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Mining Induced/Embedded Subtrees using the Level of Embedding Constraint

Tan H., Hadzic F., Dillon T. S.

Fundamenta Informaticae

2012

Vol. 119, nr 2

187-231

The increasing need for representing information through more complex structures where semantics and relationships among data objects can be more easily expressed has resulted in many semi-structured data sources. Structure comparison among semi-structured data objects can often reveal valuable information, and hence tree mining has gained a considerable amount of interest in areas such as XML mining, Bioinformatics, Web mining etc. We are primarily concerned with the task of mining frequent ordered induced and embedded subtrees from a database of rooted ordered labeled trees. Our previous contributions consist of the efficient Tree Model Guided (TMG) candidate enumeration approach for which we developed a mathematical model that provides an estimate of the worst case complexity for embedded subtree mining. This potentially reveals computationally impractical situations where one would be forced to constrain the mining process in some way so that at least some patterns can be discovered. This motivated our strategy of tackling the complexity of mining embedded subtrees by introducing the Level of Embedding constraint. Thus, when it is too costly to mine all frequent embedded subtrees, one can decrease the level of embedding constraint gradually down to 1, from which all the obtained frequent subtrees are induced subtrees. In this paper we develop alternative implementations and propose two algorithms MB3-R and iMB3-R, which achieve better efficiency in terms of time and space. Furthermore, we develop a mathematical model for estimating the worst case complexity for induced subtree mining. It is accompanied with a theoretical analysis of induced-embedded subtree relationships in terms of complexity for frequent subtree mining. Using synthetic and real world data we practically demonstrate the space and time efficiency of our new approach and provide some comparisons to the two well know algorithms for mining induced and embedded subtrees.

Proton Abstraction from 4-Nitrophenyl[bis(ethylsulphonyl)]methane with TMG, TBD and MTBD Bases in Acetonitrile

Jarczewski A., Binkowska I.

Polish Journal of Chemistry

2001

Vol. 75, nr 12

1895-1903

4-Nitrophenyl[bis(ethylsulphonyl)]methane has been synthesized and used in kinetic studies of proton abstraction induced by 1,1,3,3-tetramethylguanidine (TMG), 1,5,7-triazabicyclo[4.4.0]dec-5-ene (TBD) and 7-methyI-1,5,7-triazabicyclo[4.4.0]dec-5-ene (MTBD) bases in acetonitrile. The pK, values of this carbon acid in water and in acetonitrile solvents are 10.08 and 22.8 respectively. The electronic spectra of 4-nitrophenyl[bis(ethylsulphonyl)]methane and its anion ar well defined and temperaturę dependent. The rates of proton abstraction are large as the reaction occurs in the range of microseconds. The relaxation times were studied by spectrophotometric temperature-jump technique. The rate constants for proton transfer reaction promoted by TMG, TBD and MTBD bases in acetonitrile are: 1.39x10 5-2.1 Ix10 5; 8.8x10 6-19.2x10 6; 0.84x105-2.43x 10S [dm3 mol-1 s-1] respectively between 20-40°C. The enthalpies of activation are: deltaH# = 18.1, 28.7 and 40.0 [kJ mol-1] for TMG, TBD and MTBD respectively. The entropies of activation are all negative: deltaS# = -84.9, -13.6, -14.3 [J mol-1 deg-1] for the same sequence of bases reacting with 4-nitrophenyl[bis(ethylsulphonyl)]methane in acetonitrile solvent. The general discussion of the results obtained and their comparison with those for proton transfer reaction carried out with "normal" C-acids is given.