Use of Representative Operation Counts in Computational Testing of Algorithms

In the mathematical programming literature, researchers have conducted a large number of computational studies to assess the empirical behavior of various algorithms and have utilized CPU time as the primary measure of performance. CPU time has the following drawbacks as a measure of an algorithm's performance: it is implementation dependent, hard to replicate, and limited in the insight it provides into an algorithm's behavior. In this paper, we illustrate the notion of representative operation counts that can complement the conventional CPU time analysis and can help us (i) to identity the asymptotic bottleneck operations in an algorithm, (ii) to estimate an algorithm's running time for different problem sizes, and (iii) to obtain a fairer comparison of several algorithms. These concepts are easily incorporated into empirical studies and often yield valuable insights into an algorithm's behavior.