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Approximation Algorithms for NP-Hard Problems by Dorit Hochbaum

Approximation Algorithms for NP-Hard Problems Dorit Hochbaum ebook
Page: 620
Format: djvu
Publisher: Course Technology
ISBN: 0534949681, 9780534949686

I'd started contemplating local optimizations, simulated annealing, etc. No approximation algorithm with a ratio better than roughly 0.941 exists unless P=NP. Sanjeev Arora is one of the architects of the Probabilistically Checkable Proofs (PCP) theorem, which revolutionized our understanding of complexity and the approximability of NP-hard problems. Optimization/approximation algorithms/polynomial time/ NP-HARD. Unfortunately the problem is not only NP-complete, but also hard to approximate. Unsurprisingly, submodular maximization tends to be NP-hard for most natural choices of constraints, so we look for approximation algorithms. When an NP-complete problem must be solved, one approach is to use a polynomial algorithm to approximate the solution; the answer thus obtained will not necessarily be optimal but will be reasonably close. Note that hardness relations are always with respect to some reduction. He helped create new approximation algorithms for fundamental optimization problems such as the Sparsest Cuts problem and the Euclidean Travelling Salesman problem, and contributed to the development of semi-definite programming as a practical algorithmic tool. Many Problems are NP-Complete Does P=NP Coping with NP-Completeness The Vertex Cover Problem Smarter Brute-Force Search. NP-hard and NP-complete problems, basic concepts, non- deterministic algorithms, NP-hard and NP-complete, decision and optimization problems, graph based problems on NP Principle, Computational Geometry, Approximation algorithm. I was expecting that I'd have to find an approximate solution, as this looked like a classic hairy NP-hard optimization problem. Backtracking basic strategy, 8-Queen's problem, graph colouring, Hamiltonian cycles etc, Approximation algorithm and concepts based on approximation algorithms. Think about all the effort that's gone into finding approximation algorithms and hardness of approximation results for NP-complete problems. Many combinatorial optimization problems can be expressed as the minimization or maximization of a submodular function, including min- and max-cut, coverage problems, and welfare maximization in algorithmic game theory. Research Areas: Uses of randomness in complexity theory and algorithms; Efficient algorithms for finding approximate solutions to NP-hard problems (or proving that they don't exist); Cryptography. Often, when dealing with the class NPO, one is interested in optimization problems for which the decision versions are NP-hard. Due to the connection between approximation algorithms and computational optimization problems, reductions which preserve approximation in some respect are for this subject preferred than the usual Turing and Karp reductions. The theory of NP-completeness suggests that some problems in CS are inherently hard—that is, there is likely no possible algorithm that can efficiently solve them.