Final answer:
To handle a 10 GB data set with 56 attributes and 150 distinct values on a laptop with 512 MB of main memory, using a memory-efficient algorithm like SLIQ/SPRINT that compresses data is essential. It works by keeping only necessary statistical information in memory, making the management of Big Data possible even with limited memory resources.
Step-by-step explanation:
When working with a 10 GB data set with 56 attributes and 150 distinct values per attribute, all while having only 512 MB of main memory on a laptop, an efficient method to construct decision trees is needed. Decision tree algorithms typically require more memory than what is available, hence a popular approach is to use an algorithm that can compress lots of data, like the SLIQ/SPRINT algorithm, which builds trees by recursively partitioning the data set based on the attributes that most effectively classify the data. The key is that the algorithm only keeps the necessary statistics in memory during the computation rather than the entire data set. This technique is particularly useful when dealing with Big Data scenarios as seen in fields like astronomy, where terabytes of data must be processed efficiently with limited memory resources.
To roughly calculate the memory usage, consider that only the key statistical information is held in memory, not the entire data set. For each attribute, we'd store the count of each distinct value, the attribute's total count, and, if applicable, information about class label distributions. Assuming an integer requires 4 bytes, we take 150 (distinct values) * 4 (bytes) * 56 (attributes), resulting in 33,600 bytes, which is approximately 33 MB, well within the system's memory constraints. This simplification ignores additional metadata and control structures, but it still demonstrates that using a memory-efficient algorithm is viable.