Towards optimal locality in mesh-indexings Original Research Article

The efficiency of many data structures and algorithms relies on “locality-preserving” indexing schemes for meshes. We concentrate on the case in which the maximal distance between two mesh nodes indexed i and j shall be a slow-growing function of |i−j|. We present a new two-dimensional (2-D) indexing scheme we call H-indexing, which has superior (possibly optimal) locality in comparison with the well-known Hilbert indexings. H-indexings form a Hamiltonian cycle and we prove that they are optimally locality-preserving among all cyclic indexings. We provide fairly tight lower bounds for indexings without any restriction. Finally, illustrated by investigations concerning 2-D and 3-D Hilbert indexings, we present a framework for mechanizing upper-bound proofs for locality.