Editing Eulerian path (section)

== Applications ==
Eulerian trails are used in [[bioinformatics]] to reconstruct the [[DNA sequence]] from its fragments.<ref>{{cite journal| last1=Pevzner| first1=Pavel A.| last2=Tang| first2=Haixu| last3=Waterman| first3=Michael S.| year=2001 |title=An Eulerian trail approach to DNA fragment assembly |journal=Proceedings of the National Academy of Sciences of the United States of America |volume=98| pmid=11504945 |issue=17 |pages=9748–9753| pmc=55524 |doi=10.1073/pnas.171285098 | bibcode=2001PNAS...98.9748P| doi-access=free}}</ref> They are also used in [[CMOS]] circuit design to find an optimal [[logic gate]] ordering.<ref>{{cite journal| last1=Roy| first1=Kuntal| year=2007 |title=Optimum Gate Ordering of CMOS Logic Gates Using Euler Path Approach: Some Insights and Explanations |journal=Journal of Computing and Information Technology |volume=15 |issue=1 |pages=85–92|doi=10.2498/cit.1000731 |doi-access=free }}</ref> There are some algorithms for processing [[Tree (graph theory)|tree]]s that rely on an Euler tour of the tree (where each edge is treated as a pair of arcs).<ref>{{cite journal|last1=Tarjan|first1=Robert E.|last2=Vishkin|first2=Uzi|title=An efficient parallel biconnectivity algorithm|journal=SIAM Journal on Computing|date=1985|volume=14|number=4|pages=862–874|doi=10.1137/0214061|citeseerx=10.1.1.465.8898}}</ref><ref>{{cite journal|last1=Berkman|first1=Omer|last2=Vishkin|first2=Uzi|title=Finding level-ancestors in trees|journal=J. Comput. Syst. Sci.|date=Apr 1994|volume=48|issue=2|series=2|pages=214–230|doi=10.1016/S0022-0000(05)80002-9|doi-access=}}</ref> The [[de Bruijn sequence]]s can be constructed as Eulerian trails of [[de Bruijn graph]]s.<ref>{{Cite journal|last=Savage|first=Carla|date=January 1997|title=A Survey of Combinatorial Gray Codes|journal=SIAM Review|volume=39|issue=4|pages=605–629|doi=10.1137/S0036144595295272|issn=0036-1445}}</ref>