On representing the degree sequences of sublogarithmic-degree Wheeler graphs

We show how to store a searchable partial-sums data structure with constant query time for a static sequence $S$ of $n$ positive integers in $o \left( \frac{\log n}{(\log \log n)^2} \right)$,in$n H_k (S) + o (n)$bitsfor$k \in o \left( \frac{\log n}{(\log \log n)^2} \right)$. It follows that if a Wheeler graph on $n$ vertices has maximum degree in $o \left( \frac{\log n}{(\log \log n)^2} \right)$,thenwecanstoreitsin-andout-degreesequences$\Din$and$\Dout$in$n H_k (\Din) + o (n)$and$n H_k (\Dout) + o (n)$bits,for$k \in o \left( \frac{\log n}{(\log \log n)^2} \right)$, such that querying them for pattern matching in the graph takes constant time.