  Enumerating consistent global states of a computation is a fundamental
problem in parallel computing with applications to debug- ging, testing and
runtime verification of parallel programs. Breadth-first search (BFS)
enumeration is especially useful for these applications as it finds an
erroneous consistent global state with the least number of events possible. The
total number of executed events in a global state is called its rank. BFS also
allows enumeration of all global states of a given rank or within a range of
ranks. If a computation on n processes has m events per process on average,
then the traditional BFS (Cooper-Marzullo and its variants) requires
$\mathcal{O}(\frac{m^{n-1}}{n})$ space in the worst case, whereas ou r
algorithm performs the BFS requires $\mathcal{O}(m^2n^2)$ space. Thus, we
reduce the space complexity for BFS enumeration of consistent global states
exponentially. and give the first polynomial space algorithm for this task. In
our experimental evaluation of seven benchmarks, traditional BFS fails in many
cases by exhausting the 2 GB heap space allowed to the JVM. In contrast, our
implementation uses less than 60 MB memory and is also faster in many cases.
