Studies on Realistic Solutions to Theoretically Hard Problems

在这项研究中，我们研究了几个问题，这些问题在算法理论中流行的传统渐近分析框架内被认为是难以计算的。更具体地说，我们研究了最优印刷网点图案的设计问题和聚类问题。对于前一个问题，我们注意到差异理论可以应用于这个问题。对差异理论进行了严格的研究，并取得了许多重要的理论成果。将其与图论中的匹配概念相结合，成功地提高了解的性能。由于我们也取得了令人满意的实验结果，我们打算将结果提交给一些期刊。针对聚类问题，我们将一种算法方法应用到图像查询系统中，在图像数据库上取得了优于传统方法的良好实验结果。我们计划将结果总结成一篇论文，在不久的将来提交给一些国际期刊。

In this study we have been engaged in several problems which were thought to be computationally Hard within the traditional framework of asymptotic analysis popular in the theory of algorithms. More concretely, we have studied the problem of designing optimal dot patterns for printing and that of clustering. For the former problem, we have noticed that the discrepancy theory can be applied to the problem. The discrepancy theory has been rigorously studied and is full of important theoretical results. Combining it with the notion of matching in the graph theory, we have succeeded in improving the performance of the solutions obtained. Since we also had satisfactory experimental results, we intend to submit the result to some journal. For the problem of clustering, we have applied an algorithmic approach to image query system On image database with good experimental results that exceed results by traditional Approaches. We are planning to summarize the results in a paper to be submitted to some International journal in near future.