A unified approach to approximation algorithms for bottleneck problems
Journal of the ACM (JACM)
Excluded minors, network decomposition, and multicommodity flow
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
Improved bounds for the max-flow min-multicut ratio for planar and Kr,r-free graphs
Information Processing Letters
The Complexity of Multiterminal Cuts
SIAM Journal on Computing
Multicommodity max-flow min-cut theorems and their use in designing approximation algorithms
Journal of the ACM (JACM)
Approximation algorithms
Approximate Max-Flow Min-(Multi)Cut Theorems and Their Applications
SIAM Journal on Computing
An Efficient k-Means Clustering Algorithm: Analysis and Implementation
IEEE Transactions on Pattern Analysis and Machine Intelligence
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
Constrained K-means Clustering with Background Knowledge
ICML '01 Proceedings of the Eighteenth International Conference on Machine Learning
ICML '02 Proceedings of the Nineteenth International Conference on Machine Learning
Clustering with Instance-level Constraints
ICML '00 Proceedings of the Seventeenth International Conference on Machine Learning
Cutting and Partitioning a Graph aifter a Fixed Pattern (Extended Abstract)
Proceedings of the 10th Colloquium on Automata, Languages and Programming
Primal-Dual Approximation Algorithms for Metric Facility Location and k-Median Problems
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Efficient location area planning for personal communication systems
Proceedings of the 9th annual international conference on Mobile computing and networking
Clustering with Qualitative Information
FOCS '03 Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science
Correlation Clustering: maximizing agreements via semidefinite programming
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Maximizing Quadratic Programs: Extending Grothendieck's Inequality
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
An experimental comparison of several clustering and initialization methods
UAI'98 Proceedings of the Fourteenth conference on Uncertainty in artificial intelligence
ACM Transactions on Knowledge Discovery from Data (TKDD)
Clustering with Partial Information
MFCS '08 Proceedings of the 33rd international symposium on Mathematical Foundations of Computer Science
Solution stability in linear programming relaxations: graph partitioning and unsupervised learning
ICML '09 Proceedings of the 26th Annual International Conference on Machine Learning
Bounding and comparing methods for correlation clustering beyond ILP
ILP '09 Proceedings of the Workshop on Integer Linear Programming for Natural Langauge Processing
Constant ratio fixed-parameter approximation of the edge multicut problem
Information Processing Letters
Gesture improves coreference resolution
NAACL-Short '06 Proceedings of the Human Language Technology Conference of the NAACL, Companion Volume: Short Papers
Creating probabilistic databases from duplicated data
The VLDB Journal — The International Journal on Very Large Data Bases
Framework for evaluating clustering algorithms in duplicate detection
Proceedings of the VLDB Endowment
Clustering with partial information
Theoretical Computer Science
Correlation clustering with noisy input
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
A polynomial time approximation scheme for k-consensus clustering
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
A sharp concentration-based adaptive segmentation algorithm
ISVC'10 Proceedings of the 6th international conference on Advances in visual computing - Volume Part II
Towards a more discriminative and semantic visual vocabulary
Computer Vision and Image Understanding
Fixed-parameter tractability of multicut parameterized by the size of the cutset
Proceedings of the forty-third annual ACM symposium on Theory of computing
Improved approximation algorithms for bipartite correlation clustering
ESA'11 Proceedings of the 19th European conference on Algorithms
Overcoming browser cookie churn with clustering
Proceedings of the fifth ACM international conference on Web search and data mining
Globally optimal closed-surface segmentation for connectomics
ECCV'12 Proceedings of the 12th European conference on Computer Vision - Volume Part III
Fast planar correlation clustering for image segmentation
ECCV'12 Proceedings of the 12th European conference on Computer Vision - Volume Part VI
Finding small separators in linear time via treewidth reduction
ACM Transactions on Algorithms (TALG)
Clustering and outlier detection using isoperimetric number of trees
Pattern Recognition
Correlation clustering with stochastic labellings
SIMBAD'13 Proceedings of the Second international conference on Similarity-Based Pattern Recognition
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We consider the following general correlation-clustering problem [N. Bansal, A. Blum, S. Chawla, Correlation clustering, in: Proc. 43rd Annu. IEEE Symp. on Foundations of Computer Science, Vancouver, Canada, November 2002, pp. 238-250]: given a graph with real nonnegative edge weights and a 〈+〉/〈-〉 edge labelling, partition the vertices into clusters to minimize the total weight of cut 〈+〉 edges and uncut 〈-〉 edges. Thus, 〈+〉 edges with large weights (representing strong correlations between endpoints) encourage those endpoints to belong to a common cluster while 〈-〉 edges with large weights encourage the endpoints to belong to different clusters. In contrast to most clustering problems, correlation clustering specifies neither the desired number of clusters nor a distance threshold for clustering; both of these parameters are effectively chosen to be best possible by the problem definition.Correlation clustering was introduced by Bansal et al. [Correlation clustering, in: Proc. 43rd Annu. IEEE Syrup. on Foundations of Computer Science, Vancouver, Canada, November 2002, pp. 238-250], motivated by both document clustering and agnostic learning. They proved NP-hardness and gave constant-factor approximation algorithms for the special case in which the graph is complete (full information) and every edge has the same weight. We give an O(log n)-approximation algorithm for the general case based on a linear-programming rounding and the "region-growing" technique. We also prove that this linear program has a gap of Ω(log n), and therefore our approximation is tight under this approach. We also give an O(r3)-approximation algorithm for Kr, r-minor-free graphs. On the other hand, we show that the problem is equivalent to minimum multicut, and therefore APX-hard and difficult to approximate better than Θ(log n).