Dynamic Programming-Knapsack ProblemDynamic Programming-Knapsack Problem
Dynamic Programming-Knapsack ProblemAmrita Yadav
 
Branch and bound
Branch and boundBranch and bound
Branch and boundNv Thejaswini
 
Longest common subsequence
Longest common subsequenceLongest common subsequence
Longest common subsequenceKiran K
 
BackTracking Algorithm: Technique and Examples
BackTracking Algorithm: Technique and ExamplesBackTracking Algorithm: Technique and Examples
BackTracking Algorithm: Technique and ExamplesFahim Ferdous
 
Undecidabality
UndecidabalityUndecidabality
UndecidabalityAnshuman Biswal
 
Sum of subsets problem by backtracking 
Sum of subsets problem by backtracking Sum of subsets problem by backtracking 
Sum of subsets problem by backtracking Hasanain Alshadoodee
 
Pda
PdaPda
PdaSelf-employed
 
sum of subset problem using Backtracking
sum of subset problem using Backtrackingsum of subset problem using Backtracking
sum of subset problem using BacktrackingAbhishek Singh
 
Theory of Computation Unit 3
Theory of Computation Unit 3Theory of Computation Unit 3
Theory of Computation Unit 3Jena Catherine Bel D
 
Theory of automata and formal language
Theory of automata and formal languageTheory of automata and formal language
Theory of automata and formal languageRabia Khalid
 
SINGLE SOURCE SHORTEST PATH.ppt
SINGLE SOURCE SHORTEST PATH.pptSINGLE SOURCE SHORTEST PATH.ppt
SINGLE SOURCE SHORTEST PATH.pptshanthishyam
 
Skiena algorithm 2007 lecture20 satisfiability
Skiena algorithm 2007 lecture20 satisfiabilitySkiena algorithm 2007 lecture20 satisfiability
Skiena algorithm 2007 lecture20 satisfiabilityzukun
 
Algorithm_NP-Completeness Proof
Algorithm_NP-Completeness ProofAlgorithm_NP-Completeness Proof
Algorithm_NP-Completeness ProofIm Rafid
 

More Related Content

What's hot

Fractional knapsack class 13
Fractional knapsack class 13Fractional knapsack class 13
Fractional knapsack class 13Kumar
 
01 Knapsack using Dynamic Programming
01 Knapsack using Dynamic Programming01 Knapsack using Dynamic Programming
01 Knapsack using Dynamic ProgrammingFenil Shah
 
Ford Fulkerson Algorithm
Ford Fulkerson AlgorithmFord Fulkerson Algorithm
Ford Fulkerson AlgorithmAdarsh Rotte
 
Np completeness
Np completenessNp completeness
Np completenessRajendran
 
Dynamic Programming-Knapsack Problem
Dynamic Programming-Knapsack ProblemDynamic Programming-Knapsack Problem
Dynamic Programming-Knapsack ProblemAmrita Yadav
 
Longest common subsequence
Longest common subsequenceLongest common subsequence
Longest common subsequenceKiran K
 
BackTracking Algorithm: Technique and Examples
BackTracking Algorithm: Technique and ExamplesBackTracking Algorithm: Technique and Examples
BackTracking Algorithm: Technique and ExamplesFahim Ferdous
 
Sum of subsets problem by backtracking 
Sum of subsets problem by backtracking Sum of subsets problem by backtracking 
Sum of subsets problem by backtracking Hasanain Alshadoodee
 
sum of subset problem using Backtracking
sum of subset problem using Backtrackingsum of subset problem using Backtracking
sum of subset problem using BacktrackingAbhishek Singh
 
Theory of automata and formal language
Theory of automata and formal languageTheory of automata and formal language
Theory of automata and formal languageRabia Khalid
 
SINGLE SOURCE SHORTEST PATH.ppt
SINGLE SOURCE SHORTEST PATH.pptSINGLE SOURCE SHORTEST PATH.ppt
SINGLE SOURCE SHORTEST PATH.pptshanthishyam
 

What's hot (20)

Graph coloring using backtracking
Graph coloring using backtrackingGraph coloring using backtracking
Graph coloring using backtracking
 
