Tree algorithms

The atoms of a molecule can be partitioned into equivalence classes on the basis of a single property or a set of properties. The value of each class for the property(s) will be called the initial canonical value. The set of properties could include the atomic number, predominant in the Cahn-Ingold-Prelog system if this is used to number the atoms of the molecule, or the number of ligand atoms, which is the property 

ACS Symposium Series American Chemical Society Washington, DC, 1977. 

saturated carbon atoms. There are many others, perhaps with the value of 6.1, aromatic carbon atoms or 6.2, doubly bonded carbon atoms, etc. If we further include the number of attached hydrogen atoms we can have the equivalence classes of 

2 and 6.0.1 referring to saturated methylene and methinyl carbon atoms respectively. Adding the ring size we then distinguish the class with the initial canonical value 6.0.2.5 from the class with the initial canonical value 6.0.2.6. 

Different schemes of canonicalization can be distinguished by the properties selected to establish the initial canonical value and whether the ligands of each atom are characterized by a tree of such initial canonical values or the sum of such values obtained by a successive summation process to be detailed later. 

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Our multipole code D-PMTA, the Distributed Parallel Multipole Tree Algorithm, is a message passing code which runs both on workstation clusters and on tightly coupled machines such as the Cray T3D/T3E [11]. Figure 3 shows the parallel performance of D-PMTA on a moderately large simulation on the Cray T3E the scalability is not affected by adding the macroscopic option. 

W. T. Rankin and J. A. Board, Jr., A Portable Distributed Implementation of the Parallel Multipole Tree Algorithm, Proceedings, Fourth IEEE International Symposium on High Performance Distributed Computing, IEEE Computer Society Press (1995), pp. 17-22. 

Rankin, W., Board, J. A portable distributed implementation of the parallel multipole tree algorithm. IEEE Symposium on High Performance Distributed Computing. Duke University Technical Report 95-002. 

The first tree induction algorithm is called ID3 (Iterative Dichotomizer version 3) and was developed by Quinlan [38]. Subsequent improved versions of ID3 are C4.5 and C5. In our study, we used MC4 decision tree algorithm which is available in the MLC++ package [39]. MC4 and C4.5 use the same algorithm with different default parameter settings. 

Descriptor requirements present a significant difference between MP and decision tree methods such as RP. Whereas two-state descriptors are not suitable for MP, these types of descriptors are typically required for decision tree algorithms because at each branch the presence or absence of specific feature(s) must be detected in order to recursively divide a molecular dataset. 

Booth KS, Lueker GS (1976) Testing for the consecutive ones property, interval graphs, and graph planarity using Pff Tree algorithms. J Comput Syst Sci 13 335-379... 

Choose single-tree algorithm or optimality criterion... 

Salzberg, S. (1995). Locating protein coding regions in human DNA using a decision tree algorithm. J ComputBiol 2,473-85. 

MITree-K k-partitioning matrix incision tree algorithm... 

For large message sizes, where the latency term can be ignored, Rabenseifner s algorithm should provide improved performance relative to the binomial tree algorithm, especially when the number of processes is large. 

An all-reduce operation can be performed as an all-to-one reduction followed by a one-to-all broadcast, and, using the binomial tree algorithm for... 

The canonicalization procedure of Professor Ugi s group is a tree algorithm, in which the initial canonical value is composed of the atomic number and the coordination number of the atom. (If one of these two numbers makes the atom unique in the molecule then only the one number is used as the initial canonical value.)... 

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