The Algorithm Shop

1. Medium Access Control CC-MAC CSMA-MPS B-MAC CMAC BitMAC μ-MAC BMA AI-LMAC ARC • Empirical tests • Numerical evaluations • Theoretical proofs for stationary settings G-MAC f-MAC FLAMA DMAC E2-MAC HMAC EMACs LMAC LPL MMAC MR-MAC PicoRadio PCM PACT MFP PMAC O-MAC PMAC The Algorithm Shop Ad Hoc Networks Looking for a MAC protocol

2. Relocation Analysis of Stabilizing MAC Algorithmsfor Large-Scale Mobile Ad Hoc Networks Pierre Leone, Geneva (Switzerland) Marina Papatriantafilou, Chalmers (Sweden) Elad Michael Schiller, Chalmers (Sweden)

3. Challenges Collisions When neighboring nodes simultaneously broadcast Collision Collision Collision Collision Collision Collision

4. Challenges Collisions Mobile nodes Random moves

5. Challenges Collisions Mobile nodes Random moves Possibly adversarial

6. Challenges Collisions Mobilenodes Transient faults Modeling the location of mobile nodes Arbitrary violations of the assumptions that model the locations Short-lived malfunctions hardware/software

7. Opportunities Synchronization Clock synchronization algorithms and/or GPS

8. Opportunities Synchronization Wireless broadcast A powerful primitive ensuring that: Nodes reach nearby nodes and receive the same messages

9. Our approach Stabilization Assume that after the last transient fault the system state is random Steady state behaviors do not depend on that random state • Natural self-stabilizing extensions • arbitrary starting state • guaranteed system recovery • using periodic restarts • Our negative results hold for self-stabilizing systems

10. 1 2 3 Negative Results Bounded Relocation Rate Relocation Analysis Outline

11. Relocation Analysis Random moves Each mobile node randomly moves in the Euclidian plane Two mobile nodes can directly communicate if their distance is less than a threshold

12. Relocation Analysis Random moves Evolving graphs Ferreira’04, Avin et al.’08 G=(G1, G2, …) In time t , graph Gt ∊ G models the communications and interferences • In the short run • Gt , Gt+1 ∊ G • Many mobile nodes have similar neighborhoods in Gt and Gt+1 • e.g., large communication radius In the long run this similarity disappears There are independent random relocationsof the mobile nodes e.g., Gt,Gt+x are independent when x → ∞

13. Relocation Analysis Between Gt, Gt+1∊ G, α|V| nodes relocate to new neighborhoods α∊in [0, 1] is the relocationrate Relocating nodes and their new neighborhoods are chosen randomly • Random moves • Evolving graphs • Relocation rate

14. Relocation Analysis Between Gt, Gt+1∊ G, α|V| nodes relocate to new neighborhoods α∊in [0, 1] is the relocationrate Relocating nodes and their new neighborhoods are chosen randomly • Random moves • Evolving graphs • Relocation rate • Our assumptions are different from: • Random walks • do not consider short-term (independent) random relocations • Population protocols • do not consider long-term neighborhood similarity

15. Relocation Analysis Between Gt, Gt+1∊ G, α|V| nodes relocate to new neighborhoods α∊in [0, 1] is the relocationrate Relocating nodes and their new neighborhoods are chosen randomly Low rate = less collisions • Random moves • Evolving graphs • Relocation rate

16. Relocation Analysis Between Gt, Gt+1∊ G, α|V| nodes relocate to new neighborhoods α∊in [0, 1] is the relocation rate Relocating nodes and their new neighborhoods are chosen randomly High rate=more collisions • Random moves • Evolving graphs • Relocation rate

17. Relocation Analysis Between Gt, Gt+1∊ G, α|V| nodes relocate to new neighborhoods α∊in [0, 1] is the relocation rate Relocating nodes and their new neighborhoods are chosen randomly • Random moves • Evolving graphs • Relocation rate • Useful in analyzing MAC algorithms • Random relocation causes unexpected interferences • Expressiveness • A single parameter defines the rate of unexpected interferences • Simpler proofs than Kinetic models

