Joanna Berlińska (auth.), Roman Wyrzykowski, Jack Dongarra,'s Parallel Processing and Applied Mathematics: 8th PDF

By Joanna Berlińska (auth.), Roman Wyrzykowski, Jack Dongarra, Konrad Karczewski, Jerzy Wasniewski (eds.)

ISBN-10: 3642144020

ISBN-13: 9783642144028

ISBN-10: 3642144039

ISBN-13: 9783642144035

This e-book constitutes the court cases of the eighth foreign convention on Parallel Processing and utilized arithmetic, PPAM 2009, held in Wroclaw, Poland, in September 2009.

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Extra info for Parallel Processing and Applied Mathematics: 8th International Conference, PPAM 2009, Wroclaw, Poland, September 13-16, 2009, Revised Selected Papers, Part II

Example text

3. Up to which amount of grid jobs and resources does the EA improve the best heuristically generated schedule? 26 W. Jakob et al. As the two benchmark scenarios based on large degrees of dependencies have turned out to be harder than those using small degrees [2,13], they are used here for the experiments. They are denoted sRlD and lRlD (small or large Resource alternatives / large Dependencies). As pointed out in [2] and [13], their time and cost limits were set so tightly that the heuristics could not solve them without violating these soft constraints.

We know that basic inequalities are satisfied by equality: (z1 ) O1 = q1 /S = α3 /D (z2,2 ) (q1 + q2 )/S = O2 (z3,3 ) (q1 + q2 + q3 )/S = O3 (z2 ) O2 = q2 /s1 = α2 /D = O3 = q3 /s1 = α/D = (z3 ) (z4,4 ) (z4 ) O4 = q4 /s1 = 1/D = (q1 + q2 + q3 + q4 )/S = O4 . The equal signs are labeled by labels of used equalities. Similarly the inequality signs are labeled by labels of sufficient conditions in following text. We can also easily verify that the equation (znorm ) holds. , nonbasic) inequalities: (z2,3 ) q2 + q3 = (α + α2 )s1 /D ≤A α(s1 + s2 )/D = (s1 + s2 )O3 2 (z2,4 ) q2 + q3 + q4 = (1 + α + α )s1 /D ≤B (s1 + s2 + s3 )/D = (s1 + s2 + s3 )O4 (z3,4 ) q3 + q4 = (1 + α)s1 /D ≤A (s1 + s2 )/D = (s1 + s2 )O4 .

All other inequalities are turned into equations. The upper bound coefficients are values of nonzero dual variables. These give the matching upper bound on the competitive ratio, which is obtained by summing up the corresponding inequalities multiplied by these coefficients. Note that all nonbasic dual variables have coefficients of zero value (and thus are not listed), because of the dual complementary slackness of linear programing. Now we show how to check the correctness of Case I. The correctness of all other cases and all other restrictions in this paper can be checked in the same way.

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Parallel Processing and Applied Mathematics: 8th International Conference, PPAM 2009, Wroclaw, Poland, September 13-16, 2009, Revised Selected Papers, Part II by Joanna Berlińska (auth.), Roman Wyrzykowski, Jack Dongarra, Konrad Karczewski, Jerzy Wasniewski (eds.)


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