Complexity of Sub-Bus Mesh Computations

We investigate the time complexity of several fundamental problems on the subbus mesh parallel computer with p processors. The problems include computing the PARITY and MAJORITY of p bits, the SUM of p numbers of length O(logp) and the MINIMUM of p numbers. It is shown that in one dimension the time to compute any of these problems is (log p). In two dimensions the time to compute any of PARITY, MAJORITY, and SUM is ( logp log log p ). It was previously shown that the time to compute MINIMUM in two dimensions is (log log p) [21, 31]. This is a revision of University of Washington Technical Report No. 93-10-02. This paper will appear in SIAM Journal on Computing. Condon's research was supported by NSF, grant numbers CCR-9100886 and CCR-9257241. Ladner's and Lampe's research was supported by NSF, grant number CCR-9108314. Part of Ladner's research was done while visiting Victoria University of Wellington, New Zealand. Sinha's research was supported by NSF/DARPA grant number CCR-8907960 and NSF grant number CCR-8858799.