Group Decision Diagram
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README.md Update README.md Feb 1, 2019

README.md

Group Decision Diagram

Group Decision Diagram (GDD) is a data structure to maintain a subset of a permutation group. This is a C++ implementation of GDD.

Install

This is a header-only library. Please copy the files in ./include

Usage

#include <bits/stdc++.h>
#include "gdd.hh"
#include "permutation.hh"
#include "memoryusage.hh"
#include "util.hh"

using namespace std;

int main() {
  Permutation R = Permutation::parse(24, "(12,13,15,14)(9,1,18,21)(11,3,16,23)");
  Permutation U = Permutation::parse(24, "(0,1,3,2)(8,4,16,12)(9,5,17,13)");
  Permutation F = Permutation::parse(24, "(8,9,11,10)(2,12,21,7)(3,14,20,5)");

  int n = U.n;
  vector<Permutation> gen = {R, U, F};
  
  GroupDecisionDiagram gdd(gen);
  auto order = gdd.groupOrder();
  cout << "Group Order = " << order << endl;

  int z = gdd.top;
  for (Permutation g: gen) {
    z = gdd.cup(z, gdd.sing
    
    
 \
 ton(g));
    z = gdd.cup(z, gdd.singleton(g.inv()));
  }

  cout << "i: time | #GDDSize | #TotalGDDSize | Cardinality" << endl;
  auto prev = order; prev = 1;
  int w = gdd.top;

  for (int iter = 1; iter < 15; ++iter) {
    w = gdd.cartesianProduct(z, w);
    cout << iter << ": " << diff << " | ";
    auto count = gdd.cardinality(w);
    cout << gdd.numberOfNodes(w) << " | " << gdd.node.size() << " | " << count << " || " << count - prev << endl;
    if (count == order) break;
    prev = count;
  }
  return 0;
}
> g++ main.cc
> ./a.out

Performance

Rubik Cube's puzzle:

(k) 3 4 5 6 7
#Conf. 1,068 10,011 93,840 878,880 8,221,632
GDD (size) 6,537 58,850 476,497 3,641,049 26,721,270
GDD (time) 0.02s 0.30s 3.54s 35.04s 338.2s
piDD (size) 26,166 247,770 2,319,674 21,062,444
piDD (time) 0.11s 1.80s 23.4s 247.3s (\ge) 7200s
rhoDD (size) 36,799 331,549 2,978,733 26,715,003
rhoDD (time) 0.51s 6.36s 58.5s 572.9s (\ge) 7200s

piDD, rhoDD are existing data structure for the same purpose.

Reference

  • Takanori Maehara and Yuma Inoue (2019): "Group Decision Diagram (GDD): A Compact Representation for Permutations", in Proceedings of the 33rd AAAI Conference on Artificial Intelligence (AAAI'19), Honolulu, Hawaii, United States, January 27--February 01, 2019.