One of the big challenges in automated verification is the annotation burden. In particular, to make verification compositional, we need contracts for all the functions but writing and maintaining contracts for a large codebase is a significant overhead and discovering the contracts for an existing codebase is a lot of work. This paper focusses on discovering contracts that describe what parts of a heapallocated data structure a function depends on in order to support separation logic based verification of memory safety along the lines of Smallfoot.
In particular, they are interested in finding the precondition of a function: what parts of a function’s arguments does a function depend on? And they want the precondition discovered to be as small as possible. (This is a form of “shape analysis”.)
The bulk of the paper deals with analysing individual functions. A short section then describes the fixpoint calculation to propagate analysis results from one function to another.
What stands out about this paper is the experimental results: they are able to analyse device drivers, the Linux kernel, Gimp, OpenSSL, etc. and infer sufficiently strong contracts for between 42% and 61% of the functions in those codebases. There seem to be two key features of their analysis that lead to this success (and the performance of their tool).

They are able to cope with partial analyses: imprecision and issues such as function pointers have a local effect on analysis but they are able to keep going.

The analysis tends to proceed bottom up whereas many alternative analyses they mention seem to have been top down.
That said, they suggest that a topdown pass might be worth adding to further improve the precision of analysis. Presumably this helps propagate information that a function is always called with the data structure in some shape.
Notes related to Compositional shape analysis by means of biabduction
Annotation burden, Lazy initialization of symbolic values, Modular verification, Separation logic
Papers related to Compositional shape analysis by means of biabduction
 A local shape analysis based on separation logic [distefano:tacas:2006]
 Underconstrained execution: Making automatic code destruction easy and scalable [engler:issta:2007]
 Generalized symbolic execution for model checking and testing [khurshid:tacas:2003]
 Practical, loweffort equivalence verification of real code [ramos:cav:2011]
 Underconstrained symbolic execution: Correctness checking for real code [ramos:sec:2015]
 Scalable error detection using boolean satisfiability [xie:popl:2005]