Abstract
We present a randomized parallel list ranking algorithm for distributed memory multiprocessors. A simple version requires, with high probability, log(3p)+log ln(n)=Õ(log p+log log n) communication rounds (h-relations with h=Õ(n/p)) and Õ(n/p) local computation. An improved version requires, with high probability, only r ≤ (4k+6) log (2/3p)+8=Õ(k log p) communication rounds where k= min{i ≥ 0¦ln(i+1) n ≤ (2/3p)2i+1}. Note that k < ln* (n) is an extremely small number. For \(n \leqslant 10^{10^{100} }\)and p ≥ 4, the value of k is at most 2. For a given number of processors, p, the number of communication rounds required is, for all practical purposes, independent of n. For \(n \leqslant 10^{10^{100} }\)and 4 ≤ p ≤ 2048, the number of communication rounds in our algorithm is bounded, with high probability, by 118. We conjecture that the actual number of communications rounds will not exceed 50.
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Dehne, F., Song, S.W. (1996). Randomized parallel list ranking for distributed memory multiprocesors. In: Jaffar, J., Yap, R.H.C. (eds) Concurrency and Parallelism, Programming, Networking, and Security. ASIAN 1996. Lecture Notes in Computer Science, vol 1179. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0027774
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DOI: https://doi.org/10.1007/BFb0027774
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