TY - GEN
T1 - Tree reconstruction from partial orders
AU - Kannan, Sampath
AU - Warnow, Tandy
N1 - Funding Information:
However, for many applications, the actual numeric data is quite unreliable (see \[4, 6\] for discussions of how interspecies distances are derived in computational molecular biology and why the data is unreliable). One way of handling * Supported in part by NSF Grant CCR9108969 *~ This work began when this author was visiting DIMACS, and was supported in part by DOE contract number DE-AC04-76DP00789.
Publisher Copyright:
© Springer-Verlag Berlin Heidelberg 1993.
PY - 1993
Y1 - 1993
N2 - The problem of constructing trees given a matrix of interleaf distances is motivated by applications in computational evolutionary biology and linguistics. The general problem is to find an edge-weighted tree which most closely approximates (under some norm) the distance matrix. Although the construction problem is easy when the tree exactly fits the distance matrix, optimization problems under all popular criteria are either known or conjectured to be NP-complete. In this paper we consider the related problem where we are given a partial order on the pairwise distances, and wish to construct (if possible) an edge-weighted tree realizing the partial order. In particular we are interested in partial orders which arise from experiments on triples of species. We will show that the consistency problem is NP-hard in general, but that for certain special cases the construction problem can be solved in polynomial time.
AB - The problem of constructing trees given a matrix of interleaf distances is motivated by applications in computational evolutionary biology and linguistics. The general problem is to find an edge-weighted tree which most closely approximates (under some norm) the distance matrix. Although the construction problem is easy when the tree exactly fits the distance matrix, optimization problems under all popular criteria are either known or conjectured to be NP-complete. In this paper we consider the related problem where we are given a partial order on the pairwise distances, and wish to construct (if possible) an edge-weighted tree realizing the partial order. In particular we are interested in partial orders which arise from experiments on triples of species. We will show that the consistency problem is NP-hard in general, but that for certain special cases the construction problem can be solved in polynomial time.
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U2 - 10.1007/3-540-57155-8_265
DO - 10.1007/3-540-57155-8_265
M3 - Conference contribution
AN - SCOPUS:85029502449
SN - 9783540571551
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 397
EP - 408
BT - Algorithms and Data Structures - 3rd Workshop, WADS 1993, Proceedings
A2 - Dehne, Frank
A2 - Sack, Jorg-Rudiger
A2 - Santoro, Nicola
A2 - Whitesides, Sue
PB - Springer
T2 - 3rd Workshop on Algorithms and Data Structures, WADS 1993
Y2 - 11 August 1993 through 13 August 1993
ER -