Online Steiner Forest with Recourse

2026-05-10

AI Summary

This work addresses the online Steiner forest problem under recourse constraints, where terminal pairs arrive online and the algorithm must dynamically maintain a low-cost subgraph connecting all revealed terminal pairs while minimizing the number of edge modifications per request. We present the first systematic design of online algorithms with low recourse, integrating techniques from online algorithm design, graph connectivity maintenance, and amortized analysis. Our approach achieves a constant competitive ratio while guaranteeing only O(log n) amortized edge insertions or deletions per request, substantially reducing structural changes without compromising solution quality.

Abstract

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.

Problem

• Online Steiner Forest
• Recourse
• Competitive Ratio
• Graph Connectivity
• Amortized Recourse

Innovation

• online Steiner forest
• recourse
• competitive ratio
• amortized recourse
• dynamic graph algorithms