Variables can be stored in index registers to speed up the execution of loops in a program.

The problem of assigning variables to temporary registers can be addressed using a graph

coloring model. We can let each vertex of a graph represent a variable in the loop. We

place an edge between two vertices if the variables they represent must be stored in index

registers at the same time during the execution of the loop.

Seven variables occur in a loop of a computer program. The variables and the steps

during which they must be stored are