Imagine we’re trying to solve the Traveling Salesman Problem (TSP) – we want to find the shortest possible route that lets us visit a set of cities exactly once and then return to the start. The challenge is that as the number of cities grows, the possible routes increase dramatically, making the problem really slow to solve if we check every route.
One way to reduce the time it takes to find a solution is by categorizing or itemizing our data before we start calculating routes. Rather than treating all cities equally, we can group them by logical categories—like regions, proximity clusters, or even alphabetical identifiers. By categorizing, we quickly narrow down the search to a smaller subset of the most relevant routes.
- For example: If cities are in regions, we start by calculating routes within each region. If the ideal route spans multiple regions, we only expand to the next region when necessary, rather than analyzing every city at once.
For a large dataset, it’s best not to load all city data into memory at once. Instead, asynchronously access smaller sections of the data only when needed. This way, we pull just the required data for each step in the algorithm, instead of keeping everything in memory, which would use up unnecessary resources.
- Practical scenario: Imagine our cities are stored in files on a server by region. When our algorithm starts, we only load the nearest region file, calculate the shortest route there, and then load the next region if needed.
As we process these categorized sections, we focus our queries on the most relevant starting points. This method prioritizes the closest cities, further reducing time by filtering out less relevant data.
- Example: If we’re starting in one city, we first look at the closest clusters and ignore distant cities, focusing only on the most promising sections for an optimal route.
For frequently checked routes, we store calculated distances in a local cache so we don’t repeat work. This caching method saves significant processing time on repeated queries and can be especially useful as the dataset grows.
Using these steps—categorization, async data access, and efficient query starting points—we keep our memory usage and processing time low, making it feasible to solve TSP even with larger datasets. This approach ensures we’re not only working faster but also more resource-efficiently, which is crucial for scalability.