Consequently, assuming intersection and symmetric difference as primitive operations, the union of two sets can be well " defined " in terms of symmetric difference by the right-hand side of the equality
22.
Consequently, assuming intersection and symmetric difference as primitive operations, the union of two sets can be well " defined " in terms of symmetric difference by the right-hand side of the equality
23.
However, the symmetric difference of the eventual optimal matching and of the partial matching " M " found by the initial phases forms a collection of vertex-disjoint augmenting paths and alternating cycles.
24.
The Ford Fulkerson algorithm finds it by repeatedly finding an augmenting path from some to some and updating the matching M by taking the symmetric difference of that path with M ( assuming such a path exists ).
25.
An alternate interpretation of the Jaccard distance is as the ratio of the size of the symmetric difference A \ triangle B = ( A \ cup B )-( A \ cap B ) to the union.
26.
If M is a matching, and P is an augmenting path relative to M, then the symmetric difference of the two sets of edges, M \ oplus P, would form a matching with size | M | + 1.
27.
A measure can be extended to a complete one by considering the ?-algebra of subsets which differ by a negligible set from a measurable set, that is, such that the symmetric difference of and is contained in a null set.
28.
The power set of any set becomes an abelian group under the operation of symmetric difference, with the empty set as the neutral element of the group and every element in this group being its own intersection as the multiplication of the ring.
29.
As the symmetric difference of " I " with any augmenting path gives a larger independent set, the task thus reduces to searching for augmenting paths until no more can be found, analogously as in algorithms for finding maximum matchings.
30.
The set of all even subgraphs of a graph is closed under symmetric difference, and may thus be viewed as a vector space over GF ( 2 ); this vector space is called the " cycle space " of the graph.
