Abstract
We consider the trace reconstruction problem on a tree (TRPT): a binary sequence is broadcast through a tree channel where we allow substitutions, deletions, and insertions; we seek to reconstruct the original sequence from the sequences received at the leaves. The TRPT is motivated by the multiple sequence alignment problem in computational biology. We give a simple recursive procedure giving strong reconstruction guarantees at low mutation rates. To our knowledge, this is the first rigorous trace reconstruction result on a tree in the presence of indels.
Original language | English |
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Pages (from-to) | 3852-3874 |
Number of pages | 23 |
Journal | Stochastic Processes and their Applications |
Volume | 122 |
Issue number | 12 |
DOIs | |
State | Published - Dec 2012 |
Bibliographical note
Funding Information:The second author was supported by a Sloan Foundation Fellowship and NSF CAREER Award CCF-0953960 . The fourth author was supported by NSF grant DMS-1007144 .
Funding
The second author was supported by a Sloan Foundation Fellowship and NSF CAREER Award CCF-0953960 . The fourth author was supported by NSF grant DMS-1007144 .
Funders | Funder number |
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National Science Foundation | 1248176, CCF-0953960, DMS-1007144 |
Alfred P. Sloan Foundation |
Keywords
- Branching processes
- Markov models on trees
- Phylogenetic inference