Abstract
Broadcasting a message from one to many processors in a network corresponds to concurrent reading on a random access shared memory parallel machine. Computing the trees of a forest, the level of each node in its tree and the path between two nodes are problems that can easily be solved with concurrent reading in a time logarithmic in the maximum height of a tree. Solving such problems with exclusive reading requires a time logarithmic in the number of nodes, implying message passing between disjoint pairs of processors on a distributed system. Allowing concurrent reading in parallel algorithm design for distributed computing might be advantageous in practice if these problems are faced on shallow trees with some specific constraints. We show an application to LZC (Lempel-Ziv-Compress)-compressed file decoding, whose parallelization employs these computations on such trees for realistic data. On the other hand, zipped files do not have this advantage, since they are compressed by the Lempel–Ziv sliding window technique.
Highlights
Parallel random access machines (PRAMs) are out of fashion today, but an apology of this model can still be done from the point of view of parallel algorithm design
We show an application to LZC compressed file decoding [5,6], whose parallelization employs these computations on such trees for realistic data
The number of iterations of the decoding algorithm is much less than ten units when expressed on the parallel random access shared memory machine [10], and about ten units when expressed in the MapReduce parallel programming paradigm [11], as we will show in this paper
Summary
Parallel random access machines (PRAMs) are out of fashion today, but an apology of this model can still be done from the point of view of parallel algorithm design. The Euler tour technique makes the parallel computation of several tree functions possible, as preorder, post-order, and computing the number of descendants of each node in logarithmic time with a linear number of processors. The number of iterations of the decoding algorithm is much less than ten units when expressed on the parallel random access shared memory machine [10], and about ten units when expressed in the MapReduce parallel programming paradigm [11], as we will show in this paper This makes it attractive in those cases (which are the most common in practice) where compression is performed very rarely, while the frequent reading of raw data needs fast decompression.
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