# maximal theoretical sorting efficiency

Article: Hot Chips XXI Preview
By: Richard Cownie (tich.delete@this.pobox.com), September 9, 2009 9:10 am
Emil (Emil@example.com) on 9/8/09 wrote:
---------------------------

>I tried to find what the maximum theoretical sorting efficiency could be. Some
>places claim O(N log N) but don't reference how they get to this value.

The inputs can be in N! = N*(N-1)*(N-2)*...*1 possible
orders. And a sorting algorithm based on pairwise
comparisons must do enough pairwise comparisons to
distinguish each of those possible input orders. So
if you do C comparisons, then you must have

2**C >= N!

=> C >= log(N!)

And log(N!) is O(N*logN)
[consider the first N/2 terms in the product
N*(N-1)*(N-2)*...(N/2)
That gives us N/2 terms each of which is >= N/2
so N*log(N) >= log(N!) >= (N/2)*(log(N)-log(2))

hence O(N*log(N))]

An algorithm working with K-way comparisons rather than
2-way comparisons can generate logK bits at each operation.
But that's only a constant factor, so it's still O(NlogN).

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OOOE for low powerMichael S2009/08/29 11:16 AM
OOOE for low powerJukka Larja2009/08/29 09:40 PM
OOOE for low powerMichael S2009/08/30 12:04 AM
OOOE and cache/mem sizesRichard Cownie2009/08/28 05:30 PM
OOOE and cache/mem sizesLinus Torvalds2009/08/31 10:53 PM
OOOE and cache/mem sizesRichard Cownie2009/09/01 04:15 AM
OOOE and pipe length etc.AM2009/09/01 08:35 AM
OOOE and pipe length etc.Jouni Osmala2009/09/01 08:57 AM
OOOE and clock rateAM2009/09/02 01:34 AM
OOOE and clock rateJouni Osmala2009/09/02 05:35 AM
OOOE and clock rateMartin Høyer Kristiansen2009/09/02 06:19 AM
OOOE and clock rateanon2009/09/02 09:43 PM
OOOE and clock rateAM2009/09/03 02:52 AM
OOOE and clock rateJouni Osmala2009/09/03 07:34 AM
OOOE impactsAM2009/09/04 02:04 AM
OOOE impactsDavid Kanter2009/09/04 10:12 AM
OOOE impactsJouni Osmala2009/09/06 12:16 PM
OOOE impactsAM2009/09/07 03:47 AM
OOOE impactsMartin Høyer Kristiansen2009/09/07 06:03 AM
Does IBM lie about PPC603 being OoO chip?AM2009/09/08 03:13 AM
No, but...Michael S2009/09/08 07:05 AM
No, but...hobold2009/09/09 05:09 AM
OOOE impactsJS2009/09/07 06:34 AM
Are Sandpile and others wrong about 0.28 um?AM2009/09/08 03:12 AM
OOOE impactssomeone2009/09/08 06:43 AM
OOOE impactsJouni Osmala2009/09/07 07:48 AM
OOOE costsDavid Kanter2009/09/07 12:07 PM
OOOE impactsAM2009/09/08 03:11 AM
OOOE impactsJouni Osmala2009/09/10 01:53 AM
OOOE impactsAM2009/09/11 04:35 AM
OOOE impactsJouni Osmala2009/09/11 08:38 AM
OOOE impactsAM2009/09/12 05:06 AM
OOOE impactsJouni Osmala2009/09/12 11:36 PM
OOOE impactsAM2009/09/14 04:39 AM
OOOE impactsJouni Osmala2009/09/14 06:18 AM
if-ex distanceAM2009/09/15 05:16 AM
small addendumAM2009/09/19 03:54 AM
small addendumJouni Osmala2009/09/19 09:51 PM
small addendumAM2009/09/20 06:54 AM
small addendumJouni Osmala2009/09/20 01:16 PM
small addendumThiago Kurovski2009/09/20 04:51 PM
small addendumJouni Osmala2009/09/20 09:21 PM
small addendumThiago Kurovski2009/09/21 06:59 AM
small addendumAM2009/09/21 03:14 AM
small addendumJukka Larja2009/09/21 10:21 PM
small addendumAM2009/09/22 03:01 AM
small addendumJukka Larja2009/09/22 11:31 PM
small addendumAM2009/09/23 08:35 AM
small addendumJukka Larja2009/09/23 10:31 PM
small addendumAM2009/09/24 12:13 AM
OT metadiscussionJukka Larja2009/09/24 09:39 PM
OT metadiscussionAM2009/09/25 05:18 AM
Back to bitsMichael S2009/09/25 07:14 AM
Back to bitsThiago Kurovski2009/09/25 11:24 AM
