K d tree_cpp

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K D Tree Code designed for an Uber interview. It uses a heap array for space-efficiency and bucket-sort over median-of-medians.

Identifying intersections among a set of d-dimensional rectangular regions (d-rectangles) is a common problem in many simulation and modeling applications. Since algorithms for computing intersections over a large number of regions can be computationally demanding, an obvious solution is to take advantage of the multiprocessing capabilities of modern multicore processors. Unfortunately, many solutions employed for the Data Distribution Management service of the High Level Architecture are either inefficient, or can only partially be parallelized. In this paper we propose the Interval Tree Matching (ITM) algorithm for computing intersections among d-rectangles. ITM is based on a simple Interval Tree data structure, and exhibits an embarrassingly parallel structure. We implement the ITM algorithm, and compare its sequential performance with two widely used solutions (brute force and sort-based matching). We also analyze the scalability of ITM on shared-memory multicore processors. The results show that the sequential implementation of ITM is competitive with sort-based matching; moreover, the parallel implementation provides good speedup on multicore processors.

An O(n+m) in time and O(1) in space search-algorithm for substr, length m, in target string, length n. Simpler than trie or Knuth-Morris-Pratt. Can be reduced to O(n) using Group Theoretic O(1)-updatable hash that replaces the cumulative sum, which requires an O(m) verification step because "+" is commutative and cannot distinguish between anagrams: a+b+c = a+c+b = c+a+b etc. I am not uploading the hash, because it means giving away R&D I do in quantum simulations.

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