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

Different approximation algorithms have their advantages and disadvantages. Approaches include approximation algorithms, heuristics, average-case analysis, and exact exponential-time algorithms: all are essential. Moreover, we prove that better approximation algorithms do not exist unless NP-complete problems admit efficient algorithms. We show both problems to be NP-hard and prove limits on approximation for both problems. The traveling salesman problem (TSP) is an NP-complete problem. Baker [JACM 41,1994] introduces a k-outer planar graph decomposition-based framework for designing polynomial time approximation scheme (PTAS) for a class of NP-hard problems in planar graphs. Because all of these problems are NP-hard, the primary goal of this research is to produce polynomial-time, approximation algorithms for each problem considered. A simple factor-2 approximation just walks around the spanning tree and can be computed in O(n log n) time with simple algorithms! Approximation Algorithm for NP-hard problems by Dorit Hochbaum is a set of chapters by different contributors. Comparing Algorithms for the Traveling Salesman Problem. We present integer programs for both GOPs that provide exact solutions. SAT (boolean satisfiability, the "canonical" NP-hard problem) is a really tough nut to crack, whereas for example euclidean TSP (traveling salesman) is hard to solve optimally but has simple and fast algorithms that guarantee to solve it to within a constant factor of the optimum. Perhaps, the best source on approximation algorithms.