TY - GEN

T1 - Using semi-definite programming to enhance supertree resolvability

AU - Moran, Shlomo

AU - Rao, Satish

AU - Snir, Sagi

PY - 2005

Y1 - 2005

N2 - Supertree methods are used to construct a large tree over a large set of taxa, from a set of small trees over overlapping subsets of the complete taxa set. Since accurate reconstruction methods are currently limited to a maximum of few dozens of taxa, the use of a supertree method in order to construct the tree of life is inevitable. Supertree methods are broadly divided according to the input trees: When the input trees are unrooted, the basic reconstruction unit is a quartet tree. In this case, the basic decision problem of whether there exists a tree that agrees with all quartets is NP-complete. On the other hand, when the input trees are rooted, the basic reconstruction unit is a rooted triplet, and the above decision problem has a polynomial time algorithm. However, when there is no tree which agrees with all triplets, it would be desirable to find the tree that agrees with the maximum number of triplets. However, this optimization problem was shown to be NP-hard. Current heuristic approaches perform mincut on a graph representing the triplets inconsistency and return a tree that is guaranteed to satisfy some required properties. In this work we present a different heuristic approach that guarantees the properties provided by the current methods and give experimental evidence that it significantly outperforms currently used methods. This method is based on divide and conquer where we use a semi-definite programming approach in the divide step.

AB - Supertree methods are used to construct a large tree over a large set of taxa, from a set of small trees over overlapping subsets of the complete taxa set. Since accurate reconstruction methods are currently limited to a maximum of few dozens of taxa, the use of a supertree method in order to construct the tree of life is inevitable. Supertree methods are broadly divided according to the input trees: When the input trees are unrooted, the basic reconstruction unit is a quartet tree. In this case, the basic decision problem of whether there exists a tree that agrees with all quartets is NP-complete. On the other hand, when the input trees are rooted, the basic reconstruction unit is a rooted triplet, and the above decision problem has a polynomial time algorithm. However, when there is no tree which agrees with all triplets, it would be desirable to find the tree that agrees with the maximum number of triplets. However, this optimization problem was shown to be NP-hard. Current heuristic approaches perform mincut on a graph representing the triplets inconsistency and return a tree that is guaranteed to satisfy some required properties. In this work we present a different heuristic approach that guarantees the properties provided by the current methods and give experimental evidence that it significantly outperforms currently used methods. This method is based on divide and conquer where we use a semi-definite programming approach in the divide step.

UR - http://www.scopus.com/inward/record.url?scp=33646203435&partnerID=8YFLogxK

U2 - 10.1007/11557067_8

DO - 10.1007/11557067_8

M3 - Conference contribution

AN - SCOPUS:33646203435

SN - 3540290087

SN - 9783540290087

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 89

EP - 103

BT - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

T2 - 5th International Workshop on Algorithms in Bioinformatics, WABI 2005

Y2 - 3 October 2005 through 6 October 2005

ER -