  We present a shared-memory algorithm to compute high-quality solutions to the
balanced $k$-way hypergraph partitioning problem. This problem asks for a
partition of the vertex set into $k$ disjoint blocks of bounded size that
minimizes the connectivity metric (i.e., the sum of the number of different
blocks connected by each hyperedge). High solution quality is achieved by
parallelizing the core technique of the currently best sequential partitioner
KaHyPar: the most extreme $n$-level version of the widely used multilevel
paradigm, where only a single vertex is contracted on each level. This approach
is made fast and scalable through intrusive algorithms and data structures that
allow precise control of parallelism through atomic operations and fine-grained
locking. We perform extensive experiments on more than 500 real-world
hypergraphs with up to $140$ million vertices and two billion pins (sum of
hyperedge sizes). We find that our algorithm computes solutions that are on par
with a comparable configuration of KaHyPar while being an order of magnitude
faster on average. Moreover, we show that recent non-multilevel algorithms
specifically designed to partition large instances have considerable quality
penalties and no clear advantage in running time.
