A worst-case algorithm for semi-online updates on decomposable problems

Abstract

An alternative description, and a more straightforward analysis, of Dobkin and Suri´s algorithm to maintain the maximum of a symmetric bivariate function is given. Furthermore, the amortized update time of this algorithm is made worst-case. As an application of the resulting algorithm, it follows e.g. that the diameter (or closest pair) of a planar point set can be maintained under semi-online updates in O((log n)^{2}) time per update in the worst case. A simplified version of the algorithm is applied to obtain a data structure for decomposable searching (resp. set.) problems, in which semi-online updates can be performed efficiently, even in the worst case. The amortized version of this algorithm is an extension of Bentleys logarithmic method.