  Large scale numerical experiments are commonplace today in theoretical
physics. The high performance algorithms described herein are the most compact,
efficient methods known for representing and analyzing systems modeled well by
sets or graphs. After studying how these implementations maximize instruction
throughput and optimize memory access patterns, we apply them to causal set
quantum gravity, in which spacetime is represented by a partially ordered set.
We build upon the low-level set and graph algorithms to optimize the
calculation of the causal set action, and then discuss how to measure
boundaries of a discrete spacetime. We then examine the broader applicability
of these algorithms to greedy information routing in random geometric graphs
embedded in Lorentzian manifolds, which requires us to find new closed-form
solutions to the geodesic differential equations in
Friedmann-Lemaitre-Robertson-Walker spacetimes. Finally, we consider the vacuum
selection problem in string theory, where we show a network-centered approach
yields a dynamical mechanism for vacuum selection in the context of multiverse
cosmology. These algorithms have broad applicability to many physical systems,
and they improve existing methods by reducing simulation runtimes by orders of
magnitude.
