# How to rank with few errors

@inproceedings{Mathieu2007HowTR, title={How to rank with few errors}, author={Claire Mathieu and Warren Schudy}, booktitle={STOC '07}, year={2007} }

We present a polynomial time approximation scheme (PTAS) for the minimum feedback arc set problem on tournaments. A simple weighted generalization gives a PTAS for Kemeny-Young rank aggregation.

## 255 Citations

### Approximation Schemes for the Betweenness Problem in Tournaments and Related Ranking Problems

- Mathematics, Computer ScienceAPPROX-RANDOM
- 2011

We settle the approximability status of the Minimum Betweenness problem in tournaments by designing a polynomial time approximation scheme (PTAS). No constant factor approximation was previously…

### A randomized approximation algorithm for computing bucket orders

- Computer ScienceInf. Process. Lett.
- 2009

### The Feedback Arc Set Problem with Triangle Inequality Is a Vertex Cover Problem

- MathematicsAlgorithmica
- 2013

We consider the (precedence constrained) Minimum Feedback Arc Set problem with triangle inequalities on the weights, which finds important applications in problems of ranking with inconsistent…

### Fully Proportional Representation as Resource Allocation: Approximability Results

- EconomicsIJCAI
- 2013

Good approximation algorithms are shown for the satisfaction-based utilitarian cases, and inapproximability results for the remaining settings are shown.

### Tight Upper Bounds for Minimum Feedback Arc Sets of Regular Graphs

- MathematicsWG
- 2013

The Feedback problem is one of the classical \(\mathcal{NP}\)-hard problems. Given a graph with n vertices and m arcs, it asks for a subset of arcs whose deletion makes a graph acyclic. An equivalent…

### Online Ranking for Tournament Graphs

- MathematicsWAOA
- 2010

Both the maximization and the minimization versions of the problem of producing a global ranking of items given pairwise ranking information on tournaments (max acyclic subgraph, feedback arc set) are studied.

### Multiclass MinMax rank aggregation

- Computer Science2017 IEEE International Symposium on Information Theory (ISIT)
- 2017

A new family of minmax rank aggregation problems under two distance measures, the Kendall τ and the Spearman footrule, and a number of constant-approximation algorithms for solving them are described.

### An Efficient Semi-Streaming PTAS for Tournament Feedback ArcSet with Few Passes

- Computer Science, MathematicsITCS
- 2022

This work presents the first semi-streaming polynomial-time approximation scheme (PTAS) for the minimum feedback arc set problem on directed tournaments in a small number of passes and presents a new time/space trade-off for 1-pass algorithms that solve the tournament feedback arcs set problem.

### On Maximum Rank Aggregation Problems

- EconomicsIWOCA
- 2013

The rank aggregation problem consists in finding a consensus ranking on a set of alternatives, based on the preferences of individual voters. These are expressed by permutations, whose distance can…

### Computing Kemeny Rankings from d-Euclidean Preferences

- Computer ScienceADT
- 2021

This work proposes an algorithm that finds an embeddable Kemeny ranking in d-Euclidean elections and achieves a polynomial runtime and thus demonstrates the algorithmic usefulness of the dEuclidesan restriction.

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This work presents a polynomial time approximation scheme (PTAS) for Kemeny-Young rank aggregation, which is a simple weighted generalization that gives a PTAS for Kemany- young rank aggregation.

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