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## Re: [Help-glpk] Simplex vertex neighborhood

 From: sgerber Subject: Re: [Help-glpk] Simplex vertex neighborhood Date: Fri, 16 Aug 2013 13:50:47 -0400 User-agent: Roundcube Webmail/0.8.2

```Hi Matteo

```
Thank you, this is very helpful. I am really interested in the geometric neighborhood.
```
This sentence is paragraph is a little confusing:

```
```In case of primal degeneracy, instead, you have a (possibly
exponential) n. of different bases B*_1, B*_2, .... associated with a
single vertex x*, and each such basis can produce up to n-m adjacent
vertices, meaning that the total number of adjacent vertices can
explode.  In other words,  if x is vertex geometrically adjacent to
x*, you can still reach x through a single pivot from a CERTAIN basis
B*_k associated with x*, but you have to try all possible such bases
B*_1, B^*_2, ... to find the B*_k that works.
```
```
```
Did you really mean the total number of adjacent vertices cen explode? or the total number of bases representing the neighboring vertices can explode?
```

Thanks
Sam

```