CS 598 CSC : Combinatorial Optimization Lecture
نویسنده
چکیده
Roughly speaking, an optimization problem has the following outline: given an instance of the problem, find the “best” solution among all solutions to the given instance. We will be mostly interested in discrete optimization problems where the instances and the solution set for each instance is from a discrete set. This is in contrast to continuous optimization where the input instance and the solution set for an instance can come from a continuous domain. Some of these distinctions are not as clear-cut as linear programming shows. We assume familiarity with the computational complexity classes P , NP , coNP . In this class we are mainly interested in polynomial time solvable “combinatorial” optimization problems. Combinatorial optimization problems are a subset of discrete optimization problems although there is no formal definition for them. A typical problem in combinatorial optimization has a ground set E of objects and solutions correspond to some subsets of 2E (the power set of E) and a typical goal is to find either a maximum or minimum weight solution for some given weights on E. For example, in the spanning tree problem, the ground set E is the set of edges of a graph G = (V,E) and the solutions are subsets of E that correspond to spanning trees in G. We will be interested in NP optimization problems – NPO problems for short. Formally, a problem Q is a subset of Σ∗, where Σ is a finite alphabet such as binary. Each string I in Q is an instance of Q. For a string x we use |x| to denote its length. We say that Q is an NPO problem if the following hold:
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تاریخ انتشار 2010