Edge Weighting by Calculation Complexity #2
Description
Even when the knowledge graph is directed (i.e. equations are treated as if only one "direction" of evaluation is practical), there are sometimes multiple correct paths to a solution.
For example, Biot-Savart's law may be used in many instances, though it's rarely the most efficient tool available.
Thus, weighting edges by the complexity of their equations could be useful. Coloring edges in a way that indicates this weight would serve as a nice visual aid for the user when choosing between two viable paths.
It's trivial to parse for mathematical symbols. Example features:
- Presence of the source-to-field separation vector,
(which is often difficult to define)
- Presence of a cross product,
(can also be difficult to handle)
- Presence of an line, area, or volume element, in increasing order of complexity
The set of such features could be weighted, then scaled so that an equation containing all of them would have a complexity of 1.0, whereas something simple (e.g. basic arithmetic) would have a complexity of 0.0.
Line thickness can then be specified using this weight, providing a visual indication of path complexity.