- 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
Graph-Theoretic and Linear Algebra Formulations
Graph-Theoretic and Linear Algebra Formulations
- Chapter:
- (p.83) 6 Graph-Theoretic and Linear Algebra Formulations
- Source:
- Combinatorics of Genome Rearrangements
- Author(s):
Guillaume Fertin
Anthony Labarre
Irena Rusu
Eric Tannier
Steéphane Vialette
- Publisher:
- The MIT Press
This chapter demonstrates the expansion of genome rearrangement problems to a wide mathematical field, including long-standing problems in algebra. It discusses simple permutations and the interleaving graph; the overlap graph; the local complementation of a graph; the matrix tightness problem; extension to sorting by transpositions; and the intermediate case of directed local complementation.
Keywords: genome rearrangement problems, permutations, interleaving graph, overlap graph, matrix tightness, transpositions, directed local complementation
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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
