On a conjecture of Tuza about packing and covering of triangles
Discrete Mathematics
Rank aggregation methods for the Web
Proceedings of the 10th international conference on World Wide Web
Integrating Microarray Data by Consensus Clustering
ICTAI '03 Proceedings of the 15th IEEE International Conference on Tools with Artificial Intelligence
Aggregating inconsistent information: ranking and clustering
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Fitting tree metrics: Hierarchical clustering and Phylogeny
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Ordering by weighted number of wins gives a good ranking for weighted tournaments
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Discovering bucket orders from full rankings
Proceedings of the 2008 ACM SIGMOD international conference on Management of data
Finding Total and Partial Orders from Data for Seriation
DS '08 Proceedings of the 11th International Conference on Discovery Science
Developing Preference Band Model to Manage Collective Preferences
ER '08 Proceedings of the 27th International Conference on Conceptual Modeling
A note on generalized rank aggregation
Information Processing Letters
Linear Programming Based Approximation Algorithms for Feedback Set Problems in Bipartite Tournaments
TAMC '09 Proceedings of the 6th Annual Conference on Theory and Applications of Models of Computation
ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
Deterministic Pivoting Algorithms for Constrained Ranking and Clustering Problems
Mathematics of Operations Research
Deterministic algorithms for rank aggregation and other ranking and clustering problems
WAOA'07 Proceedings of the 5th international conference on Approximation and online algorithms
Improved algorithms for bicluster editing
TAMC'08 Proceedings of the 5th international conference on Theory and applications of models of computation
Ordering by weighted number of wins gives a good ranking for weighted tournaments
ACM Transactions on Algorithms (TALG)
Correlation clustering with noisy input
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Linear programming based approximation algorithms for feedback set problems in bipartite tournaments
Theoretical Computer Science
The nearest neighbor spearman footrule distance for bucket, interval, and partial orders
FAW-AAIM'11 Proceedings of the 5th joint international frontiers in algorithmics, and 7th international conference on Algorithmic aspects in information and management
Kernels for feedback arc set in tournaments
Journal of Computer and System Sciences
A polynomial kernel for feedback arc set on bipartite tournaments
ISAAC'11 Proceedings of the 22nd international conference on Algorithms and Computation
Fixed-parameter complexity of feedback vertex set in bipartite tournaments
ISAAC'11 Proceedings of the 22nd international conference on Algorithms and Computation
The feedback arc set problem with triangle inequality is a vertex cover problem
LATIN'12 Proceedings of the 10th Latin American international conference on Theoretical Informatics
A Polynomial Kernel for Feedback Arc Set on Bipartite Tournaments
Theory of Computing Systems
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We introduce new problems of finding minimum-cost rankings and clusterings which must be consistent with certain constraints (e.g. an input partial order in the case of ranking problems); we give deterministic approximation algorithms for these problems. Randomized approximation algorithms for unconstrained versions of these problems were given by Ailon, Charikar, and Newman [2] and by Ailon and Charikar [1]. Finding deterministic approximation algorithms for these problems answers an open question of Ailon et al. [2]. In particular, we give deterministic algorithms for constrained weighted feedback arc set in tournaments, constrained correlation clustering, and constrained hierarchical clustering related to finding good ultrametrics. Our algorithms follow the paradigm of Ailon et al. [2] of choosing a particular vertex as a pivot and partitioning the graph according to the pivot; unlike their algorithms, we do not choose the pivot randomly but rather use an LP relaxation to choose a good pivot deterministically. Additionally, the use of the LP relaxation allows us to impose constraints easily and analyze the results. In several cases we are able to find approximation factors for the constrained problems that improve on the factors they obtained for the unconstrained cases. We also give a combinatorial algorithm for constrained weighted feedback arc set in tournaments with weights satisfying probability constraints. This algorithm improves on the best known factor given by deterministic combinatorial algorithms for the unconstrained case.