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On Finding Dense Common Subgraphs

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arxiv 1802.06361 v1 pith:JRZYRE7O submitted 2018-02-18 cs.DS cs.CC

Moses Charikar , Yonatan Naamad , Jimmy Wu This is my paper · ORCID
classification cs.DScs.CC
keywords subgraphsapproximationcommondensefindinggivengraphsproblem
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abstract

We study the recently introduced problem of finding dense common subgraphs: Given a sequence of graphs that share the same vertex set, the goal is to find a subset of vertices $S$ that maximizes some aggregate measure of the density of the subgraphs induced by $S$ in each of the given graphs. Different choices for the aggregation function give rise to variants of the problem that were studied recently. We settle many of the questions left open by previous works, showing NP-hardness, hardness of approximation, non-trivial approximation algorithms, and an integrality gap for a natural relaxation.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Fundamental Limits of Query-Based Subgraph Detection

    math.ST 2026-07 conditional novelty 7.0 of 10

    For non-adaptive edge-query detection of arbitrary planted subgraphs, the minimum query count is governed by whether the planted graph has dense local witnesses, high-degree hubs, or just many edges.

  2. Recovery of Planted Subgraphs

    cs.IT 2026-07 unverdicted novelty 6.0 of 10

    Sharp conditions for exact recovery of general planted subgraphs in ER graphs are given by the minimal maximum subgraph density, with matching bounds, a spectral algorithm, and computational hardness results via low-d...

  3. Fair densest subgraph across multiple graphs

    cs.DS 2025-02 conditional novelty 6.0 of 10

    The authors prove that two fairness-constrained variants of the densest subgraph problem over graph snapshots are NP-hard and give integer-programming and greedy algorithms.

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