1. UCLA ENGINEERING Computer Science School of EECS, Peking University On Heterogeneous Neighbor Discovery in Wireless Sensor Networks Lin Chen † ♠, Ruolin Fan ∗, Kaigui Bian † Lin Chen #, Mario Gerla ∗, Tao Wang † and Xiaoming Li † † Peking University, Beijing, China ♠ Yale University, New Haven, CT, USA * UCLA, Los Angeles, CA, USA # University Paris-Sud, Orsay, France

2. UCLA ENGINEERING Computer Science School of EECS, Peking University A BRIEF INTRODUCTION TO NEIGHBOR DISCOVERY

3. UCLA ENGINEERING Computer Science School of EECS, Peking University Find the Neighbors to Form a Network

4. UCLA ENGINEERING Computer Science School of EECS, Peking University Power Conservation Keep radios off, turn on periodically

5. UCLA ENGINEERING Computer Science School of EECS, Peking University ND Protocol Determines the Pattern by Which Each Radio Turns ON or OFF 000001000001000001… 010000001010000001… Node A (6) Node B (2, 9) Duty Cycle: Percentage of 1 period in which a sensor/radio is active Node A’s DC = 1/6; Node B’s DC = 2/9 Period = 6 Period = 9

6. UCLA ENGINEERING Computer Science School of EECS, Peking University 010000001010000001… ND Protocol Determines the Pattern by Which Each Radio Turns ON or OFF 000001000001000001… Node A (6) Node B (2, 9) A viable neighbor discovery protocol must either implement clock synchronization or be robust in the face of clock drifts

7. UCLA ENGINEERING Computer Science School of EECS, Peking University Goals 1.Guarantee neighbor discovery within a reasonable time frame 2.Minimize the number of time slots for which the node is awake to save energy 3.Match the nodes’ awake-sleep schedules with their heterogeneous battery duty cycles as closely as possible (ie. Finer duty cycle granularity)

8. UCLA ENGINEERING Computer Science School of EECS, Peking University SOME EXISTING ND PROTOCOLS

9. UCLA ENGINEERING Computer Science School of EECS, Peking University ND Protocol Types Probabilistic Protocols  Exploits the birthday paradox  Non-deterministic: No upper bound on discovery latency Quorum Based Protocols  Exploits the geometry of a 2-D array Co-primality Based Protocols  Exploits the Chinese Remainder Theorem (CRT)

10. UCLA ENGINEERING Computer Science School of EECS, Peking University Quorum ND Protocols 1111 1 1 1 11 1 Period = 16 Duty Cycle = 7/16 Arrange time slots into a matrix formation Choose 1 row and column as the “on” slots  This ensures that nodes operating on the same duty cycle (ie. Homogeneous nodes) will discover each other within bounded time Latest development: Searchlight

11. UCLA ENGINEERING Computer Science School of EECS, Peking University Co-Prime ND Protocols Theorem: A Co-primality based neighbor discovery protocol guarantees discovery for any two nodes for any amount of clock drifts if the associated integer sets of the nodes in this network satisfy the co-prime pair property, with the worst-case discovery delay bounded by the product of the two smallest co-prime numbers, one from each set

12. UCLA ENGINEERING Computer Science School of EECS, Peking University Co-Prime ND Protocols Example from the theorem: 2 nodes with wakeup schedules of 3 and 2, respectively 100100 101010010101 Time drift by 1 time slot A: 3 B: 2 In reality, each node chooses 2 different numbers and combine their wake-up slots  Solves the problem of 2 nodes choosing the same number Latest development: Disco (only choose prime numbers)