18. 2 1 3 Relocation Analysis Bounded Relocation Rate Negative Results Outline

19. Impossibility Result Collision Claim 1: There is no efficient and deterministic MAC algorithm

20. Impossibility Result Collision Collision Focus on randomized MAC algorithms Claim 1: For arbitrary relocation rate, there is no efficient and deterministic MAC algorithm

21. Lower Bound Focus on bounded relocation rate Claim 2: For arbitrary relocation rate, oblivious strategies are the best that you can hope for … Oblivious strategies ignore the broadcast history • Consider random relocation of all nodes after every algorithm step • Learning the history is of no use 

22. 1 2 Relocation Analysis Negative Results Outline 3 Bounded Relocation Rate

23. Throughput Related Trade-off Oblivious Ignores the history of broadcasts

24. Throughput Related Trade-off Oblivious Non-oblivious P = P = P = P = • E.g., based on vertex-coloring • Luby '93

25. Throughput Related Trade-off Collision P = P = P = P = Can I use ? Can I use ? Can I use ? Can I use ? • Oblivious • Non-oblivious • E.g., based on vertex-coloring • Luby '93 • Color uniqueness: • A node has a color different than its neighbors, i.e., no collisions I will pick another one I will pick another one Great! I will keep Great! I will keep

26. Throughput Related Trade-off E.g., based on vertex-coloring Luby '93 Color uniqueness: A node has a color different than its neighbors, i.e., no collisions P = • Oblivious • Non-oblivious Next round

27. Throughput Related Trade-off Oblivious Non-oblivious Trade-off Critical-threshold relocation rate Above which oblivious is better Below which non-oblivious is better Simplifying assumptions • No dependencies among neighbors • All relocations occur once in every round • Collision detection is easy Broadcasts can inform about color choices Later today: Remove these assumptions

28. Simplifying assumptions • No dependencies among neighbors • All relocations occur once in every round • Collision detection is easy Broadcasts can inform about color choices Later today: Remove these assumptions Collision Collision Collision At most ~α|V| nodes are expected to no longer have unique colors after a round From Stationary to Non-stationary How many nodes no longer have unique colors after a round? • Uniform distribution of colors • Assume uniformityin the starting configuration • Show uniformity in every configuration that follows

29. Using the vertex-coloring algorithm (1- β)≅1/e From Stationary to Non-stationary How many nodes start having unique colors after a round? • Let y be the number of nodes with conflicting colors • Let(1- β)y be theexpected number of nodes whose colors become unique within a broadcasting round

30. From Stationary to Non-stationary • Convergence • When the recovery is slower than the relocation (1 - β) < α Recovery Conflicting Unique Relocation

31. From Stationary to Non-stationary • Convergence • When the recovery is slower than the relocation (1 - β) < α • When the relocation is slower than the recovery (1 - β) > α Recovery Conflicting Unique Relocation

32. Simplifying assumptions non-obliviousstrategy • No dependencies among neighbors • All relocations occur once in every round • Collision detection is easy Broadcasts can inform about color choices Later today: Remove these assumptions 80% Oblivious strategy 60% We discover a critical-threshold relocation rate Guaranteed throughput of non-oblivious strategies Too good to be true! We remove the simplifying assumptions and bound the recovery ratio (1- β)∊[σ(1- α) ,1/e], whereσ=(5+3/e)/32 40% 20% 0.2 0.2 0.4 0.4 0.6 0.6 0.8 0.8 Eventual Throughput Throughput Relocation Rate α

33. CSMA/CA Existing Approaches Such as Herman Tixeuil ‘04 Divided ratio time Overhead TDMA time slots Overhead Overhead • CSMA/CA in overhead part for • Local leader election • Vertex coloring • When nodes relocate in every broadcasting round • No guarantees for leader election

