set_covering_skiena.cs

//
// Copyright 2012 Hakan Kjellerstrand
//
// Licensed under the Apache License, Version 2.0 (the "License");
// you may not use this file except in compliance with the License.
// You may obtain a copy of the License at
//
//     http://www.apache.org/licenses/LICENSE-2.0
//
// Unless required by applicable law or agreed to in writing, software
// distributed under the License is distributed on an "AS IS" BASIS,
// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
// See the License for the specific language governing permissions and
// limitations under the License.

using System;
using System.Collections.Generic;
using System.Linq;
using Google.OrTools.ConstraintSolver;

public class SetCoveringSkiena
{
  /**
   *
   * Set covering.
   *
   * Example from Steven Skiena, The Stony Brook Algorithm Repository
   * http://www.cs.sunysb.edu/~algorith/files/set-cover.shtml
   * """
   * Input Description: A set of subsets S_1, ..., S_m of the
   * universal set U = {1,...,n}.
   *
   * Problem: What is the smallest subset of subsets T subset S such
   * that \cup_{t_i in T} t_i = U?
   * """
   * Data is from the pictures INPUT/OUTPUT.
   *
   *
   * Also see http://www.hakank.org/or-tools/set_covering_skiena.py
   *
   */
  private static void Solve()
  {

    Solver solver = new Solver("SetCoveringSkiena");

    int num_sets = 7;
    int num_elements = 12;
    IEnumerable<int> Sets = Enumerable.Range(0, num_sets);
    IEnumerable<int> Elements = Enumerable.Range(0, num_elements);

    // Which element belongs to which set
    int[,] belongs =
      {
        // 1 2 3 4 5 6 7 8 9 0 1 2  elements
        {1,1,0,0,0,0,0,0,0,0,0,0}, // Set 1
        {0,1,0,0,0,0,0,1,0,0,0,0}, //     2
        {0,0,0,0,1,1,0,0,0,0,0,0}, //     3
        {0,0,0,0,0,1,1,0,0,1,1,0}, //     4
        {0,0,0,0,0,0,0,0,1,1,0,0}, //     5
        {1,1,1,0,1,0,0,0,1,1,1,0}, //     6
        {0,0,1,1,0,0,1,1,0,0,1,1}  //     7
      };


    //
    // Decision variables
    //
    IntVar[] x = solver.MakeIntVarArray(num_sets, 0, 1, "x");
    IntVar z = x.Sum().VarWithName("z");
    // total number of elements in the choosen sets
    IntVar tot_elements = solver.MakeIntVar(0, num_sets*num_elements, "tot_elements");


    //
    // Constraints
    //

    // all sets must be used
    foreach(int j in Elements) {
      solver.Add( (from i in Sets select belongs[i,j] * x[i])
                   .ToArray().Sum() >= 1);
    }

    // number of used elements
    solver.Add((from i in Sets from j in Elements select x[i] * belongs[i,j])
               .ToArray().Sum() == tot_elements);

    //
    // Objective
    //
    OptimizeVar obj = z.Minimize(1);

    //
    // Search
    //
    DecisionBuilder db = solver.MakePhase(x,
                                          Solver.INT_VAR_DEFAULT,
                                          Solver.INT_VALUE_DEFAULT);

    solver.NewSearch(db, obj);

    while (solver.NextSolution()) {
      Console.WriteLine("z: {0}", z.Value());
      Console.WriteLine("tot_elements: {0}", tot_elements.Value());
      Console.WriteLine(
               "x: {0}",
               String.Join(" ", (from i in Enumerable.Range(0, num_sets)
                                 select x[i].Value().ToString()).ToArray()));

    }

    Console.WriteLine("\nSolutions: {0}", solver.Solutions());
    Console.WriteLine("WallTime: {0}ms", solver.WallTime());
    Console.WriteLine("Failures: {0}", solver.Failures());
    Console.WriteLine("Branches: {0} ", solver.Branches());

    solver.EndSearch();

  }

  public static void Main(String[] args)
  {
    Solve();
  }
}