For instance, we consider the case when (w_1 in E^*_{j}), (w_2 in E^*_{k}) and (w_3in E^*_l) for distinct j, k, l.
If we consider the on-demand instance model, designed for users not paying a yearly subscription, each instance costs $2.4 per hour, which is $1,728 for a month and more than $20,000 for a year.
We consider the following special instance ( G 1 ′, G 2 ′ ) of the problem CHORDAL- ( k+1,ℓ )-SP obtained from (G1,G2), an instance of the NP-complete problem CHORDAL- ( k,ℓ )-SP, such that there is a (k,ℓ -chordal sandwich graph G for (G1,ℓ -chordal only if there isandwich,ℓ)-chordal sandwich graph G′, k,ℓ>0 and k+ℓ ≥ 3, for ( G1,G2, G 2 ′ ).
We consider the following special instance ( G 1 ′, G 2 ′ ) of STRONGLY CHORDAL- ( k,1 -SP obtained from (G1,1 -SP a cobtainednstance ofrome NP-complete problem CHORDAL BIPARTITE-SP[6], such that there is a chordal bipartite sandwich G1aph G2(V,E) for (G1,G2) if and only if there is a strongly connect- (k,1) sandwinstanceh G′, k ≥ 1 fof ( G 1 ′, G 2 ′ ).
We consider the following special instance ( G 1 ′, G 2 ′ ) of STRONGLY CHORDAL- ( k,ℓ +1 -SP obtained from (G1, G2), an instance of the NP-complete problem STRONGLY CHORDAL- ( k,ℓ )-SP, such that there is a strongly chordal- (k,ℓ) sandwich graph G for (G1,G2) if and only if there is a strongly chordal- (k,ℓ+1 -SPndwich graph G′, k ≥ 1, ℓ ≥ 1, fobtained ′, G 2 ′ ).
Given an instance of the Steiner tree problem together with an optimal solution, we consider the scenario where this instance is modified locally by adding one of the vertices to the terminal set or removing one vertex from it.
As an instance we consider the following Ky Fan best approximation theorem.
For instance, we consider the prior probability of each base for the calculation of the positional weight and information content.
In the first instance, we consider the context free grammar complexity introduced by Jiménez-Montaño [ 60] (a description is given in Appendix One).
More precisely, if, for instance, we consider the Robinson-Foulds distance on phylogenetic trees [ 29], it is evident that the NCBI taxonomy tree shares four of its five clusters with the phylogenetic tree derived by using MP-Align.
