Algorithmic Models of Wireless Communication Magns M Halldrsson

Algorithmic Models of Wireless Communication Magnús M. Halldórsson Reykjavik University, Iceland EWSCS, 7 March, 2013 11/1

It’s Wireless World GSM 3 G Wi. Fi Ad-hoc P 2 P Wi. Max Mobility Sensor networks Ambient Ubiquitous Pervasive EWSCS, 7 March, 2013 11/2

Algorithmic Agenda • How to model wireless communication – Particularly, interference – Capture realism – Analytically feasible • How to solve fundamental problems – Algorithmic strategies – Structural properties • Modus operandi: – Ignore constant factors EWSCS, 7 March, 2013 11/3

MODELS OF INTERFERENCE EWSCS, 7 March, 2013 11/4

Tradeoffs in Models Realism Generality Models Usability for algorithms Usability for analysis EWSCS, 7 March, 2013 11/5

Models for Interference • Two standard models in wireless networking Protocol Model (graph-based, simpler) Physical Model (SINR-based, more realistic) EWSCS, 7 March, 2013 11/6

CS Models: e. g. Disk Model (Protocol Model) Reception Range Interference Range EWSCS, 7 March, 2013 11/7

Inductive independence • There is a disc that intersects at most 3 mutually non-overlapping discs • Efficient 3 -approximate algorithms for: – Independent set (maximize throughput) – Coloring (minimize latency) – Weighted independent set (maximize sustained throughput) EWSCS, 7 March, 2013 11/8

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EE Models: e. g. SINR Model (Physical Model) EWSCS, 7 March, 2013 11/10

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Hard instances for traditional graph-based models • One link per slot, in graph-based models • Single slot, in physical model (with appropriate power control) EWSCS, 7 March, 2013 11/12

Signal transmission • Radio signal diminishes as it travels • In the ideal case, the path loss is proportional to where d : distance : path loss constant (usually, 2 < < 6), depends on medium EWSCS, 7 March, 2013 11/13

=2 Uniform power Affectance u 2 3. 5 u 0. 16 5 5 w 2. 04 w H, Wattenhofer ‘ 09 EWSCS, 7 March, 2013 11/14

=2 Power control Affectance u 2 Pu = 1 3. 5 u 0. 48 5 5 Pw = 3 w 0. 68 w H, Wattenhofer ‘ 09 EWSCS, 7 March, 2013 11/15

=2 Affectance v u 3 3 u 0. 56 4 4 0. 56 3 w w EWSCS, 7 March, 2013 11/16

Core problems of wireless scheduling • Given: A set of communication links Capacity problem: Find the maximum size feasible subset of links EWSCS, 7 March, 2013 11/17

Core problems of wireless scheduling • Given: A set of communication links Capacity problem: Find the maximum size feasible subset of links Scheduling problem: Partition the links into fewest possible slots EWSCS, 7 March, 2013 11/18

The job of the MAC layer • MAC : Media Access Control • The nodes in a wireless network communicate over a shared resource: the spectrum • The task of the MAC layer is to coordinate access to the spectrum: – Who gets to talk when EWSCS, 7 March, 2013 11/19

Results on Capacity and Scheduling Capacity has constant-factor approximations for: • Uniform power in R 2, with >2. [Goussevskaia, H, Wattenhofer, Welzl‘ 09] • Any (reasonable) fixed power in general metrics [H, Mitra, SODA‘ 11] • Arbitrary power control [Kesselheim, SODA‘ 11] – Also, more recently, with power limitations [Wan‘ 12, Kesselheim‘ 12] • Uniform power with spectrum sharing (cognitive radio) [H, Mitra‘ 12] • Fixed power with variable data rates [Kesselheim‘ 12] • Uniform power with a distributed learning algorithm [Asgeirsson, Mitra ‚‘ 11] Scheduling has constant-factor approximation for: • Linear power [Fanghanel, Kesselheim, Vöcking’ 09; Tonoyan‘ 11] • Equal-length links [Goussevskaia, Oswald, Wattenhofer, ’ 07; H ‘ 09] EWSCS, 7 March, 2013 11/20

Weighted degree of v Weighted inductiveness • A link lv in a set S is t-good if av(S)+a. S(v) ≤ t. • A set of links is is t-inductive independent if any subset contains a t-good link • [H, Holzer, Mitra, Wattenhofer, SODA’ 13] Any set of links in any metric is O(1)-inductive independent, except possibly when using uniform power. • Applications: – – – Capacity algorithms (Multi-hop) distributed scheduling Connectivity Spectrum sharing auctions [Hoefer, Kesselheim, Vöcking ‘ 11, ‘ 12] Dynamic packet scheduling Kesselheim, Vöcking, DISC‘ 10 EWSCS, 7 March, 2013 11/21

EXPERIMENTAL WORK EWSCS, 7 March, 2013 11/22

Experimental Work „Putting theory to the test“ EWSCS, 7 March, 2013 11/23

Testbed experimentation EWSCS, 7 March, 2013 11/24

Experimental Group Ýmir Vigfússon Students Helga Guðmundsóttir Henning Úlfarsson Eyjólfur Ingi Ásgeirsson Joe Foley Sveinn Fannar Kristjánsson Axel Guðmundsson Sindri Magnússon EWSCS, 7 March, 2013 11/25

Theory Group • Pradipta Mitra, post-doc • Marijke Bodlaender, Ph. D. student • Hörður Ingi Björnsson, M. S. student • Eyjólfur Henning • Magnús EWSCS, 7 March, 2013 11/26

Other Collaborators • Sverrir Ólafsson, prófessor, Reykjavik University – Previously at British Telecom • Roger Wattenhofer, prófessor, ETH Zurich • Berthold Vöcking, prófessor, TU Aachen EWSCS, 7 March, 2013 11/27

Questions? Slides: Thanks to Wattenhofer Lab, ETH EWSCS, 7 March, 2013 11/28