Combinatorial complexity

D similarity search methods are quite well developed. Thus, methods which attempt to find overlapping parts (atoms and functional groups) of the molecular moieties studied were reported first [31]. As discussed above for the case of 2D searching, these methods are of combinatorial complexity. To reduce this complexity some field-based methods have been introduced. In this case, the overlap of the fields of two structures is considered as a similarity measure. 

Lok L, Brent R. Automatic generation of cellular reaction networks with Moleculizer 1.0. Nat. Biotechnol. 2005 23 131-136. Conzelmann H, Saez-Rodriguez J, Sauter T, Kholodenko BN, Gilles ED. A domain-oriented approach to the reduction of combinatorial complexity in signal transduction networks. BMC Bioinformatics 2006 7 34. 

Combinatorial complexity in transcription control results from alternative combinations of monomers that form heterodimeric transcription factors (see Figure 11-23) and from cooperative binding of transcription factors to composite control sites (see Figure 11-24). 

Klamt, S. and Stelling, J. (2002) Combinatorial complexity of pathway analysis in metabolic networks. 

Time-dependent combinatory complexity when a design has many states (FRs, DPs), which are not at equilibrium and change as a function of time (nonequilibrium)... 

Time-dependent combinatorial complexity is a combined result of type I, II, and IV complexities. Time-dependent periodic complexity is a smaller-scale complexity. 

The time-independent imaginary complexity and time-dependent periodic complexity can occur only when we must satisfy many FRs at the same time, whereas the time-independent real complexity and the time-dependent combinatorial complexity can exist regardless of the number of FRs that must be satisfied at the same time. 

There are two types of time-dependent complexity, which are defined as follows (i) the periodic complexity is defined as the complexity that only exists in a finite time period, resulting in a finite and limited number of probable combinations and (ii) the combinatorial complexity is defined as the complexity that increases as a function of time due to a continued expansion in the number of possible combinations with time, which may eventually lead to a chaotic state or a system failure. To reduce combinatorial complexity, we have to devise a means of preventing the system range from moving out of the design range (Suh 2005). 

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