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Issue No.11 - November (2002 vol.13)
pp: 1124-1138
ABSTRACT
<p><b>Abstract</b>—The computation model on which the algorithms are developed is the reconfigurable array of processors with wider bus networks (abbreviated to RAPWBN). The main difference between the RAPWBN model and other existing reconfigurable parallel processing systems is that the bus width of each network is bounded within the range <tmath>\big. [2, \lceil \sqrt{N} \rceil]\bigr.</tmath>. Such a strategy not only saves the silicon area of the chip as well as increases the computational power enormously, but the strategy also allows the execution speed of the proposed algorithms to be tuned by the bus bandwidth. To demonstrate the computational power of the RAPWBN, the channel-assignment problem is derived in this paper. For the channel-assignment problem with <tmath>\big. N\bigr.</tmath> pairs of components, we first design an <tmath>\big. O(T + \lceil {N\over w} \rceil)\bigr.</tmath> time parallel algorithm using <tmath>\big. 2N\bigr.</tmath> processors with a <tmath>\big. 2N{\hbox{-}}\rm row\bigr.</tmath> by <tmath>\big. 2N{\hbox{-}}\rm column\bigr.</tmath> bus network, where the bus width of each bus network is <tmath>\big. w{\hbox{-}}\rm bit\bigr.</tmath> for <tmath>\big. 2 \leq w \leq \lceil \sqrt{N} \ \rceil\bigr.</tmath> and <tmath>\big. T={\lfloor \log _{w} N \rfloor}+1\bigr.</tmath>. By tuning the bus bandwidth to the natural <tmath>\big. \log N{\hbox{-}}\rm bit\bigr.</tmath> and the extended <tmath>\big. N^{1/c}{\hbox{-}}\rm bit\bigr.</tmath> (<tmath>\big. N^{1/c} > \log N\bigr.</tmath>) for any constant <tmath>\big. c\bigr.</tmath> and <tmath>\big. c \geq 1\bigr.</tmath>, two more results which run in <tmath>\big. O(\log N /\log \log N)\bigr.</tmath> and <tmath>\big. O(1)\bigr.</tmath> time, respectively, are also derived. When compared to the algorithms proposed by Olariu et al. [<ref rid="bibL112417" type="bib">17</ref>] and Lin [<ref rid="bibL112414" type="bib">14</ref>], it is shown that our algorithm runs in the equivalent time complexity while significantly reducing the number of processors to <tmath>\big. O(N)\bigr.</tmath>.</p>
INDEX TERMS
Channel-assignment problem, minimum coloring problem, interval graph, list ranking, integer sorting, parallel algorithm, reconfigurable array of processors with wider bus networks.
CITATION
Shi-Jinn Horng, Horng-Ren Tsai, Yi Pan, Jennifer Seitzer, "Optimal Algorithms for the Channel-Assignment Problem on a Reconfigurable Array of Processors with Wider Bus Networks", IEEE Transactions on Parallel & Distributed Systems, vol.13, no. 11, pp. 1124-1138, November 2002, doi:10.1109/TPDS.2002.1058096
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