BibTeX
@INCOLLECTION{
         Lyons2008OtP,
       title = "On the Practical Exploitation of Scarsity",
       doi = "10.1007/978-3-540-68942-3_10",
       author = "Andrew Lyons and Jean Utke",
       abstract = "Scarsity is the notion that the Jacobian J for a given function $f: \R^n
         \rightarrow \R^m$ may have fewer than $n * m$ degrees of freedom. A scarse $J$ may be
         represented by a graph with a minimal edge count. So far, scarsity has been recognized only from a
         high-level application point of view, and no automatic exploitation has been attempted. We introduce
         an approach to recognize and use scarsity in computational graphs in a source transformation
         context. The goal is to approximate the minimal graph representation through a sequence of
         transformations including eliminations, reroutings, and normalizations, with a secondary goal of
         minimizing the transformation cost. The method requires no application-level insight and is
         implemented as a fully automatic transformation in OpenAD. This paper introduces the problem and a
         set of heuristics to approximate the minimal graph representation. We also present results on a set
         of test problems.",
       crossref = "Bischof2008AiA",
       pages = "103--114",
       booktitle = "Advances in Automatic Differentiation",
       publisher = "Springer",
       editor = "Christian H. Bischof and H. Martin B{\"u}cker and Paul D. Hovland and Uwe
         Naumann and J. Utke",
       isbn = "978-3-540-68935-5",
       issn = "1439-7358",
       year = "2008",
       ad_tools = "OpenAD",
       ad_theotech = "Scarsity"
}