Chapter 18 APPROXIMATION ALGORITHMS
نویسندگان
چکیده
Most interesting real-world optimization problems are very challenging from a computational point of view. In fact, quite often, finding an optimal or even a near-optimal solution to a large-scale optimization problem may require computational resources far beyond what is practically available. There is a substantial body of literature exploring the computational properties of optimization problems by considering how the computational demands of a solution method grow with the size of the problem instance to be solved (see e.g. Aho et al., 1979). A key distinction is made between problems that require computational resources that grow polynomially with problem size versus those for which the required resources grow exponentially. The former category of problems are called efficiently solvable, whereas problems in the latter category are deemed intractable because the exponential growth in required computational resources renders all but the smallest instances of such problems unsolvable. It has been determined that a large class of common optimization problems are classified as NP-hard. It is widely believed—though not yet proven (Clay Mathematics Institute, 2003)—that NP-hard problems are intractable, which means that there does not exist an efficient algorithm (i.e. one that scales polynomially) that is guaranteed to find an optimal solution for such problems. Examples of NP-hard optimization tasks are the minimum traveling salesman problem, the minimum graph coloring problem, and the minimum bin packing
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