# FASTcons: FAST algorithm to find consensus (median) ranking. FAST... In ConsRank: Compute the Median Ranking(s) According to the Kemeny's Axiomatic Approach

## Description

FAST algorithm to find consensus (median) ranking.

FAST algorithm to find consensus (median) ranking defined by Amodio, D'Ambrosio and Siciliano (2016). It returns at least one of the solutions. If there are multiple solutions, sometimes it returns all the solutions, sometimes it returns some solutions, always it returns at least one solution.

## Usage

 `1` ```FASTcons(X, Wk = NULL, maxiter = 50, FULL = FALSE, PS = FALSE) ```

## Arguments

 `X` is a ranking data matrix `Wk` is a vector of weights `maxiter` maximum number of iterations: default = 50. `FULL` Default FULL=FALSE. If FULL=TRUE, the searching is limited to the space of full rankings. `PS` Default PS=FALSE. If PS=TRUE the number of current iteration is diplayed

## Value

a "list" containing the following components:

 Consensus the Consensus Ranking Tau averaged TauX rank correlation coefficient Eltime Elapsed time in seconds

## Author(s)

Antonio D'Ambrosio [email protected] and Sonia Amodio [email protected]

## References

Amodio, S., D'Ambrosio, A. and Siciliano, R. (2016). Accurate algorithms for identifying the median ranking when dealing with weak and partial rankings under the Kemeny axiomatic approach. European Journal of Operational Research, 249(2), 667-676.

`EMCons` Emond and Mason branch-and-bound algorithm.
`QuickCons` Quick algorithm.
 ```1 2 3 4 5 6 7 8``` ```##data(EMD) ##X=EMD[,1:15] ##Wk=matrix(EMD[,16],nrow=nrow(X)) ##CR=FASTcons(X,Wk,maxiter=100) ##These lines produce all the three solutions in less than a minute. data(sports) CR=FASTcons(sports,maxiter=10) ```