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

Approximation algorithms for NP-hard problems. In the Traveling Salesman is an NP-Hard problem. Linear programming has been a successful tool in combinatorial optimization to achieve polynomial time algorithms for problems in P and also to achieve good approximation algorithms for problems which are NP-hard. They showed that this problem is NP-hard even to approximate, and presented several heuristic algorithms. Khot's Unique Games Conjecture (UGC) states that a certain approximation problem (known as “Unique Games” or UG) is NP hard. Currently we have approximation algorithms that can come up with “good solutions” in a fairly acceptable amount of time. In this problem, multiple missions compete for sensor resources. This is one of Karp's original NP-complete problems. One benefit of using Occam's Razor is that, if we're not One of the fascinating phenomenons of complexity is the dichotomy exhibited by many natural problems: they either have a polynomial-time algorithm (often with a low exponent) or are NP-hard, with very few examples in between. Research Areas: Uses of randomness in complexity theory and algorithms; Efficient algorithms for finding approximate solutions to NP-hard problems (or proving that they don't exist); Cryptography. Optimization/approximation algorithms/polynomial time/ NP-HARD. 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. €� traveling salesperson problem, Steiner tree. 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. A less obvious application is that the minimum spanning tree can be used to approximately solve the traveling salesman problem. Instead of trying to solve this problem exactly, we will reason about whether constant factor approximation algorithms exist, i.e.