Download presentation

Presentation is loading. Please wait.

Published byClarissa claudia Ketch Modified over 3 years ago

1
Introduction Complexity Theory 2002/03. Peter van Emde Boas KNOW YOUR NUMBERS ! The Impact of Complexity Peter van Emde Boas ILLC-FNWI-UvA 2003 See: http://staff.science.uva.nl/~peter/teaching/ct03.html

2
Introduction Complexity Theory 2002/03. Peter van Emde Boas Moore’s Law in action © Scientifi American 274, 199601, p45 Computation speed doubles every 1.5 years Corresponding rate of increase of Memory capacity

3
Introduction Complexity Theory 2002/03. Peter van Emde Boas 19821985

4
Introduction Complexity Theory 2002/03. Peter van Emde Boas 19861988

5
Introduction Complexity Theory 2002/03. Peter van Emde Boas 19901992

6
Introduction Complexity Theory 2002/03. Peter van Emde Boas 19941996

7
Introduction Complexity Theory 2002/03. Peter van Emde Boas 19982000

8
Introduction Complexity Theory 2002/03. Peter van Emde Boas 2003

9
Introduction Complexity Theory 2002/03. Peter van Emde Boas Is it really so nice ? sum := 0 for i = 1 to N do sum := sum + a[i] ; print ( sum ) Back in 1977 this would work in less than a second for N = 10 000 Can we deal with N = 400 000 000 today within a second ? sum := 0 for i = 1 to N do j:= index[i] ; sum := sum + a[j] ; print ( sum ) And what about this one ?

10
Introduction Complexity Theory 2002/03. Peter van Emde Boas Information must be moved! Source: Ph.d. Thesis Stefan Manegold Understanding, Modeling, and Improving Main-Memory Database Performance UvA Dec 16, 2002

11
Introduction Complexity Theory 2002/03. Peter van Emde Boas Information must be moved! Source: Ph.d. Thesis Peter A. Boncz Monet; A next-Generation DBMS Kernel for Query-Intensive Applications UvA Mei 31, 2002

12
Introduction Complexity Theory 2002/03. Peter van Emde Boas Know your numbers ! # InstructionsTime 1 0000.00001 sec 1 000 0000.01 secInvisible 10 000 0000.1 secPerceptive 100 000 0001 sec 1 000 000 00010 sec 10 000 000 000100 secCoffee 100 000 000 00016.7 minChat 1 000 000 000 0002 hr 47 minWHAARGH! 10 000 000 000 00027 hrthe Limit!! 100 000 000 000 00011.25 daysHopeless 1 000 000 000 000 0004 months 10 000 000 000 000 0003.33 yearsUnrealistic 100 000 000 000 000 00033 years 1 000 000 000 000 000 0003.3 century Processing times on a 100 MIPS system 1 day = 86400 sec1 000 000 sec ≈ 11 days 1 year ≈ 31 536 000 sec1 000 000 000 sec ≈ 35 years

13
Introduction Complexity Theory 2002/03. Peter van Emde Boas WHAT IS COMPLEXITY ? Relation between size of the input instance and the time required for solving this instance. Traversing a listLinearO(n) SortingO(n.logn) Multiplication QuadraticO(n 2 ) Matrix multiplicationCubicO(n 3 ) Truth table checkingExponentialO(2 n ) Naive TSPO(n!) What can be done in principle can become undoable in practice Order of growth is more relevant than the implicit constants

14
Introduction Complexity Theory 2002/03. Peter van Emde Boas The Order of growth 1020501002001000 n.00001.00002.00005.0001.0002.001 n.logn.00003.00008.00027.0006.0016.01 n 2.0001.0004.0025.01.041 n 3.001.008.1251816 min 2 n.001131 y??!!?*6min Time on a 1 MIPS system in seconds (unless stated otherwise)

15
Introduction Complexity Theory 2002/03. Peter van Emde Boas Impact of the faster machine n 1000 times as large n.logn 500 - 1000 times as large n 2 31 times as large n 3 10 times as large 2 n add 10 to input size That’s why Edmonds stated his thesis: Effective ==> Polynomial Time Complexity

16
Introduction Complexity Theory 2002/03. Peter van Emde Boas A Fallacy ?? If computation speed doubles every 2 years we can perform (2 N - 1) M operations in 2N years, where M is the number of operations performed in the first 2 years. So why worry about exponential time algorithms ?? What is wrong with this argument ?

Similar presentations

OK

$100 $200 $300 $400 $500 $100 $200 $300 $400 $500 $100 $200 $300 $400 $500 $100 $200 $300 $400 $500 $100 $200 $300 $400 $500 $100 $200 $300.

$100 $200 $300 $400 $500 $100 $200 $300 $400 $500 $100 $200 $300 $400 $500 $100 $200 $300 $400 $500 $100 $200 $300 $400 $500 $100 $200 $300.

© 2018 SlidePlayer.com Inc.

All rights reserved.

To ensure the functioning of the site, we use **cookies**. We share information about your activities on the site with our partners and Google partners: social networks and companies engaged in advertising and web analytics. For more information, see the Privacy Policy and Google Privacy & Terms.
Your consent to our cookies if you continue to use this website.

Ads by Google

Ppt on indian retail industry 2010 Ppt on 2 dimensional figures and 3 dimensional slideshow Ppt on antenatal care Ppt on enterprise resource planning Ppt on antibiotic resistance mechanism Ppt on ufo and aliens history Ppt on teachers day free download Ppt on email etiquette Ppt on hybrid air conditioning Ppt on travels and tourism