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Efficient Processing of Subsequent Densest Subgraph Query

Chia-Yang Hung, Chih-Ya Shen

TL;DR

This work introduces the Dynamic Constraint Member Selection Problem (DCMSP) and its divide-and-conquer variant (EDCMSP) to enable adaptive, dense subgraph extraction under changing size and similarity requirements. Building on SGSEL, the proposed DCSEL algorithm derives a $\frac{1}{3}$-approximation for both DCMSP and EDCMSP by decomposing the problem into subgraphs and carefully merging solutions while preserving density. The approach supports dynamic constraints and extra-node adjustments, offering practical efficiency for scalable graph mining. Experiments on Cora, Citeseer, and Pubmed demonstrate that DCSEL closely matches SGSEL in objective quality while offering improved adaptability and runtime performance under dynamic conditions.

Abstract

Dense subgraph extraction is a fundamental problem in graph analysis and data mining, aimed at identifying cohesive and densely connected substructures within a given graph. It plays a crucial role in various domains, including social network analysis, biological network analysis, recommendation systems, and community detection. However, extracting a subgraph with the highest node similarity is a lack of exploration. To address this problem, we studied the Member Selection Problem and extended it with a dynamic constraint variant. By incorporating dynamic constraints, our algorithm can adapt to changing conditions or requirements, allowing for more flexible and personalized subgraph extraction. This approach enables the algorithm to provide tailored solutions that meet specific needs, even in scenarios where constraints may vary over time. We also provide the theoretical analysis to show that our algorithm is 1/3-approximation. Eventually, the experiments show that our algorithm is effective and efficient in tackling the member selection problem with dynamic constraints.

Efficient Processing of Subsequent Densest Subgraph Query

TL;DR

This work introduces the Dynamic Constraint Member Selection Problem (DCMSP) and its divide-and-conquer variant (EDCMSP) to enable adaptive, dense subgraph extraction under changing size and similarity requirements. Building on SGSEL, the proposed DCSEL algorithm derives a -approximation for both DCMSP and EDCMSP by decomposing the problem into subgraphs and carefully merging solutions while preserving density. The approach supports dynamic constraints and extra-node adjustments, offering practical efficiency for scalable graph mining. Experiments on Cora, Citeseer, and Pubmed demonstrate that DCSEL closely matches SGSEL in objective quality while offering improved adaptability and runtime performance under dynamic conditions.

Abstract

Dense subgraph extraction is a fundamental problem in graph analysis and data mining, aimed at identifying cohesive and densely connected substructures within a given graph. It plays a crucial role in various domains, including social network analysis, biological network analysis, recommendation systems, and community detection. However, extracting a subgraph with the highest node similarity is a lack of exploration. To address this problem, we studied the Member Selection Problem and extended it with a dynamic constraint variant. By incorporating dynamic constraints, our algorithm can adapt to changing conditions or requirements, allowing for more flexible and personalized subgraph extraction. This approach enables the algorithm to provide tailored solutions that meet specific needs, even in scenarios where constraints may vary over time. We also provide the theoretical analysis to show that our algorithm is 1/3-approximation. Eventually, the experiments show that our algorithm is effective and efficient in tackling the member selection problem with dynamic constraints.
Paper Structure (15 sections, 7 theorems, 3 equations, 4 figures, 1 table, 2 algorithms)

This paper contains 15 sections, 7 theorems, 3 equations, 4 figures, 1 table, 2 algorithms.

Table of Contents

  1. Introduction
  2. Related Works
  3. Dense Subgraph Extraction
  4. Densest Subgraph Problem and Densest k-subgraph Problem
  5. Preliminaries
  6. Problem Formulation
  7. DCMSP
  8. EDCMSP
  9. Algorithm Design
  10. Theoretical Analysis
  11. Extra Nodes of Graph Adjustment
  12. Experiments
  13. Datasets
  14. Baseline
  15. Result

Key Result

lemma thmcounterlemma

Suppose $\alpha(\mathbb{F}) \leq \alpha(OPT_1)$ and $\alpha(\mathbb{F}) \leq \alpha(OPT_2)$. Then $F_1 \cup F_2$ is a $\frac{1}{3}$-approximation solution of EDCMSP. i.e., $\alpha(F_1 \cup F_2) \geq \frac{1}{3}\alpha(\mathbb{F})$.

Figures (4)

  • Figure 1: Example for SGSEL
  • Figure 2: Size constraint $p$ monotonic increase
  • Figure 3: Size constraint $p$ montonic decrease
  • Figure 4: Size constraint $p$ randomly selected

Theorems & Definitions (14)

  • lemma thmcounterlemma
  • proof
  • lemma thmcounterlemma
  • proof
  • theorem thmcountertheorem
  • proof
  • lemma thmcounterlemma
  • proof
  • lemma thmcounterlemma
  • proof
  • ...and 4 more