Fractional knapsack class 13
Fractional knapsack class 13Fractional knapsack class 13
Fractional knapsack class 13
 
Backtracking
BacktrackingBacktracking
Backtracking
 
01 Knapsack using Dynamic Programming
01 Knapsack using Dynamic Programming01 Knapsack using Dynamic Programming
01 Knapsack using Dynamic Programming
 
Ford Fulkerson Algorithm
Ford Fulkerson AlgorithmFord Fulkerson Algorithm
Ford Fulkerson Algorithm
 
Graph theory
Graph theoryGraph theory
Graph theory
 
Np completeness
Np completenessNp completeness
Np completeness
 
Trees and graphs
Trees and graphsTrees and graphs
Trees and graphs
 
Network flow problems
Network flow problemsNetwork flow problems
Network flow problems
 
Dynamic Programming-Knapsack Problem
Dynamic Programming-Knapsack ProblemDynamic Programming-Knapsack Problem
Dynamic Programming-Knapsack Problem
 
Branch and bound
Branch and boundBranch and bound
Branch and bound
 
Longest common subsequence
Longest common subsequenceLongest common subsequence
Longest common subsequence
 
BackTracking Algorithm: Technique and Examples
BackTracking Algorithm: Technique and ExamplesBackTracking Algorithm: Technique and Examples
BackTracking Algorithm: Technique and Examples
 
Undecidabality
UndecidabalityUndecidabality
Undecidabality
 
Sum of subsets problem by backtracking 
Sum of subsets problem by backtracking Sum of subsets problem by backtracking 
Sum of subsets problem by backtracking 
 
Pda
PdaPda
Pda
 
sum of subset problem using Backtracking
sum of subset problem using Backtrackingsum of subset problem using Backtracking
sum of subset problem using Backtracking
 
Theory of Computation Unit 3
Theory of Computation Unit 3Theory of Computation Unit 3
Theory of Computation Unit 3
 
Theory of automata and formal language
Theory of automata and formal languageTheory of automata and formal language
Theory of automata and formal language
 
SINGLE SOURCE SHORTEST PATH.ppt
SINGLE SOURCE SHORTEST PATH.pptSINGLE SOURCE SHORTEST PATH.ppt
SINGLE SOURCE SHORTEST PATH.ppt
 

Similar to lecture 30

Skiena algorithm 2007 lecture20 satisfiability
Skiena algorithm 2007 lecture20 satisfiabilitySkiena algorithm 2007 lecture20 satisfiability
Skiena algorithm 2007 lecture20 satisfiabilityzukun
 
Algorithm_NP-Completeness Proof
Algorithm_NP-Completeness ProofAlgorithm_NP-Completeness Proof
Algorithm_NP-Completeness ProofIm Rafid
 
lecture 29
lecture 29lecture 29
lecture 29sajinsc
 
Skiena algorithm 2007 lecture21 other reduction
Skiena algorithm 2007 lecture21 other reductionSkiena algorithm 2007 lecture21 other reduction
Skiena algorithm 2007 lecture21 other reductionzukun
 
Kernelization Basics
Kernelization BasicsKernelization Basics
Kernelization BasicsASPAK2014
 
Np completeness h4
Np completeness h4Np completeness h4
Np completeness h4Rajendran
 
P, NP and NP-Complete, Theory of NP-Completeness V2
P, NP and NP-Complete, Theory of NP-Completeness V2P, NP and NP-Complete, Theory of NP-Completeness V2
P, NP and NP-Complete, Theory of NP-Completeness V2S.Shayan Daneshvar
 
Algorithm Design and Complexity - Course 6
Algorithm Design and Complexity - Course 6Algorithm Design and Complexity - Course 6
Algorithm Design and Complexity - Course 6Traian Rebedea
 
Bt0080 fundamentals of algorithms2
Bt0080 fundamentals of algorithms2Bt0080 fundamentals of algorithms2
Bt0080 fundamentals of algorithms2Techglyphs
 