34. Existing Approaches CSMA/CA RTS/CTS dialog Request to Send / Clear to Send Facilitates short exposure time period during which a transmitted packet might be intercepted shorter than a time slot Defer RTS

35. Existing Approaches CSMA/CA RTS/CTS dialog Request to Send / Clear to Send Facilitates short exposure time period during which a transmitted packet might be intercepted shorter than a time slot Defer Defer RTS CTS

36. Existing Approaches CSMA/CA RTS/CTS dialog Request to Send / Clear to Send Facilitates short exposure time period during which a transmitted packet might be intercepted shorter than a time slot Defer Defer Data ACK

37. Our Approach Divided time slots Competition part MaxRnd rounds DATA part Competition rounds Competition rounds Competition rounds Competition rounds DATA packet DATA packet DATA packet DATA packet slot 1 slot 2 slot 3 slot 4 round 4 round 3 Max competition rounds, e.g., MaxRnd = 4 round 2 round 1

38. Our Approach Divided time slots Round based competition Recovery is facilitated because of: • Simple winner and losers • “Unlucky winners” and “lucky losers” Neighbors may choose the same slot On the k competition round, • competitors send RTS with probability 2 (k-MaxRnd ) Competition part Data part Time slot

39. Our Approach Divided time slots Round based competition Neighbors may choose the same slot On the k competition round, competitors send RTS with probability 2(k-MaxRnd ) Simple winner and losers The simple winner chooses the slot as its “permanent” one The simple losers are aware of the winner’s broadcast and continue to look for other broadcasting slots DATA RTC CTS Competition part Data part Time slot

40. Our Approach Divided time slots Round based competition Collision “Unlucky winners” and “lucky losers” “Unlucky winners” are not aware of their coalitions and continue to compete for this slot on the next round “Lucky losers” are aware of the winners’ collisions and stop competing for this slot on the next round DATA DATA RTC RTC CTS Neighbors may choose the same slot On the k competition round, • competitors send RTS with probability 2(k-MaxRnd ) Competition part Data part Time slot

41. Our Approach Divided time slots Round based competition Simplifying assumptions • No dependencies among neighbors • All relocations occur once in every round • Collision detection is easy Broadcasts can inform about color choices Later today: Remove these assumptions Simple winner and losers + “Unlucky winners” + “Lucky losers” = Recovery rate of (5+3/e)/8 • Recovery rate of (5+3/e)/8 • Recovery rate of (1- α) (5+3/e)/8 • Recovery rate of (1- α) (5+3/e)/32 Neighbors may choose the same slot On the k competition round, • competitors send RTS with probability 2(k-MaxRnd ) Competition part Data part Time slot

42. Medium Access Control CC-MAC CSMA-MPS B-MAC CMAC BitMAC μ-MAC BMA AI-LMAC ARC G-MAC The good news: the algorithm possibly can migrate from stationary settings to non-stationary ones Consider your favorite decentralized vertex-coloring algorithm f-MAC FLAMA DMAC E2-MAC HMAC EMACs LMAC LPL MMAC MR-MAC PicoRadio PCM PACT MFP PMAC O-MAC PMAC The Algorithm Shop Confused?! Let us help you! Looking for a MAC protocol

43. Conclusions • Novel throughput-related trade-off • between oblivious and non-oblivious strategies • depends on the relocation rate of mobile nodes • Circumventing the difficulties of • collision detection • modeling the locations of mobile nodes • A study of a fault-tolerant and “stateful” algorithm • Extendable to consider self-stabilization

44. Algosensors’09: 5th International Workshop onAlgorithmic Aspects of Wireless Sensor Networks July 10-11, 2009

45. Thank you for your attention Contact info. elad@chalmers.se TR-2008:23, Department of Computer Science and Engineering, Chalmers University of Technology