A numerical study of the correspondence between paths in a causal set   and geodesics in the continuum
  This paper presents the results of a computational study related to the path-geodesic correspondence in causal sets. For intervals in flat spacetimes, and in selected curved spacetimes, we present evidence that the longest maximal chains (the longest paths) in the corresponding causal set intervals statistically approach the geodesic for that interval in the appropriate continuum limit. 
Raluca Ilie, Gregory B. Thompson, and David D. Reid