3. Execution Time Measurements

In order to measure the run time of varying implementations without too much code modification, we use the time utility, available in $UNIX$-based operating systems. This brings portability to the framework, but has a consequence on the time resolution which can be not very fine and depends on the hardware. It's common for the internal processor clock to have a resolution somewhere between hundredths and millionths of a second. In our case, we have millionth of a second.

When the run time of one operator is small, e.g. the satisfiability test, we repeat the operation many times, e.g. $n$ times, to increase the accuracy of time measurement. This also reduces uninteresting overheads such as input/output run time, since these factors are divided by $n$, which is chosen as $100$. However, given that run times of complex operators such as convex hull are too long, we do not repeat these operations, i.e. $n$ is $1$.