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Semirandom Planted Bipartite Subgraphs

Authors Anand Louis , Kirtan Vora

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LIPIcs.SWAT.2026.32.pdf
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Subject Classification

ACM Subject Classification
  • Theory of computation → Graph algorithms analysis
  • Theory of computation → Approximation algorithms analysis
Keywords
  • Semirandom Models
  • Spectral Algorithms
  • Planted Subgraphs
  • Random Graphs
  • Approximate Recovery Algorithms

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Abstract

There have been many recent works studying planted subgraphs problems. The semirandom planted bipartite subgraph problem is defined as follows. Starting with a vertex set V, an arbitrary subset S ⊂ V of size k is chosen, then an arbitrary bipartite graph is added on S. After this between each pair of vertices in S × (V ⧵ S) an edge is added independently with probability p, then an arbitrary graph is added on V⧵ S. The analogous semirandom planted clique problem, where S forms a clique, has been studied starting with the work of Fiege and Kilian [Uriel Feige and Joe Kilian, 2001]; recent work by [Blasiok et al., 2024; Venkatesan Guruswami and Hsin-Po Wang, 2025] gave an algorithm for this problem when k = Ω(√{n log n}). We give an algorithm for semirandom planted bipartite subgraph problem when k = Ω(√{n log n}) and the two color classes are roughly balanced. 

Our algorithms are essentially the same as the elegant greedy algorithm of [Blasiok et al., 2024]. We generalize their idea to our setting. Handling the arbitrary nature of the bipartite graph requires some new technical ideas and is our main technical contribution.

Cite As Get BibTex

Anand Louis and Kirtan Vora. Semirandom Planted Bipartite Subgraphs. In 20th Scandinavian Symposium on Algorithm Theory (SWAT 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 370, pp. 32:1-32:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.SWAT.2026.32

Author Details

Anand Louis
  • Indian Institute of Science, Bengaluru, India
Kirtan Vora
  • Indian Institute of Science, Bengaluru, India

Funding

  • Louis, Anand: Supported in part by SERB Award CRG/2023/002896 and the Walmart Center for Tech Excellence at IISc (CSR Grant WMGT-23-0001).
  • Vora, Kirtan: Supported by Prime Minister’s Research Fellowship, India.

References

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