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Cutwidth Versus BFS-Width with Applications to Graph Reconstruction from Distance Queries

Authors Chirag Kaudan , Amir Nayyeri

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Document Identifiers

Subject Classification

ACM Subject Classification
  • Theory of computation → Shortest paths
Keywords
  • Graph algorithms
  • graph theory
  • cutwidth
  • pathwidth
  • BFS-width

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Abstract

Eppstein, Goodrich, and Liu [ESA 2025] introduced a new graph parameter, called BFS-width, and gave polylogarithmic bounds on it for bounded bandwidth graphs. Their bounds naturally imply several applications, e.g. in graph reconstruction via shortest path distance queries, graph drawing, and matrix reordering. 
We study this parameter for a broader class of graphs, namely bounded cutwidth graphs. We prove a sublinear upper bound on the BFS-width of bounded cutwidth graphs and show that our bounds are asymptotically tight. Our upper bound implies the first deterministic algorithm for reconstructing a bounded cutwidth graph with a subquadratic number of shortest path distance queries.

Cite As Get BibTex

Chirag Kaudan and Amir Nayyeri. Cutwidth Versus BFS-Width with Applications to Graph Reconstruction from Distance Queries. In 20th Scandinavian Symposium on Algorithm Theory (SWAT 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 370, pp. 24:1-24:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.SWAT.2026.24

Author Details

Chirag Kaudan
  • Oregon State University, Corvallis, OR, USA
Amir Nayyeri
  • Oregon State University, Corvallis, OR, USA

Funding

The authors were supported by NSF grants CCF-1941086 and CCF-2311180.

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