Introduction to the Theory of Computation, Winter 2003 A. Hevia and J. Mao S...
Introduction to the Theory of Computation, Winter 2003 A. Hevia and J. Mao S... Introduction to the Theory of Computation, Winter 2003 A. Hevia and J. Mao S...
Introduction to the Theory of Computation, Winter 2003 A. Hevia and J. Mao S...parmeet834
 
Important Cuts and (p,q)-clustering
Important Cuts and (p,q)-clusteringImportant Cuts and (p,q)-clustering
Important Cuts and (p,q)-clusteringASPAK2014
 
Iterative Compression
Iterative CompressionIterative Compression
Iterative CompressionASPAK2014
 
Solving connectivity problems via basic Linear Algebra
Solving connectivity problems via basic Linear AlgebraSolving connectivity problems via basic Linear Algebra
Solving connectivity problems via basic Linear Algebracseiitgn
 

Similar to lecture 30 (20)

Skiena algorithm 2007 lecture20 satisfiability
Skiena algorithm 2007 lecture20 satisfiabilitySkiena algorithm 2007 lecture20 satisfiability
Skiena algorithm 2007 lecture20 satisfiability
 
Algorithm_NP-Completeness Proof
Algorithm_NP-Completeness ProofAlgorithm_NP-Completeness Proof
Algorithm_NP-Completeness Proof
 
lecture 29
lecture 29lecture 29
lecture 29
 
Skiena algorithm 2007 lecture21 other reduction
Skiena algorithm 2007 lecture21 other reductionSkiena algorithm 2007 lecture21 other reduction
Skiena algorithm 2007 lecture21 other reduction
 
Kernelization Basics
Kernelization BasicsKernelization Basics
Kernelization Basics
 
Approx
ApproxApprox
Approx
 
Np completeness h4
Np completeness h4Np completeness h4
Np completeness h4
 
Reductions
ReductionsReductions
Reductions
 
P, NP and NP-Complete, Theory of NP-Completeness V2
P, NP and NP-Complete, Theory of NP-Completeness V2P, NP and NP-Complete, Theory of NP-Completeness V2
P, NP and NP-Complete, Theory of NP-Completeness V2
 
Algorithm Design and Complexity - Course 6
Algorithm Design and Complexity - Course 6Algorithm Design and Complexity - Course 6
Algorithm Design and Complexity - Course 6
 
Bt0080 fundamentals of algorithms2
Bt0080 fundamentals of algorithms2Bt0080 fundamentals of algorithms2
Bt0080 fundamentals of algorithms2
 
class23.ppt
class23.pptclass23.ppt
class23.ppt
 
Introduction to the Theory of Computation, Winter 2003 A. Hevia and J. Mao S...
Introduction to the Theory of Computation, Winter 2003 A. Hevia and J. Mao S... Introduction to the Theory of Computation, Winter 2003 A. Hevia and J. Mao S...
Introduction to the Theory of Computation, Winter 2003 A. Hevia and J. Mao S...
 
Stochastic Process Exam Help
Stochastic Process Exam HelpStochastic Process Exam Help
Stochastic Process Exam Help
 
Important Cuts and (p,q)-clustering
Important Cuts and (p,q)-clusteringImportant Cuts and (p,q)-clustering
Important Cuts and (p,q)-clustering
 
Lecture26
Lecture26Lecture26
Lecture26
 
Iterative Compression
Iterative CompressionIterative Compression
Iterative Compression
 
Solving connectivity problems via basic Linear Algebra
Solving connectivity problems via basic Linear AlgebraSolving connectivity problems via basic Linear Algebra
Solving connectivity problems via basic Linear Algebra
 
