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Online Steiner Forest with Recourse

Authors Yaowei Long , Sepideh Mahabadi , Sherry Sarkar , Jakub Tarnawski

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  • Theory of computation → Online algorithms
Keywords
  • Online algorithms with recourse
  • Steiner forest
  • Network design

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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.

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Yaowei Long, Sepideh Mahabadi, Sherry Sarkar, and Jakub Tarnawski. Online Steiner Forest with Recourse. In 53rd International Colloquium on Automata, Languages, and Programming (ICALP 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 374, pp. 141:1-141:25, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.ICALP.2026.141

Author Details

Yaowei Long
  • University of Michigan, Ann Arbor, MI, USA
Sepideh Mahabadi
  • Microsoft Research, Redmond, WA, USA
Sherry Sarkar
  • Carnegie Mellon University, Pittsburgh, PA, USA
Jakub Tarnawski
  • Microsoft Research, Redmond, WA, USA

Acknowledgements

The authors want to thank Roie Levin and Anupam Gupta for helpful discussions.

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