A 6-approximation algorithm for computing smallest common aon-supertree with application to the reconstruction of glycan trees

Authors:
Kiyoko F. Aoki-Kinoshita;Minoru Kanehisa;Ming-Yang Kao;Xiang-Yang Li;Weizhao Wang
Affiliations:
Dept. of Bioinformatics, Fac. of Engineering, Soka University;Bioinformatics Center, Institute for Chemical Research, Kyoto University, and Human Genome Center, Institute of Medical Science, University of Tokyo;Dept. of Electrical Engineering and Computer Science, Northwestern University;Dept. of Computer Science, Illinois Institute of Technology;Dept. of Computer Science, Illinois Institute of Technology
Venue:
ISAAC'06 Proceedings of the 17th international conference on Algorithms and Computation
Year:
2006

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Abstract

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 Ti 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.