Property testing and its connection to learning and approximation
Journal of the ACM (JACM)
Cluster Graph Modification Problems
WG '02 Revised Papers from the 28th International Workshop on Graph-Theoretic Concepts in Computer Science
Approximation schemes for clustering problems
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
A Randomized Approximation Scheme for Metric MAX-CUT
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
A Sublinear Time Approximation Scheme for Clustering in Metric Spaces
FOCS '99 Proceedings of the 40th Annual 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
Machine Learning
Maximizing Quadratic Programs: Extending Grothendieck's Inequality
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
Optimal Inapproximability Results for Max-Cut and Other 2-Variable CSPs?
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
O(√log n) approximation algorithms for min UnCut, min 2CNF deletion, and directed cut problems
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Aggregating inconsistent information: ranking and clustering
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
On Non-Approximability for Quadratic Programs
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Clustering with qualitative information
Journal of Computer and System Sciences - Special issue: Learning theory 2003
Seeking stable clusters in the blogosphere
VLDB '07 Proceedings of the 33rd international conference on Very large data bases
ACM SIGACT News
A Local-Search 2-Approximation for 2-Correlation-Clustering
ESA '08 Proceedings of the 16th annual European symposium on Algorithms
Efficient query routing by improved peer description in P2P networks
Proceedings of the 3rd international conference on Scalable information systems
A more effective linear kernelization for cluster editing
Theoretical Computer Science
An online blog reading system by topic clustering and personalized ranking
ACM Transactions on Internet Technology (TOIT)
Correlation Clustering Revisited: The "True" Cost of Error Minimization Problems
ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
On finding graph clusterings with maximum modularity
WG'07 Proceedings of the 33rd international conference on Graph-theoretic concepts in computer science
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
Improved approximation algorithms for bipartite correlation clustering
ESA'11 Proceedings of the 19th European conference on Algorithms
Chromatic correlation clustering
Proceedings of the 18th ACM SIGKDD international conference on Knowledge discovery and data mining
A more effective linear kernelization for Cluster Editing
ESCAPE'07 Proceedings of the First international conference on Combinatorics, Algorithms, Probabilistic and Experimental Methodologies
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We continue the investigation of problems concerning correlation clustering or clustering with qualitative information, which is a clustering formulation that has been studied recently [5, 7, 8, 3]. The basic setup here is that we are given as input a complete graph on n nodes (which correspond to nodes to be clustered) whose edges are labeled + (for similar pairs of items) and - (for dissimilar pairs of items). Thus we have only as input qualitative information on similarity and no quantitative distance measure between items. The quality of a clustering is measured in terms of its number of agreements, which is simply the number of edges it correctly classifies, that is the sum of number of - edges whose endpoints it places in different clusters plus the number of + edges both of whose endpoints it places within the same cluster.In this paper, we study the problem of finding clusterings that maximize the number of agreements, and the complementary minimization version where we seek clusterings that minimize the number of disagreements. We focus on the situation when the number of clusters is stipulated to be a small constant k. Our main result is that for every k, there is a polynomial time approximation scheme for both maximizing agreements and minimizing disagreements. (The problems are NP-hard for every k ≥ 2.) The main technical work is for the minimization version, as the PTAS for maximizing agreements follows along the lines of the property tester for Max k-CUT from [13].In contrast, when the number of clusters is not specified, the problem of minimizing disagreements was shown to be APX-hard [7], even though the maximization version admits a PTAS.