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Arpit Bhayani Blogs
001 Ai Topological Sort

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Shared from "Arpit Bhayani Blogs" on Inkdown

TLDR: Fractional Cascading - Speeding Up Multiple Binary Searches

Date: 2020-05-10 Source: https://arpitbhayani.me/blogs/fractional-cascading

Overview

Explore Binary Search variations k-searches, unified search & fractional cascading. Optimize search time in k sorted lists! Binary Search is an algorithm that finds the position of a target value in a sorted list.

Key Points

  • Binary Search is an algorithm that finds the position of a target value in a sorted list.
  • Time and Space Complexity: Each of the k lists have size n and we know the time complexity of performing a binary search in one list of n elements is O(log(n)).
  • Preprocess: The preprocessing is done in two phases; in the first phase, we compute a position tuple for each element and associate it with the same.
  • Working: Given a target value, we perform a binary search in the above auxiliary list and get the smallest element greater than or equal to this target value.
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003 Rag Production
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  • Complexity: We are performing binary search just once on the list of size k n hence, the time complexity of this approach is O(log(kn)) which is a huge improvement over the k-binary searches approach where it was O(klog(n)).
  • Preprocess: Preprocessing is a super-critical step in fractional cascading because it is responsible for speeding up the iterative binary searches.

    • Takeaway

    Fractional Cascading is used in FD-Trees which are used in databases to address the asymmetry of read-write speeds in tree indexing on the flash disk.