- Title Pages
- Preface
- Acknowledgments
-
1 Introduction -
2 Genomes as Permutations -
3 Distances between Unsigned Permutations -
4 Distances between Signed Permutations -
5 Rearrangements of Partial Orders -
6 Graph-Theoretic and Linear Algebra Formulations -
7 Generalities -
8 Distances between Arbitrary Strings -
9 Distances between Balanced Strings -
III Multichromosomal Models -
10 Paths and Cycles -
11 Cycles of a Permutation -
12 Set Systems and the Syntenic Distance -
IV Multigenomic Models -
13 Median and Halving Problems -
14 Rearrangement Phylogenies -
15 Software -
16 Open Problems -
A Graph Theory -
B Complexity Theory - [UNTITLED]
- Glossary
- Bibliography
- Index
Rearrangements of Partial Orders
Rearrangements of Partial Orders
- Chapter:
- (p.75) 5 Rearrangements of Partial Orders
- Source:
- Combinatorics of Genome Rearrangements
- Author(s):
Guillaume Fertin
Anthony Labarre
Irena Rusu
Eric Tannier
Steéphane Vialette
- Publisher:
- The MIT Press
Zheng et al. introduced a new representation of a genome in terms of a partially ordered set (often abbreviated as “poset”). In this model, any linear extension of a poset represents a possible total order of the genome. In the context of posets, a genome rearrangement problem is to find a linear extension in each poset such that a criterion (number of reversals, number of breakpoints, etc.) is optimized. This chapter focuses on handling rearrangements of gene partial orders.
Keywords: genome rearrangement, partially ordered sets, posets, linear extension
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- Title Pages
- Preface
- Acknowledgments
-
1 Introduction -
2 Genomes as Permutations -
3 Distances between Unsigned Permutations -
4 Distances between Signed Permutations -
5 Rearrangements of Partial Orders -
6 Graph-Theoretic and Linear Algebra Formulations -
7 Generalities -
8 Distances between Arbitrary Strings -
9 Distances between Balanced Strings -
III Multichromosomal Models -
10 Paths and Cycles -
11 Cycles of a Permutation -
12 Set Systems and the Syntenic Distance -
IV Multigenomic Models -
13 Median and Halving Problems -
14 Rearrangement Phylogenies -
15 Software -
16 Open Problems -
A Graph Theory -
B Complexity Theory - [UNTITLED]
- Glossary
- Bibliography
- Index