Teori pnp
Teori pnpTeori pnp
Teori pnp
 
Internship
InternshipInternship
Internship
 

More from sajinsc

lecture 28
lecture 28lecture 28
lecture 28sajinsc
 
lecture 27
lecture 27lecture 27
lecture 27sajinsc
 
lecture 26
lecture 26lecture 26
lecture 26sajinsc
 
lecture 25
lecture 25lecture 25
lecture 25sajinsc
 
lecture 24
lecture 24lecture 24
lecture 24sajinsc
 
lecture 23
lecture 23lecture 23
lecture 23sajinsc
 
lecture 22
lecture 22lecture 22
lecture 22sajinsc
 
lecture 21
lecture 21lecture 21
lecture 21sajinsc
 
lecture 20
lecture 20lecture 20
lecture 20sajinsc
 
lecture 19
lecture 19lecture 19
lecture 19sajinsc
 
lecture 18
lecture 18lecture 18
lecture 18sajinsc
 
lecture 17
lecture 17lecture 17
lecture 17sajinsc
 
lecture 16
lecture 16lecture 16
lecture 16sajinsc
 
lecture 15
lecture 15lecture 15
lecture 15sajinsc
 
lecture 14
lecture 14lecture 14
lecture 14sajinsc
 
lecture 13
lecture 13lecture 13
lecture 13sajinsc
 
lecture 12
lecture 12lecture 12
lecture 12sajinsc
 
lecture 11
lecture 11lecture 11
lecture 11sajinsc
 
lecture 10
lecture 10lecture 10
lecture 10sajinsc
 
lecture 9
lecture 9lecture 9
lecture 9sajinsc
 

More from sajinsc (20)

lecture 28
lecture 28lecture 28
lecture 28
 
lecture 27
lecture 27lecture 27
lecture 27
 
lecture 26
lecture 26lecture 26
lecture 26
 
lecture 25
lecture 25lecture 25
lecture 25
 
lecture 24
lecture 24lecture 24
lecture 24
 
lecture 23
lecture 23lecture 23
lecture 23
 
lecture 22
lecture 22lecture 22
lecture 22
 
lecture 21
lecture 21lecture 21
lecture 21
 
lecture 20
lecture 20lecture 20
lecture 20
 
lecture 19
lecture 19lecture 19
lecture 19
 
lecture 18
lecture 18lecture 18
lecture 18
 
lecture 17
lecture 17lecture 17
lecture 17
 
lecture 16
lecture 16lecture 16
lecture 16
 
lecture 15
lecture 15lecture 15
lecture 15
 
lecture 14
lecture 14lecture 14
lecture 14
 
lecture 13
lecture 13lecture 13
lecture 13
 
lecture 12
lecture 12lecture 12
lecture 12
 
lecture 11
lecture 11lecture 11
lecture 11
 
lecture 10
lecture 10lecture 10
lecture 10
 
lecture 9
lecture 9lecture 9
lecture 9
 

Recently uploaded

Industrial Policy - 1948, 1956, 1973, 1977, 1980, 1991
Industrial Policy - 1948, 1956, 1973, 1977, 1980, 1991Industrial Policy - 1948, 1956, 1973, 1977, 1980, 1991
Industrial Policy - 1948, 1956, 1973, 1977, 1980, 1991RKavithamani
 
Introduction to ArtificiaI Intelligence in Higher Education
Introduction to ArtificiaI Intelligence in Higher EducationIntroduction to ArtificiaI Intelligence in Higher Education
Introduction to ArtificiaI Intelligence in Higher Educationpboyjonauth
 
Nutritional Needs Presentation - HLTH 104
Nutritional Needs Presentation - HLTH 104Nutritional Needs Presentation - HLTH 104
Nutritional Needs Presentation - HLTH 104misteraugie
 
Kisan Call Centre - To harness potential of ICT in Agriculture by answer farm...
Kisan Call Centre - To harness potential of ICT in Agriculture by answer farm...Kisan Call Centre - To harness potential of ICT in Agriculture by answer farm...
Kisan Call Centre - To harness potential of ICT in Agriculture by answer farm...Krashi Coaching
 
A Critique of the Proposed National Education Policy Reform
A Critique of the Proposed National Education Policy ReformA Critique of the Proposed National Education Policy Reform
A Critique of the Proposed National Education Policy ReformChameera Dedduwage
 
Z Score,T Score, Percential Rank and Box Plot Graph
Z Score,T Score, Percential Rank and Box Plot GraphZ Score,T Score, Percential Rank and Box Plot Graph
Z Score,T Score, Percential Rank and Box Plot GraphThiyagu K
 
Interactive Powerpoint_How to Master effective communication
Interactive Powerpoint_How to Master effective communicationInteractive Powerpoint_How to Master effective communication
Interactive Powerpoint_How to Master effective communicationnomboosow
 
