Furthermore for many natural np hard optimization problems approximation algorithms have been developed whose accuracy nearly matches the best achievable according to the theory of np completeness thus optimization problems can be cate gorized according to the best accuracy achievable by a polynomial time approximation algorithm for each . Philip n klein neal e young approximation algorithms for np hard optimization problems algorithms and theory of computation handbook general concepts and techniques chapman hall crc 2010 raphal clifford alexandru popa maximum subset intersection information processing letters v111 n7 p323 325 march 2011. Np hard problems and approximation algorithms the following is a nonterministic algorithm for the hamiltonian cycle problem input a graph g ve step 1 guess a permutation of all vertices step 2 check if guessed permutation gives a hamitonian cycle 1 10 np hard problems 1 . Approximation algorithms for np hard p roblems 1475 o it is not clear whether the algorithm in 4 can handle the case that k grows as a function of n the analysis of the sdp rounding
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