We represented each compound by an integer vector of length 53 679 in which the occurrence of a substructure is coded as an integer value.
Given a graph G= V,E) with edge costs and an integer vector r∈Z+V associated with the nodes of V, the survivable network design problem is to find a minimum cost subgraph of G such that between every pair of nodes s,t of V, there are at least min{r(s),r(t)} edge-disjoint paths.
where c ̲ is an integer vector with 1, − 1 entries, and 1 K is an all-one column vector of length K.
expected_dims an integer vector of expected dimension.
dims an integer vector of dimensions.
On the other hand, vector b, defined in (48), is an integer vector.
The NS-descriptor is an integer vector, and the other fingerprints are binary vectors.
where p = α 1, …, α K T P = diag P 1 ( R ), …, P K ( R ) A s = ∑ m = 1 M P m ( S ) a s ( m ) ∗ a s ( m ) T A n = diag a n ∗ ⊙ a n a s ( m ) = β 1 h m ( 1 ) g 1, …, β K h m ( K ) g K T, and a n ( m ) = β 1 g 1, …, β K g K T. Further, note that p is a real integer vector with 0, 1 entries, A s is a Hermitian matrix, and A n is a real-valued matrix.
m-Orientation Sandwich ProblemInstance: Given undirected graphs G1= V,E1) and G2= V,E2) with E1⊆E2 and a non-negative integer vector m on V. Question: Does there exist a sandwich graph G= V,E) (E1⊆E⊆E2) that has an orientation (vec{G}) whose in-degree vector is m that is (d^_{vec{G}} v =m v)) for all v∈V?
Directed Degree Constrained Sandwich ProblemInstance: Given directed graphs D1= V,A1) and D2= V,A2) with A1⊆A2 and a non-negative integer vector f on V. Question: Does there exist a sandwich graph D= V,A) (A1⊆A⊆A2) such that (d^_{D} v =f v)) for all v∈V?
Undirected Degree Constrained Sandwich ProblemInstance: Given undirected graphs G1= V,E1) and G2= V,E2) with E1⊆E2 and a non-negative integer vector f on V. Question: Does there exist a sandwich graph G= V,E) (E1⊆E⊆E2) such that d G (v =f v) for all v∈V?
