A 6-Approximation Algorithm for Computing Smallest Common AoN-Supertree with Application to the Reconstruction of Glycan Trees

  • Kiyoko F. Aoki-Kinoshita
  • Minoru Kanehisa
  • Ming-Yang Kao
  • Xiang-Yang Li
  • Weizhao Wang
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4288)


A node-labeled rooted tree T (with root r) is an all-or-nothing subtree (called AoN-subtree) of a node-labeled rooted tree T′ if (1) T is a subtree of the tree rooted at some node u (with the same label as r) of T′, (2) for each internal node v of T, all the neighbors of v in T′ are the neighbors of v in T. Tree T′ is then called an AoN-supertree of T. Given a set \({\mathcal {T}}=\{{T}_1,{T}_2,\cdots, {T}_n\}\) of nnode-labeled rooted trees, smallest common AoN-supertree problem seeks the smallest possible node-labeled rooted tree (denoted as \({\textbf{LCST}}\)) such that every tree T i in \({\mathcal {T}}\) is an AoN-subtree of \({\textbf{LCST}}\). It generalizes the smallest superstring problem and it has applications in glycobiology. We present a polynomial-time greedy algorithm with approximation ratio 6.


Leaf Node Internal Node Approximation Ratio Child Node Glycan Structure 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Kiyoko F. Aoki-Kinoshita
    • 1
  • Minoru Kanehisa
    • 2
  • Ming-Yang Kao
    • 3
  • Xiang-Yang Li
    • 4
  • Weizhao Wang
    • 4
  1. 1.Dept. of BioinformaticsFac. of Engineering, Soka University 
  2. 2.Bioinformatics Center, Institute for Chemical ResearchKyoto University, and Human Genome Center, Institute of Medical Science, University of Tokyo 
  3. 3.Dept. of Electrical Engineering and Computer ScienceNorthwestern University 
  4. 4.Dept. of Computer ScienceIllinois Institute of Technology 

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