  In this short paper, we characterize symmetric locality. In designing
algorithms, compilers, and systems, data movement is a common bottleneck in
high-performance computation, in which we improve cache and memory performance.
We study a special type of data reuse in the form of repeated traversals, or
re-traversals, which are based on the symmetric group. The cyclic and sawtooth
traces are previously known results in symmetric locality, and in this work, we
would like to generalize this result for any re-traversal. Then, we also
provide an abstract framework for applications in compiler design and machine
learning models to improve the memory performance of certain programs.
