The EDGE Language: Extended General Einsums for Graph Algorithms
arxiv(2024)
摘要
In this work, we propose a unified abstraction for graph algorithms: the
Extended General Einsums language, or EDGE. The EDGE language expresses graph
algorithms in the language of tensor algebra, providing a rigorous, succinct,
and expressive mathematical framework. EDGE leverages two ideas: (1) the
well-known foundations provided by the graph-matrix duality, where a graph is
simply a 2D tensor, and (2) the power and expressivity of Einsum notation in
the tensor algebra world. In this work, we describe our design goals for EDGE
and walk through the extensions we add to Einsums to support more complex
operations common in graph algorithms. Additionally, we provide a few examples
of how to express graph algorithms in our proposed notation. We hope that a
single, mathematical notation for graph algorithms will (1) allow researchers
to more easily compare different algorithms and different implementations of a
graph algorithm; (2) enable developers to factor complexity by separating the
concerns of what to compute (described with the extended Einsum notation) from
the lower level details of how to compute; and (3) enable the discovery of
different algorithmic variants of a problem through algebraic manipulations and
transformations on a given EDGE expression.
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