In this survey, we address the worst-case, average-case, and generic-case time complexity of the word problem and some other algorithmic problems in several classes of groups and show that it is often the case that the average-case complexity of the word problem is linear with respect to the length of an input word, which is as good as it gets if one considers groups given by generators and defining relations. At the same time, there are other natural algorithmic problems, for instance, the geodesic (decision) problem or Whitehead's automorphism problem, where the average-case time complexity can be sublinear, even constant.

翻译：本综述探讨多类群中词问题及其他算法问题的最坏情况、平均情况和一般情况时间复杂度，并指出：在由生成元和定义关系给出的群中，词问题的平均情况复杂度通常与输入词长度呈线性关系，这是此类群所能达到的最佳复杂度。与此同时，存在其他自然算法问题，例如测地线（判定）问题或Whitehead自同构问题，其平均情况时间复杂度可达到次线性甚至常数级别。