How to rank with few errors

  title={How to rank with few errors},
  author={Claire Mathieu and Warren Schudy},
  booktitle={STOC '07},
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. 

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

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

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

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

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

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

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

  • Pan LiO. Milenkovic
  • Computer Science
    2017 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

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

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

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.



The importance of being biased

(MATH) We show that the Minimum Vertex Cover problem is NP-hard to approximate to within any factor smaller than $10\sqrt{5}-21 \approx 1.36067$, improving on the previously known hardness result for

Ranking Tournaments

  • N. Alon
  • Mathematics
    SIAM J. Discret. Math.
  • 2006
It is shown that the feedback arc set problem for tournaments is NP-hard under randomized reductions, which settles a conjecture of Bang-Jensen and Thomassen.

An Approximation Algorithm for Feedback Vertex Sets in Tournaments

It is obtained that a 2.5-approximation polynomial time algorithm for the feedback vertex set problem in any tournament to possess the min-max relation on packing and covering directed cycles is found.

How to rank with few errors: A PTAS for Weighted Feedback Arc Set on Tournaments

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.

Packing directed circuits fractionally

There is a set ofO (k logk log k logk) vertices meeting all directed circuits ofG, such that no “fractional” packing of directed circuit ofG has value >k, when every vertex is given “capacity” 1.

On the maximum cardinality of a consistent set of arcs in a random tournament

  • W. Vega
  • Mathematics
    J. Comb. Theory, Ser. B
  • 1983

Divide-and-conquer approximation algorithms via spreading metrics

A polynomial time approximation algorithm for problems modelled by the novel divide-and-conquer paradigm, whose approximation factor is O (mi.tau), is presented.

Aggregating inconsistent information: Ranking and clustering

This work almost settles a long-standing conjecture of Bang-Jensen and Thomassen and shows that unless NP⊆BPP, there is no polynomial time algorithm for the problem of minimum feedback arc set in tournaments.

The computational difficulty of manipulating an election

A voting rule is exhibited that efficiently computes winners but is computationally resistant to strategic manipulation, showing how computational complexity might protect the integrity of social choice.

A new rounding procedure for the assignment problem with applications to dense graph arrangement problems

Abstract.We present a randomized procedure for rounding fractional perfect matchings to (integral) matchings. If the original fractional matching satisfies any linear inequality, then with high