Capturing structure in hard combinatorial problems

Stefan Szeider
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Abstract

For many hard combinatorial problems that arise from real-world applications, the conventional theory of algorithms and complexity cannot give reasonable (i.e., polytime) performance guarantees and considers such problems as intractable. Nevertheless, heuristics-based algorithms and solvers work surprisingly well on real-world instances, which suggests that our world may be “friendly enough” to make many typical computational tasks poly-time- challenging the value of the conventional worst-case complexity view in CS (Bart Selman, 2012). Indeed, there is an enormous gap between theoretical performance guarantees and the empirically observed performance of solvers. Efficient solvers exploit the “hidden structure” of real-world problems, and so a theoretical framework that explains practical problem hardness and easiness must not ignore such structural aspects.
在难组合问题中捕获结构
对于现实应用中出现的许多困难的组合问题,传统的算法和复杂性理论不能给出合理的(即多时)性能保证,并认为这类问题难以处理。然而,基于启发式的算法和求解器在现实世界的实例中工作得非常好,这表明我们的世界可能“足够友好”,可以使许多典型的计算任务多时间-挑战CS中传统的最坏情况复杂性视图的价值(Bart Selman, 2012)。事实上,在理论性能保证和经验观察到的求解器性能之间存在着巨大的差距。有效的求解者利用了现实世界问题的“隐藏结构”,因此解释实际问题的难易程度的理论框架不能忽视这些结构方面。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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