HEINZ NIXDORF INSTITUTE University of Paderborn Algorithms and Complexity NODES NODES Offering Dynamics to Emerging Structures Offering Dynamics to Emerging Structures February 31 st , 2011 Andreas Cord-Landwehr Peter Kling Friedhelm Meyer auf der Heide Peter Pietrzyk NODES - Offering Dynamics to Emerging Structures Algorithms and Complexity 1
The Idea HEINZ NIXDORF INSTITUTE University of Paderborn Solve tasks locally, improve solutions by dynamics 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 Controlled Dynamics: Nodes can change the system (add/remove edges, change 1 weights, colors, IDs,. . . ) External Dynamics: The system changes and nodes must react to changes (positions, 2 weights, values,. . . ) The Goal: Strategies to solve global tasks by using local operations and dynamics. NODES - Offering Dynamics to Emerging Structures Algorithms and Complexity 2
Flip An Example HEINZ NIXDORF INSTITUTE University of Paderborn How to get robust networks by local operations? Algorithms and Complexity initial graph The Problem Networks can have very weak structures and leav- ing of single nodes can destroy connectivity. r a n d o m g r a p h Idea: random graphs are very robust and maintain high connectivities. NODES - Offering Dynamics to Emerging Structures Algorithms and Complexity 3
An Example HEINZ NIXDORF INSTITUTE University of Paderborn How to get robust networks by local operations? Algorithms and Complexity initial graph The Problem Networks can have very weak structures and leav- ing of single nodes can destroy connectivity. r a n d o m g r a p h 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 ( n 5 ) Flip NODES - Offering Dynamics to Emerging Structures Algorithms and Complexity 3
Backgrounds and Applications HEINZ NIXDORF INSTITUTE University of Paderborn What we are interested in, and why? 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 NODES - Offering Dynamics to Emerging Structures Algorithms and Complexity 4
Focus and Assignment HEINZ NIXDORF INSTITUTE University of Paderborn The framework to be filled with your interests 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! NODES - Offering Dynamics to Emerging Structures Algorithms and Complexity 5
HEINZ NIXDORF INSTITUTE Organization 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 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
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