Discrete Event Systems Solution to Exercise Sheet 8 1 Competitive Analysis
نویسنده
چکیده
The competitive analysis of an algorithm Alg consists of two separate steps. First, we show that for an arbitrary problem instance, the result of Alg is asymptotically at most a factor r worse than the the optimal offline result. This yields an upper bound on Alg’s result, that is costAlg ≤ r · costOpt + c. If the task is to show that Alg is constant-competitive for a constant r, then we are done. If we are interested in a tight analysis, we have to show that there is a problem instance where the result of Alg is a factor r worse than the optimal offline result. This gives a matching lower bound on the objective value of the algorithm, costAlg ≥ r · costOpt. Naturally, the second step is easier than the first one because we just have to find a “bad instance”. The first step is often much more involved. A pattern that works quite often is the following.
منابع مشابه
Discrete Event Systems Solution to Exercise Sheet 11 1 Competitive Analysis
In the script there is a definition for the competitiveness of an algorithm. However, this definition only holds if we want to evaluate an algorithm by means of its costs. Sometimes, we want to compare algorithms regarding their benefit rather than their costs. In this case, we have to be a bit careful with the definition of a c-competitive algorithm. We say that an algorithm Alg is c-competiti...
متن کاملDiscrete Event Systems Solution to Exercise Sheet 13 1 Competitive Analysis
In the script there is a definition for the competitiveness of an algorithm. However, this definition only holds if we want to evaluate an algorithm by means of its costs. Sometimes, we want to compare algorithms regarding their benefit rather than their costs. In this case, we have to be a bit careful with the definition of a c-competitive algorithm. We say that an algorithm Alg is c-competiti...
متن کاملDiscrete Event Systems Solution to Exercise Sheet 12 1 Competitive Analysis
In the script there is a definition for the competitiveness of an algorithm. However, this definition only holds if we want to evaluate an algorithm by means of its costs. Sometimes, we want to compare algorithms regarding their benefit rather than their costs. In this case, we have to be a bit careful with the definition of a c-competitive algorithm. We say that an algorithm Alg is c-competiti...
متن کاملRecent Developments in Discrete Event Systems
This article is a brief exposure of the process approach to a newly emerging area called "discrete event systems" in control theory and summarizes some of the recent developments in this area. Discrete event systems is an area of research that is developing within the interstices of computer, control and communication sciences. The basic direction of research addresses issues in the analysis an...
متن کامل