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A 4.509-Approximation Algorithm for Generalized Min Sum Set Cover

Authors Amey Bhangale , Yezhou Zhang

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LIPIcs.ICALP.2026.29.pdf
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Subject Classification

ACM Subject Classification
  • Theory of computation → Approximation algorithms analysis
Keywords
  • Generalized Min Sum Set Cover
  • Approximation Algorithm
  • Min latency set cover
  • Linear programming
  • Knapsack cover inequalities

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Abstract

We study the generalized min-sum set cover (GMSSC) problem, where given a collection of hyperedges E with arbitrary covering requirements {k_e ∈ ℤ^+ : e ∈ E}, the objective is to find an ordering of the vertices that minimizes the total cover time of the hyperedges. A hyperedge e is considered covered at the first time when k_e of its vertices appear in the ordering.
We present a 4.509-approximation algorithm for GMSSC, improving upon the previous best-known guarantee of 4.642 [Nikhil Bansal et al., 2021]. Our approach retains the general LP-based framework of Bansal, Batra, Farhadi, and Tetali [Nikhil Bansal et al., 2021] but provides an improved analysis that narrows the gap toward the lower bound of 4-approximation assuming P≠NP. Our analysis takes advantage of the constraints of the linear program in a nontrivial way, along with new lower-tail bounds for the sums of independent Bernoulli random variables, which could be of independent interest.

Cite As Get BibTex

Amey Bhangale and Yezhou Zhang. A 4.509-Approximation Algorithm for Generalized Min Sum Set Cover. In 53rd International Colloquium on Automata, Languages, and Programming (ICALP 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 374, pp. 29:1-29:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.ICALP.2026.29

Author Details

Amey Bhangale
  • Department of Computer Science and Engineering, University of California, Riverside, CA, USA
Yezhou Zhang
  • Department of Computer Science and Engineering, University of California, Riverside, CA, USA

Funding

  • Bhangale, Amey: Supported by the Hellman Fellowship award and NSF CAREER award 2440882.
  • Zhang, Yezhou: Supported by the Hellman Fellowship award and NSF CAREER award 2440882.

References

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