Tree searching

In the worst case, the backtracking algorithm will form a search tree of depth n, where n is the number of atoms in the query graph. Also, in this case a separate sub-tree search process for each atom of the target graph will be initiated. That is why the linear multiplier m is apphed to Eq. (7). 

Kumar, V., and Kanal, L.N., A general branch and bound formulation for understanding and synthesizing and/or tree search procedures. Art. Intell. 21 179-198 (1983). 

Lipton, M Still, W. C. The multiple minimum problem in molecular modeling. Tree searching internal coordinate conformational space. J. Comp. Chem. 1988, 9, 343-355. 

Floquet et al. (1985) proposed a tree searching algorithm in order to synthesize chemical processes involving reactor/separator/recycle systems interlinked with recycle streams. The reactor network of this approach is restricted to a single isothermal CSTR or PFR unit, and the separation units are considered to be simple distillation columns. The conversion of reactants into products, the temperature of the reactor, as well as the reflux ratio of the distillation columns were treated as parameters. Once the values of the parameters have been specified, the composition of the outlet stream of the reactor can be estimated and application of the tree searching algorithm on the alternative separation tasks provides the less costly distillation sequence. The problem is solved for several values of the parameters and conclusions are drawn for different regions of operation. 

R. J. Dakin. A tree search algorithm for mixed integer programming problems. Computer J., 8 250,1965. 

P. Floquet, L. Pibouleau, and S. Domenech. Reactor separator sequences synthesis by a tree searching algorithm. Process System Engineering, Symp. Series, 92 415, 1985. 

T. K. Pho and L. Lapidus. Topics in computer-aided design Part II. Synthesis of optimal heat exchanger networks by tree searching algorithms. AlChEJ., 19 1182,1973. 

Fig. 4.6 (a) Feature Tree search result based on query (left) retrieves a high ranked (rank 5) active compound with low 2D similarity. The corresponding feature trees are also... 

STS (Synthesis Tree Search) Infochem 158 http //www.infochem.de/en/company/ index.shtml... 

To solve a problem of this first class is to perform a tree search. Ponton and Donaldson use heuristics to select each next match and find only one solution, often a good one but not always. Pho and Lapidus propose a total enumeration scheme, but, for very large problems (10 streams), suggest a fallible lookahead strategy to eliminate branches. Lee, Masso and Rudd,... 

Pho, T.K. and Lapidus, L., "Topics in Computer-Aided Design Part II. Synthesis of Optimal Heat Exchanger Networks by Tree Search Algorithms," AlChE Journal, Vol. 19, No. 6, pp 1182-1189, November 1973. 

Thus ligands are often incrementally built within the active site. The principle of the FlexX algorithm is that, physicochemical properties provide the most useful information for ligand placement. Once a set of favorable placement of the base fragment (the core part of the ligand from where the incremental construction starts) has been computed, the ligand building can be started. The incremental construction is formulated as a tree search (Fig. 14) problem. 

The BB method (Gupta and Ravindran, 1985 Nabar and Schrage, 1991 Borchers and Mitchell, 1992) starts by solving first the continuous NLP relaxation. If all discrete variables take discrete values, the search is stopped. Otherwise, it performs a tree search in the space of the integer variables y/, i G /,... 

Approach of Text Problem Spaces Tree Searches Control Knowledge Overview the Principle of Electron Flow Nucleophiles Electrophiles... 

Figure 1.1 A generic problem space and some strategies for tree searches in the problem space.

When generating a class of integrals with non-trivial angular momentum, there are usually very many sequences in which (67) can be applied and the task of determining the most efficient sequence can be discussed as a tree-search problem. OS did not provide a solution to this problem however and, as such, the OS algorithm is not completely well-defined. 

As a general rule, the construction of the [mOInO] using the VRR is considerably more expensive than the subsequent contraction and HRR steps. However, if one is dealing with integral classes of high angular momentum and low contraction or with derivatives of such classes with respect to nuclear motion, the HRR step can become sufficiently expensive to warrant optimization and Ryu, Lee and Lindh [59b] have recently studied this problem. Recognizing that efficient application of the HRR involves a complicated tree-search problem, they devised a heuristic solution which eliminates 13%, 25%, 38% and 44%, respectively, of the Flops which previous HRR implementations had needed for (fflff), (gg gg), (hh hh) and (ii ii) classes. 

At first glance, there is not much more that can be said about this transformation. The RR (70) is extremely simple and is easy to use and it might appear that our analysis can probe no further. However, as Ryu, Lee and Lindh have shown [59b], if one wishes to apply (70) in a way that minimizes the number of Flops involved, a complicated tree-search problem must first be solved. These authors were unable to solve the general problem but gave heuristic solutions which clearly indicated that substantial savings were available. However, this is not the approach which is followed in the HGP-PRISM algorithm... 

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. 

If no noncriticized conformation can be found, the least criticized suggestions are chosen for further refinement. Another tree search is performed to look for conformational units that can be deformed to solve the problem (i.e., changing one torsional angle in an acyclical unit, or assigning a deformed template to a cyclical unit). 

M. Lipton and W. C. Still,/, Comput. Chem., 9(4), 343 (1988). The Multiple Minimum Problem in Molecular Modeling. Tree Searching Internal Coordinate Conformational Space. 

Quartet puzzling is a relatively rapid tree-searching algorithm available for ML tree building (Strinuner and von Haeseler, 1996) and is available in PUZZLE. 

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