Algorithms for Deducing a Timeline / Chronology

Question

I'm looking for leads on algorithms to deduce the timeline/chronology of a series of novels. I've split the texts into days and created a database of relationships between them, e.g.: X is a month before Y, Y and Z are consecutive, date of Z is known, X is on a Tuesday, etc. There is uncertainty ('month' really only means roughly 30 days) and also contradictions. I can mark some relationships as more reliable than others to help resolve ambiguity and contradictions.

What kind of algorithms exist to deduce a best-fit chronology from this kind of data, assigning a highest-probability date to each day? At least time is 1-dimensional but dealing with a complex relationship graph with inconsistencies seems non-trivial. I have a CS background so I can code something up but some idea about the names of applicable algorithms would be helpful. I guess what I have is a graph with days as nodes as relationships as edges.

Answer 1

A simple, crude first approximation to your problem would be to store information like "A happened before B" in a directed graph with edges like "A -> B". Test the graph to see whether it is a Directed Acyclic Graph (DAG). If it is, the information is consistent in the sense that there is a consistent chronology of what happened before what else. You can get a sample linear chronology by printing a "topological sort" (topsort) of the DAG. If events C and D happened simultaneously or there is no information to say which came before the other, they might appear in the topsort as ABCD or ABDC. You can even get the topsort algorithm to print all possibilities (so both ABCD and ABDC) for further analysis using more detailed information.

If the graph you obtain is not a DAG, you can use an algorithm like Tarjan's algorithm to quickly identify "strongly connected components", which are areas of the graph which contain chronological contradictions in the form of cycles. You could then analyze them more closely to determine which less reliable edges might be removed to resolve contradictions. Another way to identify edges to remove to eliminate cycles is to search for "minimum feedback arc sets". That's NP-hard in general but if your strongly connected components are small the search could be feasible.