/// <summary>
/// Given a list of cycles return those which are independent (⊕-sum)
/// from the current basis.
/// </summary>
/// <param name="cycles">cycles of a given .Length</param>
/// <returns>cycles which were independent</returns>
private List <Cycle> Independent(IEnumerable <Cycle> cycles)
{
var independent = new List <Cycle>();
foreach (var cycle in cycles)
{
if (basis.IsIndependent(cycle))
{
independent.Add(cycle);
}
}
return(independent);
}
/// <summary>
/// Generate the minimum cycle basis from a precomputed set of initial
/// cycles. This constructor allows on to specify that the graph is
/// connected which allows an optimisation to be used.
/// </summary>
/// <param name="initial">set of initial cycles.</param>
/// <param name="connected">the graph is known to be connected</param>
/// <exception cref="System.ArgumentNullException">null InitialCycles provided</exception>
internal MinimumCycleBasis(InitialCycles initial, bool connected)
{
CheckNotNull(initial, nameof(initial), "No InitialCycles provided");
this.graph = initial.Graph;
this.basis = new GreedyBasis(initial.GetNumberOfCycles(), initial.GetNumberOfEdges());
// a undirected unweighted connected graph there are |E| - (|V| + 1)
// cycles in the minimum basis
int lim = connected ? initial.GetNumberOfEdges() - graph.Length + 1 : int.MaxValue;
// processing by size add cycles which are independent of smaller cycles
foreach (var cycle in initial.GetCycles())
{
if (basis.Count < lim && basis.IsIndependent(cycle))
{
basis.Add(cycle);
}
}
}
public virtual void Independence()
{
var c1 = new Mock <Cycle>((InitialCycles)null, (ShortestPaths)null, (int[])null);
var c2 = new Mock <Cycle>((InitialCycles)null, (ShortestPaths)null, (int[])null);
var c3 = new Mock <Cycle>((InitialCycles)null, (ShortestPaths)null, (int[])null);
c1.SetupGet(c => c.EdgeVector).Returns(BitArrays.FromString("111000000000"));
c2.SetupGet(c => c.EdgeVector).Returns(BitArrays.FromString("000111000000"));
c3.SetupGet(c => c.EdgeVector).Returns(BitArrays.FromString("111111000000"));
c1.SetupGet(c => c.Length).Returns(3);
c2.SetupGet(c => c.Length).Returns(3);
c3.SetupGet(c => c.Length).Returns(6);
var basis = new GreedyBasis(3, 12);
Assert.IsTrue(basis.IsIndependent(c1.Object));
Assert.IsTrue(basis.IsIndependent(c2.Object));
Assert.IsTrue(basis.IsIndependent(c3.Object));
basis.Add(c1.Object);
Assert.IsTrue(basis.IsIndependent(c2.Object));
Assert.IsTrue(basis.IsIndependent(c2.Object));
basis.Add(c2.Object);
Assert.IsFalse(basis.IsIndependent(c3.Object));
}
