setpartition_unrank

README

Setpartition_unrank

A Go library to lexicographically unrank set partitions

Authors

• Amaury CURIEL, Sorbonne Univerisity, LIP6, Paris
• Antoine GENITRINI, Sorbonne University, LIP6, Paris

Installation

To import the library you need first to create a Go project. In your terminal enter the following command :

go mod init your_project

Then, you need to get the setpartition_unrank library. In your project folder, where is stored the go.mod file enter this command :

go get github.com/AMAURYCU/setpartition_unrank

You are now ready to use our library

License

GPL-3.0

Demo

First of all, ensure to have followed the installation step. In the folder where your go.mod file is, enter the following command :

go get github.com/AMAURYCU/setpartition_unrank

then you can import the library puting the following line in the head of your Go project

import "github.com/AMAURYCU/setpartition_unrank/XXXXX"

where

XXXXX

should be replaced with one of the following command

parallelunranking //to run the efficient parallel algorithm
precalcul //to run the algorithm with precomputation step
statistic //to make some statistics on the library

An example of program that lists all set partitions of the set [|1,10|] in 5 blocks :

package main

import (
	"fmt"
	"math/big"

	"github.com/AMAURYCU/setpartition_unrank/parallelunranking"
)

func main() {
	c := parallelunranking.Stirling2Columns(10, 5).Col1[10]
	c.Sub(&c, big.NewInt(1))
	for k2 := big.NewInt(0); k2.Cmp(&c) < 1; k2.Add(k2, big.NewInt(1)) {
        // 10 stand for [|1,10|], 5 for 5 blocks, *k2 to iterate over sets partitions
        // and for to use S3V5 (you should always use it)
		fmt.Println(parallelunranking.UnrankDicho(10, 5, *k2, 4), k2)
	}
}
//output (the last lines): 
/*
...
[[1 10] [2 9] [3 7 8] [4] [5 6]] 42515
[[1 10] [2 9] [3 7 8] [4 5] [6]] 42516
[[1 10] [2 9] [3 7 8] [4 6] [5]] 42517
[[1 10] [2 9] [3 8] [4] [5 6 7]] 42518
[[1 10] [2 9] [3 8] [4 5] [6 7]] 42519
[[1 10] [2 9] [3 8] [4 5 6] [7]] 42520
[[1 10] [2 9] [3 8] [4 5 7] [6]] 42521
[[1 10] [2 9] [3 8] [4 6] [5 7]] 42522
[[1 10] [2 9] [3 8] [4 6 7] [5]] 42523
[[1 10] [2 9] [3 8] [4 7] [5 6]] 42524
*/

Documentation

Documentation

Performance

The computation time for the function parallelunranking.UnrankDicho(n, k, r) is less than 1 second for n = 1000, about 30 seconds for n = 3000, and approximately 5 minutes for n = 5000 on a modern computer.

Executable application

The git repo has a main.gofile that can be executed entering this command :

go run main.go -operation [A/R/G] -mode [P/S] [arguments] where :

Operations:
  A: to generate all partitions of n1 in n2 non-empty disjoints subsets - Requires 2 numeric arguments
  R: to randomly pickup one partition of n1 in n2 non-empty disjoints subsets - Requires 2 numeric arguments
  G: to have an overview of the performance of the algorithm 
  partitionning n1 in n2 non-empty disjoints subsets with n3 points - Requires 3 numeric arguments
Modes:
  P: parallel
  S: sequential
  -mode string
    	Specify mode: P or S
  -operation string
    	Specify operation: A, R or G

For example :

go run main.go -operation R -mode P 50 5

will output:

[[1 5 11 32 34 39 43 44 45 48] [2 3 7 8 12 14 25 28 29 37] 
[4 20 22 24 26 35 38 47] [6 9 10 13 19 33 36 40] 
[15 16 17 18 21 23 27 30 31 41 42 46 49 50]]

warning : the G operation does not require -mode arguments

Related

This project is related to the implementation of our paper : Lexicographic unranking algorithms for the Twelvefold Way