  In this paper, we propose a greedy cycle direction heuristic to improve the
generalized $\mathbf{R}$ redundancy quorum cycle technique. When applied using
only single cycles rather than the standard paired cycles, the generalized
$\mathbf{R}$ redundancy technique has been shown to almost halve the necessary
light-trail resources in the network. Our greedy heuristic improves this
cycle-based routing technique's fault-tolerance and dependability.
  For efficiency and distributed control, it is common in distributed systems
and algorithms to group nodes into intersecting sets referred to as quorum
sets. Optimal communication quorum sets forming optical cycles based on
light-trails have been shown to flexibly and efficiently route both
point-to-point and multipoint-to-multipoint traffic requests. Commonly cycle
routing techniques will use pairs of cycles to achieve both routing and
fault-tolerance, which uses substantial resources and creates the potential for
underutilization. Instead, we use a single cycle and intentionally utilize
$\mathbf{R}$ redundancy within the quorum cycles such that every point-to-point
communication pairs occur in at least $\mathbf{R}$ cycles. Without the paired
cycles the direction of the quorum cycles becomes critical to the fault
tolerance performance. For this we developed a greedy cycle direction heuristic
and our single fault network simulations show a reduction of missing pairs by
greater than 30%, which translates to significant improvements in fault
coverage.
