Rigorous Theory of Preprocessing UiB styreseminaret 24.10

UiB styreseminaret

FEDOR V. FOMIN

Rigorous Theory of Preprocessing

24.10.2012

Algorithms (way to do something)

I A methodical procedure for solving a problem or carrying outa task

I At the very heart of what programming is, but completelyindependent from the programing language

I Not only contribute to the way a computer runs, but they alsocontribute to the speed and effectiveness of all of thecomputer’s software, programs, commands and capabilities

Algorithms are everywhere

Algorithms are everywhere

Phyloso

phy

Can com

puters t

hink, Tu

ring test

Earth ScienceWeather prediction

Web Searching

Google's Pag

eRank algorith

m

Cryptography and

SecurityPublic Key alg

orithm, Network

Security, e-voting

ClasicsEuclid's algorithm Sieve of EratosthenesGames

Chess

Biologygene sequencing

genetic algorithmsalgorithmic life...

EconimicsRoth-Shapley Nobel prize 2012Stock trading

Medicinehealth care algorithms: diabetes management, preterm birth prevention, psychosis management

Sociologymodeling cultural evolution

determining social influence

Why some algorithms are bad?

Problem: Your electrocar has to be recharged every 70 kms. Find a shortest possible path from A to B

A

B

80

50

50

10Algorithm: Try all possible paths

and select the optimal one


2 paths 12 paths 184

8512 122816 575780564

789360053252few minutes

on supercomputer

32665984869816424 hours

on supercomputer

410442087026324968046.5 years


250000 years!!!


250000 years!!!

Moore's law: Every 2 yearsCPU speed doubles

No hope that our grand-grand…-grand-childrenbe able to find solution?

What is wrong?

We just used stupid algorithm!

I On the other hand, there are many natural algorithmicproblems around us for which no good algorithms are known!

I If we do not know a good algorithm, is it because of ourmental constrains or this is because no such algorithm exists?

P vs NP

I Most of the fundamental questions in Computer Science andMathematics: Is P6= NP?

I Millenium Problems of Clay Mathematical Insititute.

$ 1.000.000 Question

Preprocessing

I Algorithms with humble goals: not solving the problem; justtrying to simplify it

Preprocessing. Chess Example

8

7

6

5

4

3

2

1

a b c d e f g h

Figure 1: King, Queen, Bishop, kNight, Rook and Pawn

1

- White to start and to mate in two moves

Preprocessing. Chess Example

8

7

6

5

4

3

2

1

a b c d e f g h


1

8

7

6

5

4

3

2

1

a b c d e f g h


1

Preprocessing. Train management

- We want a minimum-sized subset of stations S such that every train stops at least at one station from S


- Rule 1 If S(t) ⊆ S(t′), then remove t

S(t)={B,D}S(t')={B}

Reduction Rules:

t

t′

A

B

C

D


- Rule 2 If T (s) ⊆ T (s′), then remove s

Reduction Rules:A

B

C

D


K.Weihe, ALEX, 1998: Similar preprocessing for real-world datafrom the German and European train schedules (25.000 stations,154.000 trains and 160.000 single train stops) the data reductionmerely took a few minutes to reduce the original, huge input graphinto a graph consisting of disjoint components of size at most 50.

Preprocessing is ubiquitous

I Commercial linear program solvers like CPLEX

I Navigation systems

I Microarray data analysis for the classification of cancer types

I ...

Theory of Computing for the 21st century

“While theoretical work on models of computation andmethods for analyzing algorithms has had enormouspayoff, we are not done. In many situations, simplealgorithms do well. We don’t understand why! It isapparent that worst-case analysis does not provide usefulinsights on the performance of algorithms and heuristicsand our models of computation need to be furtherdeveloped and refined.”

Condon, Edelsbrunner, Emerson, Fortnow, Haber, Karp,Leivant, Lipton, Lynch, Parberry, Papadimitriou, Rabin,Rosenberg, Royer, Savage, Selman, Smith, Tardos, andVitter, Challenges for theory of computing: Report for anNSF-sponsored workshop on research in theoretical computer science,1999.

About the project

I The main research goal of this project is the quest for rigorousmathematical theory explaining the power and failure ofheuristics/preprocessing.

I This is a fundamental-research-project but this research canhave a strong impact on the development of new algorithmsfor the real world applications.

Fundamental research: Not so uncommon opinion

Fundamental research is a way to receive money for

doing nothing

Another opinion

"People cannot foresee the future well enough to predict what's going to develop from basic research. If we only did applied research, we would still be making

better spears." George Smoot

Basic research lays down the foundation for the applied science: when basic work is done first, then applied spin-offs often eventually result

from this research.

This project

I We have a phenomena: an important family of algorithmsthat often work well. Nobody knows why and when.

I If we understand this phenomena, good chance we would beable to create many useful algorithms

Quality of research

What is good and what is bad?

Quality of research

Quality of education

About the project. Data

I 2.227.000 EUR to cover

I 6 years of PhD (2 positions) and 8 years of Researchassistants at postdoctoral level

I 50% of my salary

About the project. Data

I UiB gives 4.219.985 NOK (25% of ERC)

I Plans were to have 4 years of Research assistants atpostdoctoral level

What has been changed in my (personal) life

I Got flowers from Research Department

I Salary increased (+1 on government scale)

I Met the rector

I Has to learn many new things about paper work: finance andadministration.

I Know where to buy bed linens, towels, etc.

I Less time for family

What has been changed in my (professional) life

I Research environment — the best one can imagine

I Prof. Pinar Heggernes & Jan Arne Telle; Prof. Saket Saurabh(ERC Starting grant, starts from Jan.1), Daniel Lokshtanov(Moon fond) + bright PhD students and postdocs.

I For five years I will be able to work on interesting, and Ibelieve, important things

Future?

I Bergen as the Norwegian centre of fundamental research inInformatics

I Some help can be required.

Rigorous Theory of Preprocessing UiB styreseminaret 24.10

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