最优分形编码是np困难的

M. Ruhl, H. Hartenstein
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引用次数: 52

摘要

在分形压缩中,信号是由一个不动点(吸引子)是原始数据近似值的压缩变换的参数编码的。因此,分形编码可以看作是在一组可容许的压缩变换中寻找吸引子最接近给定信号的变换的优化问题。基于拼贴定理的标准分形编码方案只产生次优解。我们通过MAXCUT的约简证明了确定最优分形码的问题是np困难的。据我们所知,这是第一次分析分形编码的内在复杂性。此外,我们还证明了标准分形编码并不是这个问题的近似算法。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Optimal fractal coding is NP-hard
In fractal compression a signal is encoded by the parameters of a contractive transformation whose fixed point (attractor) is an approximation of the original data. Thus fractal coding can be viewed as the optimization problem of finding in a set of admissible contractive transformations the transformation whose attractor is closest to a given signal. The standard fractal coding scheme based on the collage theorem produces only a suboptimal solution. We demonstrate by a reduction from MAXCUT that the problem of determining the optimal fractal code is NP-hard. To our knowledge, this is the first analysis of the intrinsic complexity of fractal coding. Additionally, we show that standard fractal coding is not an approximating algorithm for this problem.
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