Enhancing Group Search with Graph Techniques

群论是数学中的一个领域，它研究称为群的代数结构，它可以用来描述任何对象的对称性。因此，群论在病毒学、量子计算、网络安全和通信理论中有着广泛的应用。群还用于寻找和减少搜索问题中的对称性，这在现代人工智能中是至关重要的。因此，尽快发现群及其性质并计算基本的群运算，是许多英国世界领先的研究领域的核心，并将对经济成功产生广泛的影响。群论中的算法研究将带来继承的循环改进，因为寻找子群的计算技术之一，其性质或计算运算本身就是一种搜索算法。因此，改进分组搜索也将提高对其他应用程序的搜索。目前的分组搜索技术是先进的，但仍在为扩展问题而苦苦挣扎。我们建议使用图搜索问题中常用的搜索技术，并将其应用于分组理论搜索算法。这些技巧是(1)(习得的)搜索过程中的不好的子句，然后将通知进一步的搜索步骤，(2)以明确定义的间隔从顶部重新开始搜索，以及(3)对搜索决策使用加权排序。我们发现，在图问题中使用这些技术可以将搜索速度加快至少两个数量级。我们预计，在群体问题中，性能的提高将是相同的或更好的。此外，这些技术允许以一种简单的方式并行化当前的顺序算法，而不需要设计/设计全新的算法。加速解决群体问题的算法，使它们能够很容易地并行化，将进一步影响病毒学等应用，在病毒学中，群体理论被用来描述病毒的结构和几何特性。

Group theory is a field in mathematics which investigates algebraic structures called groups, which can be used to describe the symmeties of any object. Thus, group theory has wide-reaching applications in virology, quantum computing, cyber security and communications theory. Groups are also used in finding and reducing symmetries within search problems, which is vital in modern Artificial Intelligence. So finding groups, their properties and computing fundamental group operations as fast as possible, is at the core of many UK world leading research areas and will have wide reaching impact in economic successes.There is an inherit circular improvement that will come from the research in algorithms in group theory, as one of the computational techniques used in finding subgroups, their properties or computing operations is a type of search algorithm itself. Thus, improving search in groups will improve the search for other applications as well.The current search techniques in groups are advanced but are still struggling with scaling issues. We are proposing to use search techniques commonly used in graph search problems and apply them to group theoretical search algorithms. Such techniques are(1) (learned) nogood clauses during search which then will inform further search steps, (2) restarting the search from the top at well defined intervals, and (3) using weighted orderings on the search decisions.We have found that using these techniques in graph problems sped up the search by at least two orders of magnitude. We expect the performance improvements to be the same or better across the board in group problems.Further, these techniques allow for a simple way of parallelising the current sequential algorithms, without the need to design/engineer a whole new algorithm. Speeding up algorithms which solve group problems and enabling them to be easily parallelisable will further impact applications such as virology, where group theory is used to describe the structural and geometrical properties of viruses.