1. 1 The Power of Non-Uniform Wireless Power ETH Zurich – Distributed Computing Group Magnus M. Halldorsson Reykjavik University Stephan Holzer ETH Zürich Pradipta Mitra Reykjavik University Roger Wattenhofer ETH Zürich TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AA A AA A Presented by Klaus-Tycho Förster Slides by Stephan Holzer and Roger Wattenhofer ETH Zürich

2. ETH Zurich – Distributed Computing Group Stephan HolzerSODA 2013 Wireless Communication

3. ETH Zurich – Distributed Computing Group Stephan HolzerSODA 2013 Wireless Communication EE, Physics Maxwell Equations Simulation, Testing ‘Scaling Laws’ Network Algorithms CS, Applied Math [Geometric] Graphs Worst-Case Analysis Any-Case Analysis

4. ETH Zurich – Distributed Computing Group Stephan HolzerSODA 2013 Interference Range CS Models: e.g. Disk Model (Protocol Model) Reception Range

5. ETH Zurich – Distributed Computing Group Stephan HolzerSODA 2013 5

6. EE Models: e.g. SINR Model (Physical Model)

7. ETH Zurich – Distributed Computing Group Stephan HolzerSODA 2013

8. Signal-To-Interference-Plus-Noise Ratio (SINR) Formula Minimum signal- to-interference ratio Power level of sender u Path-loss exponent Noise Distance between two nodes Received signal power from sender Received signal power from all other nodes (=interference)

9. ETH Zurich – Distributed Computing Group Stephan HolzerSODA 2013 The Capacity of a Network (How many concurrent wireless transmissions can you have)

10. ETH Zurich – Distributed Computing Group Stephan HolzerSODA 2013 … is a well-studied problem in Wireless Communication The Capacity of Wireless Networks Gupta, Kumar, 2000 [Toumpis, TWC’03] [Li et al, MOBICOM’01] [Gastpar et al, INFOCOM’02] [Gamal et al, INFOCOM’04] [Liu et al, INFOCOM’03] [Bansal et al, INFOCOM’03] [Yi et al, MOBIHOC’03] [Mitra et al, IPSN’04] [Arpacioglu et al, IPSN’04] [Giridhar et al, JSAC’05] [Barrenechea et al, IPSN’04] [Grossglauser et al, INFOCOM’01] [Kyasanur et al, MOBICOM’05] [Kodialam et al, MOBICOM’05] [Perevalov et al, INFOCOM’03] [Dousse et al, INFOCOM’04] [Zhang et al, INFOCOM’05] etc…

11. ETH Zurich – Distributed Computing Group Stephan HolzerSODA 2013 The Capacity of a Network (How many concurrent wireless transmissions can you have) Power control helps: arbitrarily better than uniform power (worst case) Arbitrary power: O(1)-Approximation Complex optimization problem Simpler ways?

12. ETH Zurich – Distributed Computing Group Stephan HolzerSODA 2013 Oblivious Power (usually: small constant) This Paper

13. ETH Zurich – Distributed Computing Group Stephan HolzerSODA 2013 Old Definitions v w

14. ETH Zurich – Distributed Computing Group Stephan HolzerSODA 2013 New Crucial Definitions

15. ETH Zurich – Distributed Computing Group Stephan HolzerSODA 2013 Structural Property * *= for non-weak links

16. ETH Zurich – Distributed Computing Group Stephan HolzerSODA 2013 Algorithm

17. ETH Zurich – Distributed Computing Group Stephan HolzerSODA 2013 Applications any p-power

18. ETH Zurich – Distributed Computing Group Stephan HolzerSODA 2013 Applications any p-power

19. ETH Zurich – Distributed Computing Group Stephan HolzerSODA 2013 Applications

20. ETH Zurich – Distributed Computing Group Stephan HolzerSODA 2013 Summary SINR-model capacity max. Length- oblivious power 3 (out of >5) applications

21. ETH Zurich – Distributed Computing Group Stephan HolzerSODA 2013 Thanks!