Algorithmic Graph Theory Part V - Approximation Algorithms for

79 Pages·2013·1.26 MB·English

by  Martin

AlgorithmicGraphTheory
PartV -ApproximationAlgorithms
for GraphProblems
MartinMilanicˇ
[email protected]
UniversityofPrimorska,Koper,Slovenia
DipartimentodiInformatica
Universita` degliStudidiVerona,March2013
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Coping with NP-hardness
Thereare severalapproacheson howto dealwith (the
intractability of) NP-hard problems:
polynomialalgorithmsforparticularinputinstances
approximationalgorithms
heuristics, local optimization
“efficient” exponentialalgorithms
randomizedalgorithms
parameterizedcomplexity
(fixed-parametertractable (FPT)algorithms)
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What we’ll do
Basic Definitions.
1
2-Approximation Algorithm for Vertex Cover.
2
Approximation Algorithms for the Metric TSP.
3
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BASICS OF APPROXIMATION ALGORITHMS.
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Coping with NP-hardness
Heuristics:
intuitive algorithms;
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Coping with NP-hardness
Heuristics:
intuitive algorithms;
guaranteedto run in polynomialtime;
3/26
Coping with NP-hardness
Heuristics:
intuitive algorithms;
guaranteedto run in polynomialtime;
noguaranteeonqualityof solution.
3/26
Coping with NP-hardness
Heuristics:
intuitive algorithms;
guaranteedto run in polynomialtime;
noguaranteeonqualityof solution.
Approximationalgorithms:
guaranteedto run in polynomialtime;
3/26
Coping with NP-hardness
Heuristics:
intuitive algorithms;
guaranteedto run in polynomialtime;
noguaranteeonqualityof solution.
Approximationalgorithms:
guaranteedto run in polynomialtime;
guaranteedto find “high quality”solution,say within1% of
optimum;
3/26
Coping with NP-hardness
Heuristics:
intuitive algorithms;
guaranteedto run in polynomialtime;
noguaranteeonqualityof solution.
Approximationalgorithms:
guaranteedto run in polynomialtime;
guaranteedto find “high quality”solution,say within1% of
optimum;
Obstacle:
needto proveasolution’s valueis close to optimum,
withouteven knowingwhatthe optimumvalueis!
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