In the online Steiner forest problem we are given a graph $G$, and a sequence of terminal pairs $(u_i,v_i)$ which arrive in an online fashion. We are asked to maintain a low-cost subgraph in which each $u_i$ is connected to $v_i$ for all the pairs that have arrived so far. If we are not allowed to delete edges from our solution, then the best possible competitive ratio is $Θ(\log n)$. In this work, we initiate the study of low-recourse algorithms for online Steiner forest. We give an algorithm that maintains a constant-competitive solution and has an amortized recourse of $O(\log n)$, i.e., inserts and deletes $O(\log n)$ edges per demand on average.

翻译：在在线Steiner森林问题中，给定一个图$G$，以及按在线方式到达的终端对序列$(u_i,v_i)$。要求维护一个低成本的子图，使得对于已到达的所有终端对，每个$u_i$均与$v_i$相连。若不允许从解中删除边，则最佳竞争比为$Θ(\log n)$。本文首次研究了在线Steiner森林的低追索算法。我们提出一种算法，能够维护一个常数竞争比的解，并实现均摊追索$O(\log n)$，即每个需求平均插入和删除$O(\log n)$条边。