The Graph Isomorphism Problem

Fortin, Scott

doi:10.7939/r3sx64c5k

Cited by 31 publications

(1 citation statement)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…LEs are equivalent if their graph representations are isomorphic. This is, in general, a problem in its own complexity class GI ∈ NP which is not known to be in either P or NP-complete [52]. Fortunately, there exists implementations such as the nauty 2 software [53] which can solve this problem in polynomial time for many graphs.…”

Section: Norm-basedmentioning

confidence: 99%

Accelerating off-lattice kinetic Monte Carlo simulations to predict hydrogen vacancy-cluster interactions in $α$-Fe

Williams¹,

Galindo-Nava²

2022

Preprint

View full text Add to dashboard Cite

We present an enhanced off-lattice kinetic Monte Carlo (OLKMC) model, based on a new method for tolerant classification of atomistic local-environments that is invariant under Euclidean-transformations and permutations of atoms. Our method ensures that environments within a norm-based tolerance are classified as equivalent. During OLKMC simulations, our method guarantees to elide the maximum number of redundant saddle-point searches in symmetrically equivalent local-environments. Hence, we are able to study the trapping/detrapping of hydrogen from up to five-vacancy clusters and simultaneously the effect hydrogen has on the diffusivity of these clusters. These processes occur at vastly different timescales at room temperature in body-centred cubic iron. We are able to predict the diffusion pathways of clusters/complexes without a priori assumptions of their mechanisms, not only reproducing previously reported mechanisms but also discovering new ones for larger complexes. We detail the hydrogen-induced changes in the clusters' diffusion mechanisms and find evidence that, in contrast to mono-vacancies, the introduction of hydrogen to larger clusters can increase their diffusivity. We compare the effective hydrogen diffusivity to Oriani's classical theory of trapping, finding general agreement and some evidence that hydrogen may not always be in equilibrium with traps, when the traps are mobile. Finally, we are able to compute the trapping atmosphere of meta-stable states surrounding non-point traps, opening new avenues to better understand and predict hydrogen embrittlement in complex alloys.

show abstract

Section: Norm-basedmentioning

confidence: 99%

Accelerating off-lattice kinetic Monte Carlo simulations to predict hydrogen vacancy-cluster interactions in $α$-Fe

Williams¹,

Galindo-Nava²

2022

Preprint

View full text Add to dashboard Cite

show abstract

Untitled

Bustince

Barrenechea

Pagola

2008

Int. J. Intell. Syst.

View full text Add to dashboard Cite

On the Complexity of Polytope Isomorphism Problems

Kaibel

Schwartz

2003

Graphs and Combinatorics

View full text Add to dashboard Cite

We show that the problem to decide whether two (convex) polytopes, given by their vertex-facet incidences, are combinatorially isomorphic is graph isomorphism complete, even for simple or simplicial polytopes. On the other hand, we give a polynomial time algorithm for the combinatorial polytope isomorphism problem in bounded dimensions. Furthermore, we derive that the problems to decide whether two polytopes, given either by vertex or by facet descriptions, are projectively or affinely isomorphic are graph isomorphism hard. MSC 2000: 52B05, 05C60, 52B11, 68R10 ⋆ Supported by a DFG Gerhard-Hess-Forschungsförderungspreis donated to Günter M. Ziegler (Zi 475/2-3).

show abstract

The Graph Isomorphism Problem

Cited by 31 publications

References 0 publications

Accelerating off-lattice kinetic Monte Carlo simulations to predict hydrogen vacancy-cluster interactions in $α$-Fe

Accelerating off-lattice kinetic Monte Carlo simulations to predict hydrogen vacancy-cluster interactions in $α$-Fe

Untitled

On the Complexity of Polytope Isomorphism Problems

Contact Info

Product

Resources

About