Back to bitsWilco2009/09/25 03:18 PM
Back to bitsThiago Kurovski2009/09/26 09:12 AM
Back to bitsMichael S2009/09/26 08:54 AM
Back to bitsThiago Kurovski2009/09/26 09:05 AM
Back to bitsMichael S2009/09/26 09:16 AM
Agree, with very minor change.Jouni Osmala2009/09/25 09:37 PM
Back to bitsAM2009/09/26 06:16 AM
Back to bitsMichael S2009/09/26 09:13 AM
OT metadiscussionDavid Kanter2009/09/25 12:23 PM
OT metadiscussionAM2009/09/26 05:55 AM
OT metadiscussionJukka Larja2009/09/25 11:33 PM
OT metadiscussionAM2009/09/26 05:50 AM
OT metadiscussionJukka Larja2009/09/27 02:16 AM
OT metadiscussionMichael S2009/09/27 04:58 AM
OT metadiscussionAM2009/09/28 04:07 AM
OT metadiscussionAM2009/09/28 03:43 AM
OT metadiscussionJukka Larja2009/09/29 12:45 AM
OT metadiscussionAM2009/09/30 03:13 AM
OT metadiscussionJukka Larja2009/10/01 01:34 AM
OT metadiscussionAM2009/10/01 04:05 AM
OT metadiscussionJukka Larja2009/10/02 12:38 AM
OT metadiscussionAM2009/10/03 07:19 AM
OT metadiscussionJukka Larja2009/10/04 03:38 AM
OT metadiscussionAM2009/10/04 08:27 AM
OT metadiscussionJukka Larja2009/10/04 11:48 PM
OT metadiscussionAM2009/10/05 07:13 AM
About teachingJukka Larja2009/10/05 11:36 PM
About teachingAM2009/10/06 04:37 AM
About teachingJukka Larja2009/10/07 03:15 AM
About teachinganon2009/10/07 12:39 PM
About teachingAM2009/10/08 03:11 AM
About teachingJukka Larja2009/10/09 04:10 AM
About teachingAM2009/10/09 05:40 AM
About teachingJukka Larja2009/10/09 09:02 PM
About teachingAM2009/10/09 11:24 PM
About teachingJukka Larja2009/10/10 10:50 PM
About teachingAM2009/10/12 02:02 AM
About teachingJukka Larja2009/10/12 10:51 PM
About teachingAM2009/10/13 04:06 AM
About teachingJukka Larja2009/10/13 11:33 PM
About teachingAM2009/10/14 03:36 AM
About teachingJukka Larja2009/10/14 08:19 PM
About teachingAM2009/10/15 04:22 AM
About teachingSalvatore De Dominicis2009/10/12 02:23 AM
About teachingDean Kent2009/10/12 12:25 PM
About teachingSalvatore De Dominicis2009/10/13 02:11 AM
OT metadiscussionSeni2009/09/26 06:26 AM
OT metadiscussionWilco2009/09/26 08:08 AM
OT metadiscussionJukka Larja2009/09/27 02:18 AM
OT metadiscussionMichael S2009/09/27 05:12 AM
small addendumJouni Osmala2009/09/24 10:04 PM
small addendumAM2009/09/25 05:04 AM
extra stage in EV6AM2009/09/26 06:29 AM
PPC603 does OoOEhobold2009/09/08 05:40 AM
OOOE impactssomeone2009/09/08 05:39 AM
EV6AM2009/09/09 04:33 AM
OOOE and clock rateSeni2009/09/02 09:11 AM
OOOE and clock rateLinus Torvalds2009/09/02 06:48 PM
OOOE and clock rateanon2009/09/02 11:55 PM
OOOE and clock rateWilco2009/09/03 12:44 AM
OOOE and clock rateJouni Osmala2009/09/03 01:02 AM
OOOE and ItaniumAM2009/09/03 01:27 AM
OOOE and clock rateMartin Høyer Kristiansen2009/09/03 03:41 AM
OOOE and clock rateanon2009/09/03 01:12 AM
OOOE and clock rateWilco2009/09/03 02:10 AM
POWER6 skewed pipelinePaul A. Clayton2009/09/03 11:22 AM
POWER6 skewed pipelineAnon42009/09/03 07:00 PM
OOOE and clock rateMr. Camel2009/09/03 03:40 AM
OOOE and clock rateRichard Cownie2009/09/03 06:42 AM
OOOE and pipe length etc.Richard Cownie2009/09/01 09:01 AM
OOOE and pipe length etc.AM2009/09/02 01:32 AM
OOOE and pipe length etc.Richard Cownie2009/09/02 07:49 AM
LRB choice of P54AM2009/09/03 01:40 AM
LRB choice of P54Gian-Carlo Pascutto2009/09/03 01:45 AM
LRB choice of P54AM2009/09/03 03:18 AM
LRB choice of P54Gian-Carlo Pascutto2009/09/03 03:55 AM
LRB choice of P54AM2009/09/03 04:28 AM
LRB choice of P54Gian-Carlo Pascutto2009/09/03 05:29 AM
