The name is absent

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• it contains every branch of the cell

• all routes are non-intersecting (i.e., no branch appears in more than one route)

• it contains the fewest routes possible,

and we denote an optimal set of routes by 7£. After a little thought, we can conclude
that we can build an optimal set of routes entirely of routes which begin with leaves.
Thus we know that if there are L leaves in a cell, then we need to store only L routes,
and hence dim(7?.) = L. Thus the smaller the ratio of L/В the better this method
should be. It also follows that every TZ contains at least one R such that dim(R) = 1.
Algorithm 3 implements Branch-Ortho with a set of optimal routes, which is obtained
by proceeding outside-in from leaves to soma.

3.3.2.3 V-Slim: A Snapshot Elimination Algorithm

In order to implement the Branch-Ortho algorithm in any generality, we must
ensure that the snapshot set does not become so large that computing the SVDs
of the POD and DEIM inner product matrices becomes prohibitively slow. Since
the SVD scales as O(max(n, A)³), taking more snapshots will dramatically increase
the computation time to obtain the reduced bases. For small numbers of snapshots
(dim(<S) < 1000) this may not be so bad, but if Branch-Ortho generates many thou-
sands of snapshots (as may be the case for highly-branched cells) then the SVD step
may become prohibitively slow.

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