I know nothing about distributed programming, but Leslie Lamport's paper [1] from 1978 about distributed systems already reads very close to the typical intro in special relativity about clock synchronization. I would be surprised if there is not already a body of research about whether:

1) Relativity in the physical world arises if we consider some distributed model of computation

2) Physical laws, in particular speed of light, affecting algorithm complexity limits

[1] http://lamport.azurewebsites.net/pubs/time-clocks.pdf