NP-hard problems in hierarchical-tree clustering
Acta Informatica
A general method to speed up fixed-parameter-tractable algorithms
Information Processing Letters
Machine Learning
Cluster graph modification problems
Discrete Applied Mathematics - Discrete mathematics & data mining (DM & DM)
Graph-Modeled Data Clustering: Exact Algorithms for Clique Generation
Theory of Computing Systems
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
Invitation to data reduction and problem kernelization
ACM SIGACT News
Detecting Critical Regions in Covert Networks: A Case Study of 9/11 Terrorists Network
ARES '07 Proceedings of the The Second International Conference on Availability, Reliability and Security
Generating all maximal induced subgraphs for hereditary and connected-hereditary graph properties
Journal of Computer and System Sciences
Applying Modular Decomposition to Parameterized Cluster Editing Problems
Theory of Computing Systems
A more effective linear kernelization for cluster editing
Theoretical Computer Science
Algorithms and Experiments for Clique Relaxations--Finding Maximum s-Plexes
SEA '09 Proceedings of the 8th International Symposium on Experimental Algorithms
Isolation concepts for efficiently enumerating dense subgraphs
Theoretical Computer Science
Deterministic Pivoting Algorithms for Constrained Ranking and Clustering Problems
Mathematics of Operations Research
Going weighted: Parameterized algorithms for cluster editing
Theoretical Computer Science
Kernelization: New Upper and Lower Bound Techniques
Parameterized and Exact Computation
Editing Graphs into Disjoint Unions of Dense Clusters
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
A parallel algorithm for enumerating all the maximal k-plexes
PAKDD'07 Proceedings of the 2007 international conference on Emerging technologies in knowledge discovery and data mining
A 2k Kernel for the cluster editing problem
COCOON'10 Proceedings of the 16th annual international conference on Computing and combinatorics
Generalized graph clustering: recognizing (p, q)-cluster graphs
WG'10 Proceedings of the 36th international conference on Graph-theoretic concepts in computer science
Alternative parameterizations for cluster editing
SOFSEM'11 Proceedings of the 37th international conference on Current trends in theory and practice of computer science
Clique Relaxations in Social Network Analysis: The Maximum k-Plex Problem
Operations Research
Kernelization through tidying: a case study based on s-plex cluster vertex deletion
LATIN'10 Proceedings of the 9th Latin American conference on Theoretical Informatics
The cluster editing problem: implementations and experiments
IWPEC'06 Proceedings of the Second international conference on Parameterized and Exact Computation
Computer Science Review
Graph-based data clustering with overlaps
Discrete Optimization
Survey of clustering algorithms
IEEE Transactions on Neural Networks
Efficient parameterized preprocessing for cluster editing
FCT'07 Proceedings of the 16th international conference on Fundamentals of Computation Theory
Parameterized Complexity
Alternative parameterizations for cluster editing
SOFSEM'11 Proceedings of the 37th international conference on Current trends in theory and practice of computer science
A generalization of Nemhauser and Trotter's local optimization theorem
Journal of Computer and System Sciences
On editing graphs into 2-club clusters
FAW-AAIM'12 Proceedings of the 6th international Frontiers in Algorithmics, and Proceedings of the 8th international conference on Algorithmic Aspects in Information and Management
A golden ratio parameterized algorithm for Cluster Editing
Journal of Discrete Algorithms
Exact combinatorial algorithms and experiments for finding maximum k-plexes
Journal of Combinatorial Optimization
Clustering with local restrictions
Information and Computation
Hi-index | 0.00 |
We introduce the $s$-Plex Cluster Editing problem as a generalization of the well-studied Cluster Editing problem; both are NP-hard and both are motivated by graph-based data clustering. Instead of transforming a given graph by a minimum number of edge modifications into a disjoint union of cliques (this is Cluster Editing), the task in the case of $s$-Plex Cluster Editing is to transform a graph into a cluster graph consisting of a disjoint union of so-called $s$-plexes. Herein, an $s$-plex is a vertex set $S$ inducing a subgraph in which every vertex has degree at least $|S|-s$. Cliques are 1-plexes. The advantage of $s$-plexes for $s\geq2$ is that they allow us to model a more relaxed cluster notion ($s$-plexes instead of cliques), better reflecting inaccuracies of the input data. We develop a provably effective preprocessing based on data reduction (yielding a so-called problem kernel), a forbidden subgraph characterization of $s$-plex cluster graphs, and a depth-bounded search tree which is used to find optimal edge modification sets. Altogether, this yields efficient algorithms in case of moderate numbers of edge modifications; this is often a reasonable assumption under a maximum parsimony model for data clustering.