Ordering by weighted number of wins gives a good ranking for weighted tournaments

@article{Coppersmith2006OrderingBW,
  title={Ordering by weighted number of wins gives a good ranking for weighted tournaments},
  author={Don Coppersmith and Lisa Fleischer and Atri Rudra},
  journal={Electron. Colloquium Comput. Complex.},
  year={2006},
  volume={TR05}
}
We consider the following simple algorithm for feedback arc set problem in weighted tournaments --- order the vertices by their weighted indegrees. We show that this algorithm has an approximation guarantee of 5 if the weights satisfy <i>probability constraints</i> (for any pair of vertices <i>u</i> and <i>v, w</i><inf><i>uv</i></inf> + w<inf><i>vu</i></inf> = 1). Special cases of feedback arc set problem in such weighted tournaments include feedback arc set problem in unweighted tournaments… 

Figures from this paper

Random tournaments : who plays with whom and how many times ?

TLDR
This study investigates an online learning problem where the learner can observe tournament graphs drawn from this distribution, and considers the probabilistic version of WFAS-T, in which the weights of the directed edges between every pair of teams sum up to one.

Ranking tournaments with no errors

TLDR
The purpose of this paper is to present a structural characterization of all CM tournaments, which yields a polynomial-time algorithm for the minimum-weight feedback arc set problem on such tournaments.

On The Structure of Parametric Tournaments with Application to Ranking from Pairwise Comparisons

TLDR
A polynomial-time algorithm is developed - Rank2Rank - that solves the MFAST problem for the rank 2 tournament class and a local-global parametric pairwise preference model is proposed which subsumes the popular Bradley-Terry-Luce/Thurstone classes to capture locally cyclic as well as globally acyclic preference relations.

Kernels for feedback arc set in tournaments

TLDR
This paper gives a polynomial time algorithm which given an input instance T to k-FAST obtains an equivalent instance T ′ on O(k) vertices, and improves the previous known bound of O( k2 ) on the kernel size for k- FAST.

Deterministic pivoting algorithms for constrained ranking and clustering problems

TLDR
D deterministic algorithms for constrained weighted feedback arc set in tournaments, constrained correlation clustering, and constrained hierarchical clustering related to finding good ultrametrics and a combinatorial algorithm that improves on the best known factor given by deterministic combinatorsial algorithms for the unconstrained case are given.

Linear vertex-kernels for several dense ranking r-CSPs

TLDR
It is proved that so-called l_r-simply characterized ranking r-CSPs admit linear vertex-kernels whenever they admit constant-factor approximation algorithms.

Fixing a Tournament

TLDR
The problem is NP-complete for general graphs and several interesting conditions on the desired winner A for which there exists a balanced single-elimination tournament which A wins, and it can be found in polynomial time.

Faster Algorithms for Feedback Arc Set Tournament, Kemeny Rank Aggregation and Betweenness Tournament

TLDR
Fixed parameter algorithms are studied for three problems: Kemeny rank aggregation, feedback arc set tournament, and betweenness tournament, where n is the number of candidates, and \(OPT \le \binom{n}{2}\) is the cost of the optimal ranking.
...

References

SHOWING 1-10 OF 27 REFERENCES

Deterministic pivoting algorithms for constrained ranking and clustering problems

TLDR
D deterministic algorithms for constrained weighted feedback arc set in tournaments, constrained correlation clustering, and constrained hierarchical clustering related to finding good ultrametrics and a combinatorial algorithm that improves on the best known factor given by deterministic combinatorsial algorithms for the unconstrained case are given.

Computing Slater Rankings Using Similarities among Candidates

TLDR
This paper shows how to decompose the Slater problem into smaller subproblems if there is a set of similar candidates, and uses the technique of similar sets to show that computing an optimal Slater ranking is NP-hard even in the absence of pairwise ties.

Ranking Tournaments

  • N. Alon
  • Mathematics
    SIAM J. Discret. Math.
  • 2006
TLDR
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.

Approximating Minimum Feedback Sets and Multicuts in Directed Graphs

TLDR
A combinatorial algorithm that computes a (1+ɛ) approximation to the fractional optimal feedback vertex set, and a generalization of these problems, in which the feedback set has to intersect only a subset of the directed cycles in the graph.

Aggregating inconsistent information: Ranking and clustering

TLDR
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.

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

Approximation alogorithms for the maximum acyclic subgraph problem

TLDR
It is found that all graphs without two-cycles contain large acyclic subgraphs, a fact which was not previously known.

Cycles in dense digraphs

TLDR
It is proved that in general β(G) ≤ γ(G), and that in two special cases: when V (G) is the union of two cliques when the vertices of G can be arranged in a circle such that if distinct u, v, w are in clockwise order and uw is a (directed) edge, then so are both uv, vw.

Approximations for the Maximum Acyclic Subgraph Problem

Deterministic Approximation Algorithms for Ranking and Clustering Problems

TLDR
Deterministic versions of randomized approximation algorithms are given for ranking and clustering problems that were proposed by Ailon, Charikar and Newman and can resolve Ailon et al.