A dynamic data structure for counting subgraphs in sparse graphs by Zdenek Dvorak and Vojtech Tuma.
Abstract:
We present a dynamic data structure representing a graph G, which allows addition and removal of edges from G and can determine the number of appearances of a graph of a bounded size as an induced subgraph of G. The queries are answered in constant time. When the data structure is used to represent graphs from a class with bounded expansion (which includes planar graphs and more generally all proper classes closed on topological minors, as well as many other natural classes of graphs with bounded average degree), the amortized time complexity of updates is polylogarithmic.
Work on data structures seems particularly appropriate when discussing graphs.
Subject identity, beyond string equivalent, can be seen as graph isomorphism or subgraph problem.
Has anyone proposed “bounded” subject identity mechanisms that correspond to the bounds necessary on graphs to make them processable?
We know how to do string equivalence and the “ideal” solution would be unlimited relationships to other subjects, but that is known to be intractable. For one thing we don’t know every relationship for any subject.
Thinking there may be boundary conditions for constructing subject identities that are more complex than string equivalence but that result in tractable identifications.
Suggestions?