15. Cache-Oblivious Algorithms

TL;DR

Analyzing the cache complexity of merge sort and multiway merge algorithms, including work and cache misses.

Transcript

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Key Insights

• 🚨 The cache complexity of merge sort is determined by the number of cache misses incurred during the merge step.
• 🚨 Multiway merge can merge multiple sorted arrays at once, taking advantage of spatial locality and reducing cache misses.

Questions & Answers

Q: What is the time complexity of merging two sorted arrays?

The time complexity of merging two sorted arrays is O(n), where n is the sum of the sizes of the two arrays.

Q: How does multiway merge differ from regular merge?

Multiway merge merges multiple sorted arrays at once, compared to regular merge which merges only two sorted arrays at a time.

Q: What is the cache complexity of merge sort?

The cache complexity of merge sort is O(n/B * log(n)), where B is the cache block size.

Summary & Key Takeaways

• Merge sort is a divide and conquer algorithm that recursively splits the input into smaller sub-arrays and merges them back together in sorted order.

• The cache complexity of merge sort is O(nlogn) because of the merge operation.

• Multiway merge is an extension of merge sort that merges more than 2 sub-arrays at a time, but still has the same cache complexity.