  Motivation: Sequence mapping is the cornerstone of modern genomics. However,
most existing sequence mapping algorithms are insufficiently general.
  Results: We introduce context schemes: a method that allows the unambiguous
recognition of a reference base in a query sequence by testing the query for
substrings from an algorithmically defined set. Context schemes only map when
there is a unique best mapping, and define this criterion uniformly for all
reference bases. Mappings under context schemes can also be made stable, so
that extension of the query string (e.g. by increasing read length) will not
alter the mapping of previously mapped positions. Context schemes are general
in several senses. They natively support the detection of arbitrary complex,
novel rearrangements relative to the reference. They can scale over orders of
magnitude in query sequence length. Finally, they are trivially extensible to
more complex reference structures, such as graphs, that incorporate additional
variation. We demonstrate empirically the existence of high performance context
schemes, and present efficient context scheme mapping algorithms.
  Availability and Implementation: The software test framework created for this
work is available from
https://registry.hub.docker.com/u/adamnovak/sequence-graphs/.
  Contact<EMAIL_ADDRESS>  Supplementary Information: Six supplementary figures and one supplementary
section are available with the online version of this article.
