Finding all sorting tandem duplication random loss operations

Matthias Bernt*, Kuan Yu Chen, Ming Chiang Chen, An Chiang Chu, Daniel Merkle, Hung Lung Wang, Kun Mao Chao, Martin Middendorf

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

15 Citations (Scopus)


A tandem duplication random loss (TDRL) operation duplicates a contiguous segment of genes, followed by the random loss of one copy of each of the duplicated genes. Although the importance of this operation is founded by several recent biological studies, it has been investigated only rarely from a theoretical point of view. Of particular interest are sorting TDRLs which are TDRLs that, when applied to a permutation representing a genome, reduce the distance towards another given permutation. The identification of sorting genome rearrangement operations in general is a key ingredient of many algorithms for reconstructing the evolutionary history of a set of species. In this paper we present methods to compute all sorting TDRLs for two given gene orders. In addition, a closed formula for the number of sorting TDRLs is derived and further properties of sorting TDRLs are investigated. It is also shown that the theoretical findings are useful for identifying unique sorting TDRL scenarios for mitochondrial gene orders.

Original languageEnglish
Pages (from-to)32-48
Number of pages17
JournalJournal of Discrete Algorithms
Issue number1
Publication statusPublished - 2011 Mar
Externally publishedYes


  • Genome rearrangement
  • Permutation
  • TDRL
  • Tandem duplication random loss

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics


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