[comp.sw.components] Cascading Divide & Conquer, Very Fast Tries

wtwolfe@hubcap.clemson.edu (Bill Wolfe) (09/04/89)

   Here are some other articles which may be of interest to readers
   of this group; I probably won't have time to review them, but they
   do seem to be quite interesting, so here's a brief summary of each:

   Cascading Divide & Conquer: 
      A Technique For Designing Parallel Algorithms
         (SIAM Journal on Computing, Vol. 18, No. 3, pp. 499-512, 5/89)
    
   This paper presents a number of general techniques for parallel
   divide-and-conquer which can be applied to any problem solvable
   by a divide-and-conquer method such that the subproblem merging
   step can be implemented using a restricted, but powerful, set of
   operations, which include (i) merging sorted lists, (ii) computing
   the values of labeling functionf on elements stored in sorted lists,
   and (iii) changing the identity of elements in a sorted list
   monotonically.  The elements stored in such sorted lists need not
   belong to a total order, so long as the computation can be specified
   so that we will never try to compare two incomparable elements.

   Efficient parallel algorithms are then presented for solving a
   number of fundamental problems from computational geometry, such 
   as finding maxima in three dimensions; several of these algorithms
   are optimal in that their time complexity per processor, multiplied
   by the number of processors, is equal to the sequential lower bound
   for the problem.


   New Trie Data Structures Which Support Very Fast Search Operations
      (Journal of Computer & System Sciences, 
         Vol. 28, No. 3, pp. 379-394, June 1984)

   A new data structure called the q-fast trie is introduced.  Given
   a set of N records whose keys are distinct nonnegative integers
   less than some initially specified bound M, a q-fast trie uses
   space O(N) and time O(square_root(log(M))) for insertions, 
   deletions, and all the retrieval operations commonly associated 
   with binary trees.  A simpler but less space efficient data 
   structure called the p-fast trie is defined.
   

   Bill Wolfe, wtwolfe@hubcap.clemson.edu