1993
DOI: 10.1007/3-540-57273-2_62
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Block gossiping on grids and tori: Deterministic sorting and routing match the bisection bound

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Cited by 47 publications
(40 citation statements)
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“…Since each neighborhood is chosen according to an i.i.d. distribution, the probability that the crowding factor in the central squarelet is larger than We used the inequality in arriving at (11) and substituted the value of in arriving at (12). Choosing and in (12), we conclude that Number of nodes in any fixed squarelet As before, using a simple union bound we have Using the Borel-Cantelli lemma, we conclude that, almost surely, the crowding factor is no more than .…”
Section: Proposition 42mentioning
confidence: 89%
“…Since each neighborhood is chosen according to an i.i.d. distribution, the probability that the crowding factor in the central squarelet is larger than We used the inequality in arriving at (11) and substituted the value of in arriving at (12). Choosing and in (12), we conclude that Number of nodes in any fixed squarelet As before, using a simple union bound we have Using the Borel-Cantelli lemma, we conclude that, almost surely, the crowding factor is no more than .…”
Section: Proposition 42mentioning
confidence: 89%
“…Our analysis on Scheme 1 mainly relies on some well-known results about two-dimensional (2-D) arrays [28], [29], which have been extensively studied in the parallel and distributed computing research community. Therefore, we first review some related definitions and results.…”
Section: B Performance Analysis Of Schemementioning
confidence: 99%
“…Lemma 2: ( [28] and [29]) -routing on arrays can be performed deterministically in time slots, with average packet delay . We now point out the correspondence between Scheme 1 and the optimal communication scheme for the 2-D array.…”
Section: B Performance Analysis Of Schemementioning
confidence: 99%
“…Let each processor be a source and destination of exactly h packets. The problem of routing the hl 2 packets to their destinations is known as h × h permutation routing and can be characterized by the following result [19].…”
Section: Theorem 44mentioning
confidence: 99%