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

Both these problems are NP-hard, which motivates our interest in their approximation. Thus unless P = NP, there are no efficient algorithms to find optimal solutions to such problems. 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. 12.3 approximation algorithms for np-hard problems 441. Yet most such problems are NP-hard. To minimum spanning trees and Huffman codes; dynamic programming, including applications to sequence alignment and shortest-path problems; and exact and approximate algorithms for NP-complete problems. 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. Many of the striking advances in theoretical computer science over the past two decades concern approximation algorithms, which compute provably near-optimal solutions to NP-hard optimization problems. Garey and Johnson, in 1978, list various possible ways to "cope" with NP-completeness, including looking for approximate algorithms and for algorithms that are efficient on average. Approximation algorithms for the traveling salesman problem 443. 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. This problem addresses the issue of timing when deploying viral campaigns. Approximation algorithms for the knapsack problem 453. We present integer programs for both GOPs that provide exact solutions. I also wanted to include just a little bit of my own opinion on why studying approximation algorithms is worthwhile.