Combinatorial Approximations for Cluster Deletion: Simpler, Faster, and Better

• URL: http://arxiv.org/abs/2404.16131v1
• Date: Wed, 24 Apr 2024 18:39:18 GMT
• Title: Combinatorial Approximations for Cluster Deletion: Simpler, Faster, and Better
• Authors: Vicente Balmaseda, Ying Xu, Yixin Cao, Nate Veldt,
• Abstract summary: Cluster deletion is an NP-hard graph clustering objective with applications in computational and social network analysis. We first provide a tighter analysis of two previous approximation algorithms, improving their approximation guarantees from 4 to 3. We show that both algorithms can be derandomized in a surprisingly simple way, by greedily taking a maximum degree in an auxiliary graph and forming a cluster around it.
• Score: 18.121514220195607
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Cluster deletion is an NP-hard graph clustering objective with applications in computational biology and social network analysis, where the goal is to delete a minimum number of edges to partition a graph into cliques. We first provide a tighter analysis of two previous approximation algorithms, improving their approximation guarantees from 4 to 3. Moreover, we show that both algorithms can be derandomized in a surprisingly simple way, by greedily taking a vertex of maximum degree in an auxiliary graph and forming a cluster around it. One of these algorithms relies on solving a linear program. Our final contribution is to design a new and purely combinatorial approach for doing so that is far more scalable in theory and practice.

Related papers

• A Differentially Private Clustering Algorithm for Well-Clustered Graphs [6.523602840064548]
  We provide an efficient ($epsilon,$delta$)-DP algorithm tailored specifically for such graphs. Our algorithm works for well-clustered graphs with $k$ nearly-balanced clusters.
  arXiv  Detail & Related papers  (2024-03-21T11:57:16Z)
• Ensemble Quadratic Assignment Network for Graph Matching [52.20001802006391]
  Graph matching is a commonly used technique in computer vision and pattern recognition. Recent data-driven approaches have improved the graph matching accuracy remarkably. We propose a graph neural network (GNN) based approach to combine the advantages of data-driven and traditional methods.
  arXiv  Detail & Related papers  (2024-03-11T06:34:05Z)
• Latent Random Steps as Relaxations of Max-Cut, Min-Cut, and More [30.919536115917726]
  We present a probabilistic model based on non-negative matrix factorization which unifies clustering and simplification. By relaxing the hard clustering to a soft clustering, our algorithm relaxes potentially hard clustering problems to a tractable ones.
  arXiv  Detail & Related papers  (2023-08-12T02:47:57Z)
• Learning the Positions in CountSketch [49.57951567374372]
  We consider sketching algorithms which first compress data by multiplication with a random sketch matrix, and then apply the sketch to quickly solve an optimization problem. In this work, we propose the first learning-based algorithms that also optimize the locations of the non-zero entries.
  arXiv  Detail & Related papers  (2023-06-11T07:28:35Z)
• Faster Approximation Algorithms for Parameterized Graph Clustering and Edge Labeling [6.599344783327054]
  Graph clustering is a fundamental task in network analysis where the goal is to detect sets of nodes that are well-connected to each other but sparsely connected to the rest of the graph. We present faster approximation algorithms for an NP-hard parameterized clustering framework called LambdaCC.
  arXiv  Detail & Related papers  (2023-06-08T02:29:37Z)
• One-step Bipartite Graph Cut: A Normalized Formulation and Its Application to Scalable Subspace Clustering [56.81492360414741]
  We show how to enforce a one-step normalized cut for bipartite graphs, especially with linear-time complexity. In this paper, we first characterize a novel one-step bipartite graph cut criterion with normalized constraints, and theoretically prove its equivalence to a trace problem. We extend this cut criterion to a scalable subspace clustering approach, where adaptive anchor learning, bipartite graph learning, and one-step normalized bipartite graph partitioning are simultaneously modeled.
  arXiv  Detail & Related papers  (2023-05-12T11:27:20Z)
• Efficient Graph Field Integrators Meet Point Clouds [59.27295475120132]
  We present two new classes of algorithms for efficient field integration on graphs encoding point clouds. The first class, SeparatorFactorization(SF), leverages the bounded genus of point cloud mesh graphs, while the second class, RFDiffusion(RFD), uses popular epsilon-nearest-neighbor graph representations for point clouds.
  arXiv  Detail & Related papers  (2023-02-02T08:33:36Z)
• Differentially-Private Hierarchical Clustering with Provable Approximation Guarantees [79.59010418610625]
  We study differentially private approximation algorithms for hierarchical clustering. We show strong lower bounds for the problem: that any $epsilon$-DP algorithm must exhibit $O(|V|2/ epsilon)$-additive error for an input dataset. We propose a private $1+o(1)$ approximation algorithm which also recovers the blocks exactly.
  arXiv  Detail & Related papers  (2023-01-31T19:14:30Z)
• Scalable and Effective Conductance-based Graph Clustering [9.938406925123722]
  We develop a graph clustering framework textitPCon. We show that many existing solutions can be reduced to our framework. Based on our framework, we propose two novel algorithms textitPCon_core and emphPCon_de with linear time and space complexity.
  arXiv  Detail & Related papers  (2022-11-22T12:45:27Z)
• Sublinear Algorithms for Hierarchical Clustering [14.124026862687941]
  We study hierarchical clustering for massive graphs under three well-studied models of sublinear computation. We design sublinear algorithms for hierarchical clustering in all three models.
  arXiv  Detail & Related papers  (2022-06-15T16:25:27Z)
• Online Dense Subgraph Discovery via Blurred-Graph Feedback [87.9850024070244]
  We introduce a novel learning problem for dense subgraph discovery. We first propose a edge-time algorithm that obtains a nearly-optimal solution with high probability. We then design a more scalable algorithm with a theoretical guarantee.
  arXiv  Detail & Related papers  (2020-06-24T11:37:33Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.