Coarse Grained Parallel Selection Laurence Boxer Department of

Coarse Grained Parallel Selection Laurence Boxer Department of Computer and Information Sciences Niagara University boxer@niagara. edu Department of Computer Science and Engineering SUNY at Buffalo PRESENTATION AT UNIVERSITY OF DISTRICT OF COLUMBIA, NOVEMBER, 2018 1

Selection Problem PRESENTATION AT UNIVERSITY OF DISTRICT OF COLUMBIA, NOVEMBER, 2018 2

Principles of Analysis of Algorithms* * This slide copied from Power. Points for Miller and Boxer, 2013 PRESENTATION AT UNIVERSITY OF DISTRICT OF COLUMBIA, NOVEMBER, 2018 3

Technical details PRESENTATION AT UNIVERSITY OF DISTRICT OF COLUMBIA, NOVEMBER, 2018 4

Example for uninitiated: PRESENTATION AT UNIVERSITY OF DISTRICT OF COLUMBIA, NOVEMBER, 2018 5

Naïve non-optimality, sequential version n log_2 n 1, 024 10, 240 2, 048 11 22, 528 4, 096 12 49, 152 8, 192 13 106, 496 16, 384 14 229, 376 32, 768 15 491, 520 65, 536 1, 048, 576 131, 072 17 2, 228, 224 262, 144 18 4, 718, 592 524, 288 19 9, 961, 472 y = n vs. y = n log_2 n 12, 000 10, 000 8, 000 6, 000 4, 000 2, 000 0 10 11 12 13 14 15 16 17 18 19 log_2 n n PRESENTATION AT UNIVERSITY OF DISTRICT OF COLUMBIA, NOVEMBER, 2018 n log_2 n 6

Application example – awarding merit scholarships E. g. , top 5% of applicants in a scholarship program are to be awarded. PRESENTATION AT UNIVERSITY OF DISTRICT OF COLUMBIA, NOVEMBER, 2018 7

Note to students – this hints at challenges of parallel computing, and opportunities. PRESENTATION AT UNIVERSITY OF DISTRICT OF COLUMBIA, NOVEMBER, 2018 8

Saukas-Song coarse grained parallel Selection algorithm PRESENTATION AT UNIVERSITY OF DISTRICT OF COLUMBIA, NOVEMBER, 2018 9

PRESENTATION AT UNIVERSITY OF DISTRICT OF COLUMBIA, NOVEMBER, 2018 10

References L. Boxer, Coarse Grained Parallel Selection, submitted. Available at https: //arxiv. org/abs/1808. 09903 L. Boxer and R. Miller, Coarse grained gather and scatter operations with applications, Journal of Parallel and Distributed Computing 64 (11) (2004), 1297 -1310. M. Blum, R. W. Floyd, V. Pratt, R. L. Rivest, and R. E. Tarjan, Bounds for selection, Journal of Computer and System Sciences 7 (1973), 448 -461. R. Miller and L. Boxer, Algorithms Sequential and Parallel, A Unified Approach, 3 rd ed. , Cengage Learning, Boston, 2013. E. L. G. Saukas and S. W. Song, A note on parallel selection on coarse-grained multicomputers, Algorithmica 24 (1999), 371 -380. PRESENTATION AT UNIVERSITY OF DISTRICT OF COLUMBIA, NOVEMBER, 2018 11