Journal of Mathematical Biology

, Volume 69, Issue 4, pp 799–816 | Cite as

Counting glycans revisited

Article

Abstract

We present an algorithm for counting glycan topologies of order \(n\) that improves on previously described algorithms by a factor \(n\) in both time and space. More generally, we provide such an algorithm for counting rooted or unrooted \(d\)-ary trees with labels or masses assigned to the vertices, and we give a “recipe” to estimate the asymptotic growth of the resulting sequences. We provide constants for the asymptotic growth of \(d\)-ary trees and labeled quaternary trees (glycan topologies). Finally, we show how a classical result from enumeration theory can be used to count glycan structures where edges are labeled by bond types. Our method also improves time bounds for counting alkanes.

Keywords

Counting glycans Counting chemical structures Counting trees Pólya’s enumeration theorem Algorithms 

Mathematics Subject Classification

92E10 

Supplementary material

285_2013_721_MOESM1_ESM.txt (3 kb)
Supplementary material 1 (txt 2 KB)
285_2013_721_MOESM2_ESM.groovy (2 kb)
Supplementary material 2 (groovy 1 KB)

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Lehrstuhl für BioinformatikFriedrich-Schiller-Universität JenaJenaGermany
  2. 2.Department of Mathematical SciencesStellenbosch UniversityMatielandSouth Africa

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