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

In 2003 proved that it is still NP-hard and gave a polynomial-time algorithm with an approximation factor of 1nm. The past few years have seen a flurry of results, including surprises such as a subexponential-time approximation algorithm, as well as algorithms for all “natural” families of instances we can think of. Problem definition; Greedy algorithm; Remarks; Related; Bibliography. It is known that the decisional subset-sum is NP-complete (I believe this result is essentially due to Karp). Also Discuss What is meant by P(n)-approximation algorithm? I normally do machine learning work, and when I'm evaluating an algorithm on a data set, I always use cross-validation to determine how effective the. Here is a review of the Set Cover problem and the classic greedy algorithm for it. Often, when dealing with the class NPO, one is interested in optimization problems for which the decision versions are NP-hard. Hence, the corresponding optimization problems (i.e. Explain NP-Complete and NP- Hard problem. Note that hardness relations are always with respect to some reduction. Approximating tree-width : Bodlaender et. NP, in the worst case, no polynomial-time algorithm guarantees a cover of cost [Math Processing Error] [2]. See [BGHK'95] for interesting applications of treewidth Eg : Choleski factorization on sparse symmetric matrices. (This blog is about how to use randomized rounding to systematically derive greedy approximation algorithms and Lagrangian-relaxation algorithms. Khot's Unique Games Conjecture (UGC) —which asserts the NP-hardness of approximating a very simple constraint satisfaction problem— has assumed a central role in the effort to understand the optimal approximation ratios achievable for various NP-hard problems. Equations are not displayed properly. There is an analogous notion of pathwidth which is also NP-complete. Al ruled out absolute approximation algorithm, (unless P = NP) for treewidth and pathwidth. Product Description This is the first book to fully address the study of approximation algorithms as a tool for coping with intractable problems. TOP 30 IMPORTANT QUESTION OF Design & Analysis of Algorithm(DAA) For GBTU/MMTU C.S./I.T. 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. Maximization and minimization problems) also cannot be solved in polynomial time (unless again P=NP). Open Problems : Perhaps the most interesting open question is to obtain a constant factor approximation for treewidth.