A new heuristic algorithm solving the linear ordering problem
Computational Optimization and Applications
Forcing matchings on square grids
Discrete Mathematics
Rank aggregation methods for the Web
Proceedings of the 10th international conference on World Wide Web
Proceedings of the 24th annual international ACM SIGIR conference on Research and development in information retrieval
A Fast and Effective Algorithm for the Feedback Arc Set Problem
Journal of Heuristics
Local Search Heuristics for k-Median and Facility Location Problems
SIAM Journal on Computing
Machine Learning
A local search approximation algorithm for k-means clustering
Computational Geometry: Theory and Applications - Special issue on the 18th annual symposium on computational geometry—SoCG2002
Aggregating inconsistent information: ranking and clustering
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
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
The Minimum Feedback Arc Set Problem is NP-Hard for Tournaments
Combinatorics, Probability and Computing
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Mining web multi-resolution community-based popularity for information retrieval
Proceedings of the sixteenth ACM conference on Conference on information and knowledge management
A Local-Search 2-Approximation for 2-Correlation-Clustering
ESA '08 Proceedings of the 16th annual European symposium on Algorithms
On the hierarchicalness of q&a posting networks
Proceedings of the 16th ACM international conference on Supporting group work
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Ranking is a fundamental activity for organizing and, later, understanding data. Advice of the form “a should be ranked before b” is given. If this advice is consistent, and complete, then there is a total ordering on the data and the ranking problem is essentially a sorting problem. If the advice is consistent, but incomplete, then the problem becomes topological sorting. If the advice is inconsistent, then we have the feedback arc set (FAS) problem: The aim is then to rank a set of items to satisfy as much of the advice as possible. An instance in which there is advice about every pair of items is known as a tournament. This ranking task is equivalent to ordering the nodes of a given directed graph from left to right, while minimizing the number of arcs pointing left. In the past, much work focused on finding good, effective heuristics for solving the problem. Recently, a proof of the NP-completeness of the problem (even when restricted to tournaments) has accompanied new algorithms with approximation guarantees, culminating in the development of a PTAS (polynomial time approximation scheme) for solving FAS on tournaments. In this article, we reexamine many existing algorithms and develop some new techniques for solving FAS. The algorithms are tested on both synthetic and nonsynthetic datasets. We find that, in practice, local-search algorithms are very powerful, even though we prove that they do not have approximation guarantees. Our new algorithm is based on reversing arcs whose nodes have large indegree differences, eventually leading to a total ordering. Combining this with a powerful local-search technique yields an algorithm that is as strong, or stronger than, existing techniques on a variety of data sets.