We consider a natural variation of cuckoo hashing proposed by Lehman and Panigrahy (2009). Each of
cn
objects is assigned
k
= 2 intervals of size
l
in a linear hash table of size
n
and both starting points are chosen independently and uniformly at random. Each object must be placed into a table cell within its intervals, but each cell can only hold one object. Experiments suggested that this scheme outperforms the variant with
blocks
in which intervals are aligned at multiples of
l
. In particular, the
load threshold
is higher, i.e. the load
c
that can be achieved with high probability. For instance, Lehman and Panigrahy (2009) empirically observed the threshold for
l
= 2 to be around
\(96.5\% \)
as compared to roughly
\(89.7\% \)
using blocks. They pinned down the asymptotics of the thresholds for large
l
, but the precise values resisted rigorous analysis.
We establish a method to determine these load thresholds for all
l
≥ 2, and, in fact, for general
k
≥ 2. For instance, for
k
=
l
= 2 we get
\(\approx 96.4995\% \)
. We employ a theorem due to Leconte, Lelarge, and Massoulié (2013), which adapts methods from statistical physics to the world of hypergraph orientability. In effect, the orientability thresholds for our graph families are determined by belief propagation equations for certain graph limits. As a side note we provide experimental evidence suggesting that placements can be constructed in linear time using an adapted version of an algorithm by Khosla (2013).