Amount of cache per core matters,and mem bandwith too (NT)Jouni Osmala2009/09/03 07:44 AM
LRB choice of P54rwessel2009/09/03 02:31 PM
LRB choice of P54AM2009/09/04 02:24 AM
LRB choice of P54anon2009/09/03 06:40 AM
LRB choice of P54a reader2009/09/03 09:20 AM
LRB choice of P54anon2009/09/03 05:57 PM
LRB choice of P54Jonathan Kang2009/09/03 02:30 PM
LRB choice of P54David Kanter2009/09/03 04:38 PM
LRB choice of P54Jonathan Kang2009/09/04 08:16 AM
LRB choice of P54anon2009/09/03 06:07 PM
LRB choice of P54AM2009/09/04 02:20 AM
LRB choice of P54Jonathan Kang2009/09/04 08:13 AM
LRB choice of P54Dan Downs2009/09/04 08:38 AM
LRB choice of P54Dan Downs2009/09/05 04:36 AM
LRB choice of P54Anon2009/09/05 02:44 PM
LRB choice of P54AM2009/09/05 12:12 AM
LRB choice of P54AM2009/09/04 02:18 AM
LRB choice of P54anon2009/09/04 08:18 PM
LRB choice of P54AM2009/09/04 11:53 PM
LRB choice of P54anon2009/09/05 04:06 AM
LRB choice of P54AM2009/09/05 09:14 AM
LRB choice of P54 - Layout?Anonymous2009/09/03 02:40 PM
LRB choice of P54 - Layout?anonymous2009/09/03 03:54 PM
LRB choice of P54Jukka Larja2009/09/03 09:58 PM
LRB choice of P54mpx2009/09/04 04:07 AM
LRB choice of P54anon2009/09/03 02:02 AM
OOOE and pipe length etc.Gian-Carlo Pascutto2009/09/03 01:40 AM
Larrabee: Pentium vs 486 vs 386Mark Roulo2009/09/03 04:26 PM
Larrabee: Pentium vs 486 vs 386Michael S2009/09/03 05:14 PM
Larrabee: Pentium vs 486 vs 386Mark Roulo2009/09/04 10:05 AM
Larrabee: Pentium vs 486 vs 386Jonathan Kang2009/09/04 10:59 AM
Larrabee: Pentium vs 486 vs 386Michael S2009/09/05 09:58 AM
Larrabee: Pentium vs 486 vs 386James2009/09/07 03:15 AM
Larrabee: Pentium vs 486 vs 386Mark Roulo2009/09/07 07:44 PM
OOOE and pipe length etc.Michael S2009/09/03 05:42 PM
LRB coreAM2009/09/04 02:09 AM
LRB coreMichael S2009/09/04 05:07 AM
LRB coreanon2009/09/04 08:27 PM
LRB coreMichael S2009/09/05 10:12 AM
LRB coreanon2009/09/05 11:03 PM
reasons for split I/D L1 cachesMichael S2009/09/06 04:10 AM
reasons for split I/D L1 cachesanon2009/09/06 06:32 AM
reasons for split I/D L1 caches?2009/09/06 10:35 AM
reasons for split I/D L1 cachesmegol2009/09/06 03:39 PM
reasons for split I/D L1 caches?2009/09/07 04:20 AM
reasons for split I/D L1 cachesanon2009/09/07 06:25 AM
cache hinting?2009/09/07 07:10 AM
cache hintinganon2009/09/07 07:35 AM
cache hinting?2009/09/07 09:10 AM
cache hintinganon2009/09/07 09:49 AM
cache hinting?2009/09/07 10:37 AM
Split and unified cachesDavid Kanter2009/09/06 01:38 PM
Split and unified cachesanon2009/09/06 11:15 PM
Split and unified cachesMichael S2009/09/07 12:40 AM
Split and unified cachesanon2009/09/07 02:24 AM
Split and unified cachesDavid Kanter2009/09/07 12:51 AM
Split and unified cachesanon2009/09/07 02:13 AM
LRB coreAM2009/09/05 12:08 AM
LRB coreLinus Torvalds2009/09/05 10:47 AM
LRB coreDavid Kanter2009/09/04 01:23 PM
LRB coreAnon2009/09/04 06:32 PM
LRB coreDavid Kanter2009/09/04 10:15 PM
LRB coreMichael S2009/09/05 10:21 AM
OOOE and cache/mem sizesa reader2009/09/01 09:19 AM
OOOE and cache/mem sizesRichard Cownie2009/09/01 09:43 AM
snapdraon?Michael S2009/08/28 06:10 AM
snapdraon?a reader2009/08/28 08:51 AM
Thanks (NT)Michael S2009/08/29 12:53 PM
snapdraon?Paul2009/08/28 01:12 PM
new POWER7 info ..EduardoS2009/08/27 03:41 PM
new POWER7 info ..Jesper Frimann2009/08/28 05:03 AM
Single threaded performanceDavid Kanter2009/08/28 10:52 AM
Hot Chips XXI Preview onlinehobold2009/08/13 07:30 AM
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