Introduction to AI in Higher Education_draft.pptx
Introduction to AI in Higher Education_draft.pptxIntroduction to AI in Higher Education_draft.pptx
Introduction to AI in Higher Education_draft.pptxpboyjonauth
 
1029-Danh muc Sach Giao Khoa khoi 6.pdf
1029-Danh muc Sach Giao Khoa khoi 6.pdf1029-Danh muc Sach Giao Khoa khoi 6.pdf
1029-Danh muc Sach Giao Khoa khoi 6.pdfQucHHunhnh
 
Beyond the EU: DORA and NIS 2 Directive's Global Impact
Beyond the EU: DORA and NIS 2 Directive's Global ImpactBeyond the EU: DORA and NIS 2 Directive's Global Impact
Beyond the EU: DORA and NIS 2 Directive's Global ImpactPECB
 
18-04-UA_REPORT_MEDIALITERAСY_INDEX-DM_23-1-final-eng.pdf
18-04-UA_REPORT_MEDIALITERAСY_INDEX-DM_23-1-final-eng.pdf18-04-UA_REPORT_MEDIALITERAСY_INDEX-DM_23-1-final-eng.pdf
18-04-UA_REPORT_MEDIALITERAСY_INDEX-DM_23-1-final-eng.pdfssuser54595a
 
Activity 01 - Artificial Culture (1).pdf
Activity 01 - Artificial Culture (1).pdfActivity 01 - Artificial Culture (1).pdf
Activity 01 - Artificial Culture (1).pdfciinovamais
 
Paris 2024 Olympic Geographies - an activity
Paris 2024 Olympic Geographies - an activityParis 2024 Olympic Geographies - an activity
Paris 2024 Olympic Geographies - an activityGeoBlogs
 
The basics of sentences session 2pptx copy.pptx
The basics of sentences session 2pptx copy.pptxThe basics of sentences session 2pptx copy.pptx
The basics of sentences session 2pptx copy.pptxheathfieldcps1
 
Web & Social Media Analytics Previous Year Question Paper.pdf
Web & Social Media Analytics Previous Year Question Paper.pdfWeb & Social Media Analytics Previous Year Question Paper.pdf
Web & Social Media Analytics Previous Year Question Paper.pdfJayanti Pande
 
Mastering the Unannounced Regulatory Inspection
Mastering the Unannounced Regulatory InspectionMastering the Unannounced Regulatory Inspection
Mastering the Unannounced Regulatory InspectionSafetyChain Software
 

Recently uploaded (20)

Industrial Policy - 1948, 1956, 1973, 1977, 1980, 1991
Industrial Policy - 1948, 1956, 1973, 1977, 1980, 1991Industrial Policy - 1948, 1956, 1973, 1977, 1980, 1991
Industrial Policy - 1948, 1956, 1973, 1977, 1980, 1991
 
Introduction to ArtificiaI Intelligence in Higher Education
Introduction to ArtificiaI Intelligence in Higher EducationIntroduction to ArtificiaI Intelligence in Higher Education
Introduction to ArtificiaI Intelligence in Higher Education
 
Nutritional Needs Presentation - HLTH 104
Nutritional Needs Presentation - HLTH 104Nutritional Needs Presentation - HLTH 104
Nutritional Needs Presentation - HLTH 104
 
Kisan Call Centre - To harness potential of ICT in Agriculture by answer farm...
Kisan Call Centre - To harness potential of ICT in Agriculture by answer farm...Kisan Call Centre - To harness potential of ICT in Agriculture by answer farm...
Kisan Call Centre - To harness potential of ICT in Agriculture by answer farm...
 
