NODES NODES Offering Dynamics to Emerging Structures Offering - - PowerPoint PPT Presentation

NODES

Offering Dynamics to Emerging Structures

NODES

Offering Dynamics to Emerging Structures

February 31st, 2011 Andreas Cord-Landwehr Peter Kling Friedhelm Meyer auf der Heide Peter Pietrzyk

NODES - Offering Dynamics to Emerging Structures Algorithms and Complexity 1

HEINZ NIXDORF INSTITUTE

University of Paderborn Algorithms and Complexity

System of nodes (organized as graph) Nodes only have local knowledge Nodes have a common goal We have two kinds of dynamics

1

Controlled Dynamics: Nodes can change the system (add/remove edges, change weights, colors, IDs,. . . )

2

External Dynamics: The system changes and nodes must react to changes (positions, weights, values,. . . )

The Goal: Strategies to solve global tasks by using local operations and dynamics.

The Idea

Solve tasks locally, improve solutions by dynamics

NODES - Offering Dynamics to Emerging Structures Algorithms and Complexity 2

HEINZ NIXDORF INSTITUTE

University of Paderborn Algorithms and Complexity

initial graph r a n d

• m

g r a p h

The Problem Networks can have very weak structures and leav- ing of single nodes can destroy connectivity. Idea: random graphs are very robust and maintain high connectivities.

Flip

An Example

How to get robust networks by local operations?

NODES - Offering Dynamics to Emerging Structures Algorithms and Complexity 3

HEINZ NIXDORF INSTITUTE

University of Paderborn Algorithms and Complexity

initial graph r a n d

• m

g r a p h

The Problem Networks can have very weak structures and leav- ing of single nodes can destroy connectivity. Idea: random graphs are very robust and maintain high connectivities. The FLIP Operation for each edge (with low probability) execute FLIP-operation then any graph converges to random graph in O(n5)

Flip

An Example

How to get robust networks by local operations?

NODES - Offering Dynamics to Emerging Structures Algorithms and Complexity 3

HEINZ NIXDORF INSTITUTE

University of Paderborn Algorithms and Complexity

Analysis of Local Strategies

What can be achieved locally? How can results be improved by local operations? Which knowledge is necessary to yield “good” results?

Theoretical and Experimental Analysis

How to design experiments? What are the worst-cases? Can we prove them? Which upper/lower bounds can we prove?

Possible Topics clusterings, colorings, spanners, communication, reliability. . . Applications

Sensornetworks, overlay-networks, “The Internet” Everywhere (in dynamic environments) where centrally controlled algorithms are infeasible

Backgrounds and Applications

What we are interested in, and why?

NODES - Offering Dynamics to Emerging Structures Algorithms and Complexity 4

HEINZ NIXDORF INSTITUTE

University of Paderborn Algorithms and Complexity

Interesting Issues: We discuss and select together interesting and challenging issues

→ you have the choice!

Locality and Dynamics: Only few local strategies are known and formally investigated

→ you work on top of current research!

Stategies: You design stategies and algorithms to solve the selected issues Analysis: Developed strategies are evaluated. . .

by experiments (simulations) by theoretical analysis

Simulator: In order to gain insights into our strategies we need a simulator

→ we create or extend one

In Short: We carry out Research together!

Focus and Assignment

The framework to be filled with your interests

NODES - Offering Dynamics to Emerging Structures Algorithms and Complexity 5

HEINZ NIXDORF INSTITUTE

University of Paderborn Algorithms and Complexity

Registration Mail to Andreas Cord-Landwehr (cola@uni-paderborn.de) (additional to registration in PAUL) Advisory Located in Research Group “Algorithms and Complexity”: Andreas Cord-Landwehr Peter Kling Friedhelm Meyer auf der Heide Peter Pietrzyk Internal Organization (planning state) First meeting at end of March (seminar topics, get in touch) Lectures are hold in April/Mai Block-seminar will take place in Mai. . . . . . following a 2-day PG Workshop Simulator Submission: August/September 2011 The project ends in March 2012

Organization

NODES - Offering Dynamics to Emerging Structures Algorithms and Complexity 6

HEINZ NIXDORF INSTITUTE

University of Paderborn Algorithms and Complexity

Thank you for your attention! Thank you for your attention!

Algorithms and Complexity Heinz Nixdorf Institute & Department of Computer Science University of Paderborn Address: Fürstenallee 11 33102 Paderborn Germany Phone: +49 5251 60-6427 Fax: +49 5251 60-6482 E-mail: cola@uni-paderborn.de Web: http://wwwhni.upb.de/en/alg/

NODES - Offering Dynamics to Emerging Structures Algorithms and Complexity 7

HEINZ NIXDORF INSTITUTE

University of Paderborn Algorithms and Complexity