Geodesic
Algorithms for Finding Proper Essential Surfaces in 3-Manifolds
Matematičeskie zametki, Tome 82 (2007) no. 4, pp. 593-597.

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In this paper, we present an algorithm which, for a given compact orientable irreducible boundary irreducible 3-manifold $M$, verifies whether $M$ contains an essential orientable surface (possibly, with boundary), whose genus is at most $N$. The algorithm is based on Haken's theory of normal surfaces, and on a trick suggested by Jaco and consisting in estimating the mean length of boundary curves in an unknown essential surface of a given genus in the given manifold.
Keywords: irreducible 3-manifold, essential surface, boundary irreducible manifold, Euler characteristic
Mots-clés : triangulation. 
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E. A. Sbrodova. Algorithms for Finding Proper Essential Surfaces in 3-Manifolds. Matematičeskie zametki, Tome 82 (2007) no. 4, pp. 593-597. http://geodesic.mathdoc.fr/item/MZM_2007_82_4_a13/

[1] W. Haken, “Theorie der Normalflächen”, Acta Math., 105:3–4 (1961), 245–375 | DOI | MR | Zbl

[2] W. Jaco, U. Oertel, “An algorithm to decide if a $3$-manifold is a Haken manifold”, Topology, 23:2 (1984), 195–209 | DOI | MR | Zbl

[3] S. Matveev, Algorithmic Topology and Classification of $3$-Manifolds, Algorithms and Computation in Mathematics, 9, Springer-Verlag, Berlin, 2003 | MR | Zbl

[4] W. Jaco, J. H. Rubinstein, E. Sedgwick, Finding planar surfaces in knot- and link-manifolds, arXiv: math.GT/0608700

[5] E. A. Sbrodova, “Ploskie poverkhnosti v trekhmernykh mnogoobraziyakh”, Sib. elektron. matem. izv., 3 (2006), 451–463 | Zbl