A Critique of the Proposed National Education Policy Reform
A Critique of the Proposed National Education Policy ReformA Critique of the Proposed National Education Policy Reform
A Critique of the Proposed National Education Policy Reform
 
INDIA QUIZ 2024 RLAC DELHI UNIVERSITY.pptx
INDIA QUIZ 2024 RLAC DELHI UNIVERSITY.pptxINDIA QUIZ 2024 RLAC DELHI UNIVERSITY.pptx
INDIA QUIZ 2024 RLAC DELHI UNIVERSITY.pptx
 
Z Score,T Score, Percential Rank and Box Plot Graph
Z Score,T Score, Percential Rank and Box Plot GraphZ Score,T Score, Percential Rank and Box Plot Graph
Z Score,T Score, Percential Rank and Box Plot Graph
 
Interactive Powerpoint_How to Master effective communication
Interactive Powerpoint_How to Master effective communicationInteractive Powerpoint_How to Master effective communication
Interactive Powerpoint_How to Master effective communication
 
Introduction to AI in Higher Education_draft.pptx
Introduction to AI in Higher Education_draft.pptxIntroduction to AI in Higher Education_draft.pptx
Introduction to AI in Higher Education_draft.pptx
 
1029-Danh muc Sach Giao Khoa khoi 6.pdf
1029-Danh muc Sach Giao Khoa khoi 6.pdf1029-Danh muc Sach Giao Khoa khoi 6.pdf
1029-Danh muc Sach Giao Khoa khoi 6.pdf
 
Beyond the EU: DORA and NIS 2 Directive's Global Impact
Beyond the EU: DORA and NIS 2 Directive's Global ImpactBeyond the EU: DORA and NIS 2 Directive's Global Impact
Beyond the EU: DORA and NIS 2 Directive's Global Impact
 
18-04-UA_REPORT_MEDIALITERAСY_INDEX-DM_23-1-final-eng.pdf
18-04-UA_REPORT_MEDIALITERAСY_INDEX-DM_23-1-final-eng.pdf18-04-UA_REPORT_MEDIALITERAСY_INDEX-DM_23-1-final-eng.pdf
18-04-UA_REPORT_MEDIALITERAСY_INDEX-DM_23-1-final-eng.pdf
 
Activity 01 - Artificial Culture (1).pdf
Activity 01 - Artificial Culture (1).pdfActivity 01 - Artificial Culture (1).pdf
Activity 01 - Artificial Culture (1).pdf
 
Mattingly "AI & Prompt Design: Structured Data, Assistants, & RAG"
Mattingly "AI & Prompt Design: Structured Data, Assistants, & RAG"Mattingly "AI & Prompt Design: Structured Data, Assistants, & RAG"
Mattingly "AI & Prompt Design: Structured Data, Assistants, & RAG"
 
TataKelola dan KamSiber Kecerdasan Buatan v022.pdf
TataKelola dan KamSiber Kecerdasan Buatan v022.pdfTataKelola dan KamSiber Kecerdasan Buatan v022.pdf
TataKelola dan KamSiber Kecerdasan Buatan v022.pdf
 
Paris 2024 Olympic Geographies - an activity
Paris 2024 Olympic Geographies - an activityParis 2024 Olympic Geographies - an activity
Paris 2024 Olympic Geographies - an activity
 
Staff of Color (SOC) Retention Efforts DDSD
Staff of Color (SOC) Retention Efforts DDSDStaff of Color (SOC) Retention Efforts DDSD
Staff of Color (SOC) Retention Efforts DDSD
 
The basics of sentences session 2pptx copy.pptx
The basics of sentences session 2pptx copy.pptxThe basics of sentences session 2pptx copy.pptx
The basics of sentences session 2pptx copy.pptx
 
Web & Social Media Analytics Previous Year Question Paper.pdf
Web & Social Media Analytics Previous Year Question Paper.pdfWeb & Social Media Analytics Previous Year Question Paper.pdf
Web & Social Media Analytics Previous Year Question Paper.pdf
 
Mastering the Unannounced Regulatory Inspection
Mastering the Unannounced Regulatory InspectionMastering the Unannounced Regulatory Inspection
Mastering the Unannounced Regulatory Inspection
 

lecture 30

  • 1. CS 332: Algorithms NP Completeness Continued: Reductions
  • 2.
  • 3.
  • 4.
  • 5.
  • 6.
  • 7.
  • 8.
  • 9.
  • 10.
  • 11.
  • 12.
  • 13.
  • 14.
  • 15.
  • 16.
  • 17.
  • 18.
  • 19.
  • 20.
  • 21.
  • 22.
  • 23.