  Since knowledge graphs (KGs) describe and model the relationships between
entities and concepts in the real world, reasoning on KGs often correspond to
the reachability queries with label and substructure constraints (LSCR).
Specially, for a search path p, LSCR queries not only require that the labels
of the edges passed by p are in a certain label set, but also claim that a
vertex in p could satisfy a certain substructure constraint. LSCR queries is
much more complex than the label-constraint reachability (LCR) queries, and
there is no efficient solution for LSCR queries on KGs, to the best of our
knowledge. Motivated by this, we introduce two solutions for such queries on
KGs, UIS and INS. The former can also be utilized for general edge-labeled
graphs, and is relatively handy for practical implementation. The latter is an
efficient local-index-based informed search strategy. An extensive experimental
evaluation, on both synthetic and real KGs, illustrates that our solutions can
efficiently process LSCR queries on KGs.
