Simultaneous solvers using same CSM / Tree?

[dehann]

Picking up from #459 (comment)

Update 25Q4, with DFG v1.0 happening soon, there are three related questions on the relationship between a factor graph and the Bayes (junction) tree used to solve the graph:

• Does one graph have just one tree at any given time, bearing in mind the motivation of having graph StateLabels:
  • StateLabel represents super-solving, like super position, that is the factor graph structure is unchanged but Monte Carlo, or parameters tweaks, or comparing algorithms:
    • Question is whether the variable ordering is a parameter of a solver algorithm, yes because we use AMD etc; but also no because variable order is NP-hard and in many ways the crux problem. Algorithms are just ignoring the variable order complexity.
• How to deal with the complexity of many trees to many StateLabels, since either the complexity should be expanded as different graphs, or different trees asssociated with different statelabels on a case by case basis.
• How persistent is the Bayes tree for different solve cases,
  • Early assumptions on fluid relinearization / recycling marginalized solutions implies the Bayes tree should be persistent.