1 What is empirical analysis?

Empirical analysis is a method of evaluating the performance of an algorithm by running it on a set of inputs and measuring the time or resources it consumes. Unlike theoretical analysis, which relies on mathematical models and assumptions, empirical analysis gives you the actual data on how an algorithm behaves in practice. Empirical analysis can help you identify the strengths and weaknesses of an algorithm, test its scalability and efficiency, and find potential bottlenecks and errors.

2 Why use empirical analysis?

Empirical analysis can complement theoretical analysis by providing real-world evidence of how an algorithm performs. Theoretical analysis can give you an upper bound or an average case of the running time of an algorithm, but it may not account for all the factors that affect the actual execution, such as hardware, software, input size, input distribution, and randomization. Empirical analysis can help you verify the theoretical predictions, measure the actual running time, and compare different algorithms on the same problem. Empirical analysis can also help you discover unexpected behaviors or anomalies that may not be apparent from the theory.

3 How to perform empirical analysis?

In order to conduct empirical analysis, you must first select an algorithm or a set of algorithms to evaluate. You should then choose a set of inputs that represent the problem domain and the anticipated scenarios. Additionally, you need to decide on a metric or a set of metrics to measure, such as time, memory, disk space, network traffic, or energy consumption. After running the algorithm or algorithms on the inputs and recording the metrics, analyze the data and draw your conclusions.

4 What factors to consider?

When performing empirical analysis, you must take into account a few factors that could influence the results and weaken the validity and reliability of your conclusions. To ensure representative inputs from the problem domain, you should use a variety of sizes and distributions to test the scalability and robustness of the algorithm. Additionally, choose metrics that are relevant, meaningful, consistent, and comparable across different algorithms and inputs. Furthermore, consider the environment in which the algorithm is running; hardware and software can affect running time and resource consumption. Minimize variations and noise in the environment, use similar conditions for all algorithms and inputs, and report details such as CPU, memory, disk, network, operating system, and compiler version when presenting results.

5 How to interpret the results?

The results of empirical analysis can provide you with valuable insights and feedback on the performance of an algorithm. However, it's important to interpret them with caution and critical thinking. Ask yourself questions such as: are the results consistent with the theoretical analysis? Are they significant and meaningful? Are they generalizable and applicable to other problems or domains? Are they reproducible and verifiable? Empirical analysis is a powerful and practical tool for measuring the actual running time of an algorithm. By following the steps and considering the factors described in this article, you can use the results to improve and optimize your algorithms with accuracy.

6 Here’s what else to consider

This is a space to share examples, stories, or insights that don’t fit into any of the previous sections. What else would you like to add?