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A Constructive Enumeration of Fullerenes
"... In this paper, a fast and complete method to enumerate fullerene structures is given. It is based on a topdown approach, and it is fast enough to generate, for example, all 1812 isomers of C 60 in less than 20 seconds on an SGIworkstation. The method described can easily be generalised for 3regul ..."
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In this paper, a fast and complete method to enumerate fullerene structures is given. It is based on a topdown approach, and it is fast enough to generate, for example, all 1812 isomers of C 60 in less than 20 seconds on an SGIworkstation. The method described can easily be generalised for 3regular spherical maps with no face having more than 6 edges in its boundary.
The generation of fullerenes
 J. Chem. Inf. Model
"... We describe an efficient new algorithm for the generation of fullerenes. Our implementation of this algorithm is more than 3.5 times faster than the previously fastest generator for fullerenes – fullgen – and the first program since fullgen to be useful for more than 100 vertices. We also note a pro ..."
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Cited by 3 (0 self)
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We describe an efficient new algorithm for the generation of fullerenes. Our implementation of this algorithm is more than 3.5 times faster than the previously fastest generator for fullerenes – fullgen – and the first program since fullgen to be useful for more than 100 vertices. We also note a programming error in fullgen that caused problems for 136 or more vertices. We tabulate the numbers of fullerenes and IPR fullerenes up to 400 vertices. We also check up to 316 vertices a conjecture of Barnette that cubic planar graphs with maximum face size 6 are hamiltonian and verify that the smallest counterexample to the spiral conjecture has 380 vertices. Note: this is the unedited version of our paper which was submitted and subsequently accepted for publication in Journal of Chemical Information and Modeling. The final edited and published version can be accessed at
Two Applications of the Divide&Conquer Principle in the Molecular Sciences
"... In this note, two problems from the molecular sciences are addressed: the enumeration of fullerenetype isomers and the alignment of biosequences. We report on two algorithms dealing with these problems both of which are based on the wellknown and widely used Divide&Conquer principle. In oth ..."
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In this note, two problems from the molecular sciences are addressed: the enumeration of fullerenetype isomers and the alignment of biosequences. We report on two algorithms dealing with these problems both of which are based on the wellknown and widely used Divide&Conquer principle. In other words, our algorithms attack the original problems by associating with them an appropriate number of much simpler problems whose solutions can be \glued together " to yield solutions of the original, rather complex tasks. The considerable improvements achieved this way exemplify that the present day molecular sciences oer many worthwhile opportunities for the eective use of fundamental algorithmic principles and architectures. 3 1
Two Applications of the Divide & Conquer Principle in the Molecular Sciences
, 1997
"... In this note, two problems from the molecular sciences are addressed: the enumeration of fullerenetype isomers and the alignment of biosequences. We report on two algorithms dealing with these problems both of which are based on the wellknown and widely used Divide &Conquer principle. In o ..."
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In this note, two problems from the molecular sciences are addressed: the enumeration of fullerenetype isomers and the alignment of biosequences. We report on two algorithms dealing with these problems both of which are based on the wellknown and widely used Divide &Conquer principle. In other words, our algorithms attack the original problems by associating with them an appropriate number of much simpler problems whose solutions can be "glued together" to yield solutions of the original, rather complex tasks. The considerable improvements achieved this way exemplify that the present day molecular sciences offer many worthwhile opportunities for the effective use of fundamental algorithmic principles and architectures. 3 1 Introduction One of the most powerful principles for solving complex tasks algorithmically is the socalled Divide&Conquer Principle. It has been applied successfully for an amazingly wide range of problems, from combinatorial optimization to matrix mu...