Given a directed acyclic graph `G`

and a path made up from its set of nodes `N`

, what is the closest approximate match to N, equipped with an intuitive notion of distance?

A path in a directed acyclic graph is essentially a string (that uses the set of nodes as the alphabet), so when comparing paths one can make use of edit distances developed for approximate string matching:

There are many algorithms for approximate string matching:

http://en.wikipedia.org/wiki/Approximate_string_matching

This string matching answers the question when the `G`

itself is also a path.. then we're merely asking to compare two strings.

Asking if an arbitrary graph `A`

built from the same set of nodes is a sub-graph of `G`

is the general case of the problem, but I'm only interested in the case where `A`

is a path and `G`

is directed & acyclic.

Any general pointers are also welcome.

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Edit: I ended up using a dynamic programming algorithm, independently also suggested in the accepted answer. Good call! It is probably the most accurate option as well, and barely more "complex" than the string-to-string case when the average # of edges per node is low.