13. UCLA ENGINEERING Computer Science School of EECS, Peking University HEDIS (QUORUM) VS TODIS (CO- PRIME)

14. UCLA ENGINEERING Computer Science School of EECS, Peking University HEDIS - The Optimized Quorum Protocol HEterogeneous DIScovery Protocol Asynchronous periodic slot-based protocol Uses n x (n-1) time slots  n depends upon the desired duty cycle δ  n ≈ 2/δ  Duty cycle granularity: 2/n  The n’s must be of the same parity to guarantee discovery  Protocol dictates all odd or all even  Example: even protocol, δ = 7% = 7/100  2/(7/100) = 200/7 ≈ 28 = n In this case, 2/n = 2/28 ≈ 0.071 Radio on for:  Slots numbered n x i  Slots numbered (n+1) x i, where i = 0, 1, 2, …, n-2

15. UCLA ENGINEERING Computer Science School of EECS, Peking University HEDIS Theorem Theorem: HEDIS guarantees neighbor discovery within bounded latency for any two nodes with the same-parity parameters n and m, given any amount of clock drift between their schedules. The average discovery latency is O(nm)

16. UCLA ENGINEERING Computer Science School of EECS, Peking University HEDIS Example 0123 4567 891011 n 1 = 4: 4x3 slots 012345 67891011 121314151617 181920212223 242526272829 n 2 = 6: 6x5 slots 01234567891011 0123456789101112131415…23242526272829 0 0 …

17. UCLA ENGINEERING Computer Science School of EECS, Peking University TODIS – The Optimized Co-Prime Protocol Triple-Odd DIScovery Protocol Duty cycle granularity too high if only prime numbers are chosen to ensure co-primality (DISCO) Observation: all prime numbers (except for 2) are odd  Odd integers are likely to be co-prime Each node chooses consecutive odd integers  Example: N a = {33, 35}; N b = {5, 7}  gcd(35, 5) = 5; gcd(35, 7) = 7  gcd(33,5) = 1 => co-prime; gcd(33, 7) = 1 => co-prime

18. UCLA ENGINEERING Computer Science School of EECS, Peking University TODIS Continued Two consecutive odd integers does not guarantee co-primality for many number combinations less than 100: {33, 35}, {75, 77}  All possible pairs yield gcd > 1 Three consecutive odd integers will do the trick  Smallest counterexample: {1600023, 1600025, 1600027} and {2046915, 2046917, 2046919} Supports duty cycle of 3(n 2 -n-1)/(n(n 2 -4)) ≈ 3/n

19. UCLA ENGINEERING Computer Science School of EECS, Peking University PERFORMANCE EVALUATION

20. UCLA ENGINEERING Computer Science School of EECS, Peking University A Comparison of ND Protocols Protocol NameParameter Restriction Average Discovery Delay Supported Duty Cycles DISCOPrime p 1, p 2, p 3, p 4 O(min{p 1 p 3, p 1 p 4, p 2 p 3, p 2 p 4 }) 1/p 1 + 1/p 2 U-ConnectPrime p 1, p 2 O(p 1 p 2 )(3p 1 +1)/2p 1 2 SearchlightPower multiples of t 1, t 2 O(t 1 t 2 )2/t 1 2 HEDISSame parity n, mO(nm)2/n TODISOdd n, mO(nm)3(n 2 -n-1)/(n(n 2 -4)) ≈ 3/n

21. UCLA ENGINEERING Computer Science School of EECS, Peking University Duty Cycle Matching - Errors Small Duty Cycles: 1, 1/2, 1/3, …, 1/100Large Duty Cycles: 0%, 1% 2%, 3%, …, 100%

22. UCLA ENGINEERING Computer Science School of EECS, Peking University CDFs of Discovery Latency

23. UCLA ENGINEERING Computer Science School of EECS, Peking University CONCLUSION

24. UCLA ENGINEERING Computer Science School of EECS, Peking University Conclusion We explore the current two main approaches of designing a heterogeneous ND protocol: quorum and co-primality We design HEDIS and TODIS, a quorum and co-primality protocol respectively Both can match battery duty cycles at a high granularity (2/n and ∼ 3/n) HEDIS performs better than TODIS in discovery latency

25. UCLA ENGINEERING Computer Science School of EECS, Peking University Thank You! Questions?