A Cogitative Algorithm for Solving the Equal Circles Packing Problem

Abstract

In the past decades, quite a large number of NP-hard problems have been formulated. These problems can be found in a large number of fields including military, political, engineering, and even business administration. The classical equal circles packing problem is one of them. Unfortunately, though much research has been done in the last two decades on these problems, the results have shown that it is not likely to have any algorithm that is fast and can solve these problems exactly [1]. Consequently, devising approximation heuristics has been an important topic in solving these problems. In [2], an enumeration-based approximation methodology, called the shifting strategy, was proposed. The strategy is of great theoretical significance since it can be regarded as the best approximation algorithm possible for this kind of problems, but it is far from being practical due to its very high polynomial complexity. Therefore, it was suggested toward the end of their paper that other kinds of heuristics with lower time complexity should be sought for practical usage.

This work was partially supported by China National Focus Programme of Fundamental Research Development, 863 National High Technology Programme, Natural Science Foundation, Science Foundation for Doctoral Training Unit and Foundation for Computer Science Open Laboratory of Software Institute of Academica Sinica.

This work was partially supported by Hong Kong Earmarked Research Grant 2050133 and CUHK Direct Grant 2050199.