By F. Desprez, S. Domas, B. Tourancheau (auth.), Luc Bougé, Pierre Fraigniaud, Anne Mignotte, Yves Robert (eds.)
This two-volume set provides the court cases of the second one foreign eu convention on Parallel Processing, EuroPar '96, held in Lyon, France, in August 1996.
EuroPar '96 was once equipped in 14 workshops protecting the complete spectrum of parallel processing. the great lawsuits represent a distinct list of the state-of-the-art in parallel processing learn and improvement: the 224 papers incorporated including 4 invited papers have been chosen from a complete of 383 submissions through authors from forty nations; 554 referees have been thinking about the choice method and the index lists 521 contributing authors.
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Extra resources for Euro-Par'96 Parallel Processing: Second International Euro-Par Conference Lyon, France, August 26–29, 1996 Proceedings, Volume II
This procedure motivates the algorithm developed in the next subsection. Split each of x and y into two n/2bit numbers: x = x1 x0 , and y = y1 y0 . There are many known ways of expressing the product xy in terms of three n/2-bit multiplications. One scheme is given below. Let u = (x1 + x0 )(y1 + y0 ), v = x1 y1 , and w = x0 y0 . Then the product is given by xy = v2n + (u − v − w)2n/2 + w. Implementation of this scheme on a 2-dim mesh runs √ into serious problems. e. the corresponding processors).
4. d(y, ui ) ≤ d(y, wi ), RT (y, wi ) = RT (ui , wi ), and j > i: By using Observation 1, RT (ui , wi ) ≤ RT (y, ui ). Also RT (ui , wi ) ≥ RT (y, ui ), as y is on the roundtrip path from ui to wi . This gives RT (ui , wi ) = RT (y, ui ). Expanding the above expression gives d(ui , y) + d(y, wi ) + d(wi , ui ) = d(ui , y) + d(y, ui ) This implies d(y, wi ) + d(wi , ui ) = d(y, ui ) As d(wi , ui ) > 0, we get d(y, wi ) < d(y, ui ) which contradicts the condition assumed. Hence this subcase cannot exist.
From wi , it will be routed towards wj . There are two subcases to be considered. – None of the nodes between wi and wj has an entry for uj . In this subcase, the packet reaches wj and from there it goes to uj . This gives RT (R, uj , wi ) = d(uj , wi ) + d(wi , wj ) + d(wj , uj ) Note, d(wi , wj ) ≤ d(wi , uj ) and RT (uj , wj ) ≤ RT (uj , wi ) because wi does not have an entry for uj . Thus, RT (R, uj , wi ) ≤ d(uj , wi ) + d(wi , uj ) + d(wj , uj ) ≤ RT (uj , wi ) + RT (uj , wj ) ≤ 2RT (uj , wi ) Hence we obtain a round-trip stretch of 2.
Euro-Par'96 Parallel Processing: Second International Euro-Par Conference Lyon, France, August 26–29, 1996 Proceedings, Volume II by F. Desprez, S. Domas, B. Tourancheau (auth.), Luc Bougé, Pierre Fraigniaud, Anne Mignotte, Yves Robert (eds.)