Geodesic
Isoperimetry in integer lattices
Discrete analysis (2018) Cet article a éte moissonné depuis la source Scholastica

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The edge isoperimetric problem for a graph $G$ is to determine, for each $n$, the minimum number of edges leaving any set of $n$ vertices. In general this problem is NP-hard, but exact solutions are known in some special cases, for example when $G$ is the usual integer lattice. We solve the edge isoperimetric problem asymptotically for every Cayley graph on $\mathbb Z^d$. The near-optimal shapes that we exhibit are zonotopes generated by line segments corresponding to the generators of the Cayley graph.
Publié le : 
@article{DAS_2018_a14,
     author = {Ben Barber and Joshua Erde},
     title = {Isoperimetry in integer lattices},
     journal = {Discrete analysis},
     year = {2018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DAS_2018_a14/}
}
TY  - JOUR
AU  - Ben Barber
AU  - Joshua Erde
TI  - Isoperimetry in integer lattices
JO  - Discrete analysis
PY  - 2018
UR  - http://geodesic.mathdoc.fr/item/DAS_2018_a14/
LA  - en
ID  - DAS_2018_a14
ER  - 
%0 Journal Article
%A Ben Barber
%A Joshua Erde
%T Isoperimetry in integer lattices
%J Discrete analysis
%D 2018
%U http://geodesic.mathdoc.fr/item/DAS_2018_a14/
%G en
%F DAS_2018_a14
Ben Barber; Joshua Erde. Isoperimetry in integer lattices. Discrete analysis (2018). http://geodesic.mathdoc.fr/item/DAS_2018_a14/