A Survey on the Densest Subgraph Problem and Its Variants

Adriano Fazzone; Atsushi Miyauchi; Francesco Bonchi; Tommaso Lanciano

RECORD

A Survey on the Densest Subgraph Problem and Its Variants

Tommaso Lanciano, Atsushi Miyauchi, Adriano Fazzone, Francesco Bonchi

Data Structures and Algorithms · Submitted 25 Mar 2023

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim This survey provides a deep overview of the fundamental results and an exhaustive coverage of the many variants proposed in the literature, with a special attention to the most recent results.

how it is stated · asserted 1.00 read the record →

Comment (0) Read on arXiv ↗

Cite ▾

arXiv ID2303.14467 (version 2)

Pith ID2GUD4NWI, Pith's permanent record of this paper and its review

CitationAdriano Fazzone, Atsushi Miyauchi, Francesco Bonchi, Tommaso Lanciano. "A Survey on the Densest Subgraph Problem and Its Variants." arXiv:2303.14467 (2023). https://pith.science/paper/2GUD4NWI

Claim paper

The compiled record

The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Open the compiled record

Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,292 input tokens.

What the abstract itself states, as probabilities: claims first 0.02 · states limitation 0.05 · human participants 0.02 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.06 · compares with prior results 0.06 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; show every role.

The Densest Subgraph Problem requires to find, in a given graph, a subset of vertices whose induced subgraph maximizes a measure of density. The problem has received a great deal of attention in the algorithmic literature since the early 1970s, with many variants proposed and many applications built on top of this basic definition. Recent years have witnessed a revival of research interest in this problem with several important contributions, including some groundbreaking results, published in 2022 and 2023. This survey provides a deep overview of the fundamental results and an exhaustive coverage of the many variants proposed in the literature, with a special attention to the most recent results. The survey also presents a comprehensive overview of applications and discusses some interesting open problems for this evergreen research topic.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	The Densest Subgraph Problem requires to find, in a given graph, a subset of vertices whose induced subgraph maximizes a measure of density.	background 1.00	0.03	0.05	asserted 1.00
s1	The problem has received a great deal of attention in the algorithmic literature since the early 1970s, with many variants proposed and many applications built on top of this basic definition.	background 1.00	0.03	0.03	asserted 1.00
s2	Recent years have witnessed a revival of research interest in this problem with several important contributions, including some groundbreaking results, published in 2022 and 2023.	background 0.99	0.05	0.07	asserted 1.00
s3	This survey provides a deep overview of the fundamental results and an exhaustive coverage of the many variants proposed in the literature, with a special attention to the most recent results.	contribution 1.00	0.71	0.15	asserted 1.00
s4	The survey also presents a comprehensive overview of applications and discusses some interesting open problems for this evergreen research topic.	contribution 0.95	0.60	0.10	asserted 1.00

What kind of paper the classifier reports this is: review 1.00 · evidence from literature 1.00.

What was examined, and what was not

sources read

arXiv listing abstract v2

not examined

full text
figures and tables
references and citing sentences
relations to other papers

levels run

P abstract

not run

S sections
T body sentences
C citations
R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper

Original abstract

The Densest Subgraph Problem requires to find, in a given graph, a subset of vertices whose induced subgraph maximizes a measure of density. The problem has received a great deal of attention in the algorithmic literature since the early 1970s, with many variants proposed and many applications built on top of this basic definition. Recent years have witnessed a revival of research interest in this problem with several important contributions, including some groundbreaking results, published in 2022 and 2023. This survey provides a deep overview of the fundamental results and an exhaustive coverage of the many variants proposed in the literature, with a special attention to the most recent results. The survey also presents a comprehensive overview of applications and discusses some interesting open problems for this evergreen research topic.

Human review

How Pith checks papers → · Full audit of this paper →

How the literature uses it

13 arXiv papers cite this in 19 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 5 sentences without a confident label

Cites it as background 12 papers

While the problem of finding the densest subgraph in simple graphs is a well-studied problem [ref] , finding dense subgraphs from multiplex networks recently attracts attention [ref] .

A Unified Core Structure in Multiplex Networks: From Finding the Densest Subgraph to Modeling User Engagement · Introduction · 0.88
This problem has been studied in the (centralized) private [ref] , LEDP [ref] , dynamic [ref] , streaming [ref] , and distributed [ref] settings; for a recent survey on densest subgraph and its variants, see [ref] .

Near-Optimal Differentially Private Graph Algorithms via the Multidimensional AboveThreshold Mechanism · Introduction · 1.00
As a fundamental problem in graph mining, the densest subgraph discovery (DSD) problem aims to discover a very “dense” subgraph from a given graph [ref] .

In-depth Analysis of Densest Subgraph Discovery in a Unified Framework · Introduction · 0.95

What it cites · 8 sentences without a confident label

Compares with 2 papers

Christiansen et al. [ref] improved the result of Sawlani and Wang [ref] by giving a deterministic algorithm providing a $(1+ϵ)$-approximation for DSP, with $((log^2 n logρ^*) / ϵ^4)$ worst-case time per edge insertion or deletion, where $ρ^*$ is the density of the densest subgraph, and $(1)$ worst-case query time.

Adaptive Out-Orientations with Applications · Streaming and Distributed · 0.87
Independently from Christiansen et al. [ref] , Chekuri and Quanrud [ref] also improved the result of Sawlani and Wang [ref] by giving a deterministic algorithm providing a $(1+ϵ)$-approximation for DSP, with $(log^2 n / ϵ^4)$ amortized time and $((log^3 n loglogn) / ϵ^6)$ worst-case time per edge insertion or deletion, and $(1)$ worst-case query time.

$(1-\epsilon)$-approximate fully dynamic densest subgraph: linear space and faster update time · Streaming and Distributed · 0.92

Discussion

Know something about this paper? Leave a comment, or highlight any passage above to comment on it.