  Register allocation (mapping variables to processor registers or memory) and
instruction scheduling (reordering instructions to increase instruction-level
parallelism) are essential tasks for generating efficient assembly code in a
compiler. In the last three decades, combinatorial optimization has emerged as
an alternative to traditional, heuristic algorithms for these two tasks.
Combinatorial optimization approaches can deliver optimal solutions according
to a model, can precisely capture trade-offs between conflicting decisions, and
are more flexible at the expense of increased compilation time.
  This paper provides an exhaustive literature review and a classification of
combinatorial optimization approaches to register allocation and instruction
scheduling, with a focus on the techniques that are most applied in this
context: integer programming, constraint programming, partitioned Boolean
quadratic programming, and enumeration. Researchers in compilers and
combinatorial optimization can benefit from identifying developments, trends,
and challenges in the area; compiler practitioners may discern opportunities
and grasp the potential benefit of applying combinatorial optimization.
