Solving Problems on Recursively Constructed Graphs by Richard B. Borie , R. Gary Parker , Craig A. Tovey.
Abstract:
Fast algorithms can be created for many graph problems when instances are confined to classes of graphs that are recursively constructed. This article first describes some basic conceptual notions regarding the design of such fast algorithms, and then the coverage proceeds through several recursive graph classes. Specific classes include trees, series-parallel graphs, k-terminal graphs, treewidth-k graphs, k-trees, partial k-trees, k-jackknife graphs, pathwidth-k graphs, bandwidth-k graphs, cutwidth-k graphs, branchwidth-k graphs, Halin graphs, cographs, cliquewidth-k graphs, k-NLC graphs, k-HB graphs, and rankwidth-k graphs. The definition of each class is provided. Typical algorithms are applied to solve problems on instances of most classes. Relationships between the classes are also discussed.
Part survey and part tutorial, this article (at 51 pages) will take some time to read in detail.
I wanted to mention it because one of the topics being discussed in the graph reading club will be the partitioning of graph databases.
I suspect, but obviously don’t know for certain, that the graph databases that are constructed in enterprise settings are not going to be random graphs. That is to say some (all?) have repetitive (if not recursive) structures that can be exploited to solve particular graph operations on those databases.
Suggestions of other resources on recursively constructed graphs?