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Approximation Algorithms for NP-Hard Problems Dorit Hochbaum
Publisher: Course Technology

Approximation algorithms for the knapsack problem 453. Study of low-distortion embeddings (which can be pursued in a more general setting) has been a highly-active TCS research topic, largely due to its role in designing efficient approximation algorithms for NP-hard problems. 12.3 approximation algorithms for np-hard problems 441. 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. Approximation algorithms for the traveling salesman problem 443. I'd started contemplating local optimizations, simulated annealing, etc. In spite of their theoretical hardness, heuristic solvers are often able to solve large realistic problem instances surprisingly fast. The Max-Cut problem is known to be NP-hard (if the widely believed {P\neq NP} conjecture is true this means that the problem cannot be solved in polynomial time). Think about all the effort that's gone into finding approximation algorithms and hardness of approximation results for NP-complete problems. 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. I was expecting that I'd have to find an approximate solution, as this looked like a classic hairy NP-hard optimization problem. Since many interesting optimization problems are computationally intractable (NP-Hard), we resort to designing approximation algorithms which provably output good solutions.