Divide conquer

One of the basic algorithmic techniques, which solves a problem by subdividing it into a usually small set of subproblems, solving those problems and then assembling their solution to a solution of the original problem (Cormen et al., 1990). The subproblems are solved in the same fashion, unless they can be solved directly without further subdivision. In contrast to the tree search described above under —> branch bound, in divide conquer algorithms we need to solve not just one but all subproblems of a problem to solve the problem. The procedure is most effective, if the subdivision is balanced in the sense that all subproblems of the same problem have about equal size. 

Divide conquer algorithms for sequence alignment are described in Chapters 2 of Volume I and Volume II, applications to the analysis of molecular similarity are described in Chapter 6 of Volume II. 

Applications of the Divide Conquer Principle in the Molecular Sciences. 

Our procedure for constructing error-free DNA molecules integrates recursive construction and error correction. It uses Divide Conquer (D C) (16, 23), the quintessential recursive problem-solving technique, to construct long DNA molecules from short oligonucleotides and to then error-correct the resulting molecules until an error-free molecule is obtained. 

Goh, S. K., Gallant, R. T., St-Amant, A., 1998, Towards Linear Scaling for the Fits of the Exchange-Correlation Terms in the LCGTO-DF Method via a Divide-and-Conquer Approach , Int. J. Quant. Chem., 69, 405. 

Yang, W., 1992, Electron Density as the Basic Variable A Divide-and-Conquer Approach to the Ab Initio Computation of Large Molecules , J. Mol. Struct. (Theochem), 255, 461. 

Yang W, Lee T (1995) A density-matrix divide-and-conquer approach for electronic-structure calculations of large molecules. J Chem Phys 103(13) 5674—5678... 

The developments in the implementation of the Kohn-Sham approach, helped also to formulate alternative formalisms aiming at approaching the linear scaling195 218"227. In particular, the divide-and-conquer approach of Yang218 have attracted much attention. 

Yang, W. 1992. Electron Density as the Basic Variable a Divide-and-Conquer Approach... 

Pattern 14.32, Use-case led system specification (p.619) or Pattern 14.33, Recursive decomposition — divide and conquer (p.621). 

Following Pattern 14.34, Make a Context Model with Use-Cases (p.623), separate the different interfaces, one for each external role (or one for each group of roles that always occur together). Alternatively, you may identify the component and its interfaces during Pattern 14.33, Recursive decomposition — divide and conquer (p.621). 

I 7 Molecular Diversity in Lead Discovery From Quantity to Quality Divide and conquer... 

Fig. 7.2 Informative design - asking the right question The most efficient means for a player to guess the correct number from 1 to 16 is a divide and conquer" strategy. However, this requires that the player ask questions in sequence and wait for an answer before asking the next. Informative design asks specific questions so that when they are answered simultaneously, the player is led to the answer. In this example, the questions are compounds either possessing (denoted by 1) or lacking (denoted by 0) a specific pharmacophore. Once the compounds are assayed, a single outcome is found to be consistent with activities and the corresponding pharmacophore is found.

A rational equation has one or more fractions in it — usually with the variable appearing in more than one numerator or denominator. In the Dividing and conquering section, earlier in this chapter, you see how to clear the equation of fractions by multiplying everything by the common denominator. Another type of rational equation is one in which you have two fractions set equal to one another. This is called a proportion. (Refer to Chapter 7 for a full description of what you can do with proportions.) One of the nicest features of proportions is that their cross products are always equal. 

C T T C crosses correspond to divide-and-conquer calculations for the same... 

The electronic coupling of donor and acceptor sites, connected via a t-stack, can either be treated by carrying out a calculation on the complete system or by employing a divide-and-conquer (DC) strategy. With the Hartree-Fock (HF) method or a method based on density functional theory (DFT), full treatment of a d-a system is feasible for relatively small systems. Whereas such calculations can be performed for models consisting of up to about ten WCPs, they are essentially inaccessible even for dimers when one attempts to combine them with MD simulations. Semiempirical quantum chemical methods require considerably less effort than HF or DFT methods also, one can afford application to larger models. However, standard semiempirical methods, e.g., AMI or PM3, considerably underestimate the electronic couplings between r-stacked donor and acceptor sites and, therefore, a special parameterization has to be invoked (see below). 

Obviously, the situation will be more difficult when additional approximations have to be employed, e.g., the divide-and-conquer scheme, an effective Hamiltonian or a perturbation approach. A central open question is which electronic states of the fragments have to be included so that reliable results, as compared with supermolecular calculations, can be provided. In any case, accounting for just one state per base pair will yield only semi-quantitative results. A careful analysis of this point is highly desirable for DNA-related systems. 

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