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A Deterministic Approach to Shortest Path Restoration in Edge Faulty Graphs

Authors Keerti Choudhary , Rishabh Dhiman

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Subject Classification

ACM Subject Classification
  • Theory of computation → Data structures design and analysis
  • Mathematics of computing → Graph algorithms
Keywords
  • Fault-tolerant Data-structures
  • Shortest Path Restoration
  • Replacement path

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Abstract

Afek, Bremler-Barr, Kaplan, Cohen, and Merritt (PODC'01) in their seminal work on shortest path restorations demonstrated that after a single edge failure in a graph G, a replacement shortest path between any two vertices s and t, which avoids the failed edge, can be represented as the concatenation of two original shortest paths in G. They also showed that we cannot associate a canonical shortest path between the vertex pairs in G that consistently allows for the replacement path (in the surviving graph) to be represented as a concatenation of these canonical paths. Recently, Bodwin and Parter (PODC'21) proposed a randomized tie-breaking scheme for selecting canonical paths for the "ordered" vertex pairs in graph G with the desired property of representing the replacement shortest path as a concatenation of canonical shortest-paths provided for ordered pairs.
An interesting open question is whether it is possible to provide a deterministic construction of canonical paths in an efficient manner. We address this question in our paper by presenting an O(mn) time deterministic algorithm to compute a canonical path family ℱ = {P_{x,y}, Q_{x,y} | x,y ∈ V} comprising of two paths per (unordered) vertex pair. Each replacement is either a PQ-path (of type P_{x,y}∘Q_{y,z}), a QP-path, a QQ-path, or a PP-path. Our construction is fairly simple and is a straightforward application of independent spanning trees. We also present various applications of family ℱ in computing fault-tolerant structures.

Cite As Get BibTex

Keerti Choudhary and Rishabh Dhiman. A Deterministic Approach to Shortest Path Restoration in Edge Faulty Graphs. In 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 327, pp. 24:1-24:10, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.STACS.2025.24

Author Details

Keerti Choudhary
  • Department of Computer Science and Engineering, IIT Delhi, India
Rishabh Dhiman
  • Department of Computer Science and Engineering, IIT Delhi, India

Funding

  • Choudhary, Keerti: The author is supported in part by Google India Algorithms Research grant 2021.

References

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