1. Clustering Murat Demirbas SUNY Buffalo

2. 2 Challenges for scalability of wireless sensor networks Energy constraint : Sending a message is expensive; depletes battery 1000x faster  Communication-efficient programs are needed Distribution of controller : Centralized solutions or predefined controllers are unsuitable  Ad hoc and efficient distribution of control are needed Faults : Message losses & corruptions, nodes fail in complex ways  Locally self-healing programs are needed

3. 3 Clustering for scaling: why and how? Why ?  Enables efficient and scalable distribution of controllers  Saves energy and reduces network contention by enabling locality of communication How ?  Should be locally-healing  To confine faults and changes within that part of the network  Should produce approximately equal-sized clusters  To achieve an even distribution of controllers  Should result in minimum overlaps  To avoid overhead of reporting to many clusterheads

4. 4 Solid-disc clustering Solid-disc clustering:  All nodes within a unit distance of the clusterhead belong only to that cluster  All clusters have a nonoverlapping unit radius solid-disc Why ?  Reduces intra-cluster signal contention  clusterhead is shielded at all sides with members, does not have to endure over-hearing nodes from other clusters  Yields better spatial coverage with clusters  aggregation at clusterhead is more meaningful since it is median of the cluster  Results in a guaranteed upper bound on the number of clusters

5. 5 Challenges for local healing of solid-disc clustering Equi-radius solid-disc clustering with bounded overlaps is not achievable in a distributed and local manner ) ((( ( )) ) ( ( ( ( ) ) )) cascading new node A B

6. 6 Our contributions Solid-disc clustering with bounded overlaps is achievable in a distributed and local manner for approximately equal radius  Stretch factor, m≥2, produces partitioning that respects solid-disc  Each clusterhead has all the nodes within unit radius of itself as members, and is allowed to have nodes up to m away of itself FLOC is locally self-healing, for m≥2  Faults and changes are contained within the respective cluster or within the immediate neighboring clusters (precisely within m+1 units)

7. 7 Our contributions … By taking unit distance to be the reliable communication radius and m be the maximum communication radius, FLOC  exploits the double-band nature of wireless radio-model  achieves communication- and energy-efficient clustering FLOC achieves clustering in O(1) time regardless of the size of the network  Time, T, depends only on the density of nodes and is constant  Through analysis, simulations, and implementations, we suggest a suitable value for T for achieving fast clustering without compromising the quality of resulting clusters

8. 8 Outline Model Justification for m≥2 Basic FLOC program Extended FLOC program Simulation & implementation results Concluding remarks

9. 9 Model Undirected graph topology Radio model is double-band *  Reliable communication within unit distance = in-band  Unreliable communication within 1 < d < m = out-band Nodes have i-band/ o-band estimation capability  Time of flight of audio for ranging, or  RSSI-based using signal-strength as indicator of distance Fault model  Fail-stop and crash  New nodes can join the network  Transient corruption of state and messages *Zhao-Govindan(03), Woo-Tong-Culler(03)

10. 10 Self-stabilization A program is self-stabilizing iff after faults stop occurring the program eventually recovers to a state from where its specification is satisfied. A self-stabilizing program is fault-local self-stabilizing if the time and number of messages required for stabilization are bounded by functions of perturbation size rather than the network size.  Perturbation size for a given state is the minimum number of nodes whose state must change to achieve a consistent state of the network.

11. 11 Problem statement A distributed, local, scalable, and self-stabilizing clustering program, FLOC, to construct network partitions such that  a unique node is designated as a leader of each cluster  all nodes in the i-band of each leader belong to that cluster  maximum distance of a node from its leader is m  each node belongs to a cluster  no node belongs to multiple clusters

12. 12 Justification for stretch factor > 2 For m≥2 local healing is achieved: a new node is  either subsumed by one of the existing clusters,  or allowed to form its own cluster without disturbing neighboring clusters (( ( )) ) ) new node subsumed (( ( ( )) ) ) (( ( ) ) ))( )( new cluster

13. 13 Basic FLOC program Status variable at each node j:  idle : j is not part of any cluster and j is not a candidate  cand : j wants to be a clusterhead, j is a candidate  c_head : j is a clusterhead, j.cluster_id==j  i_band : j is an inner-band member of a clusterhead j.cluster_id  o_band :j is an outer-band member of j.cluster_id The effects of the 6 actions on the status variable:

14. 14 FLOC actions 1.idle Λ random wait time from [0…T] expired  become a cand and bcast cand msg 2.receiver of cand msg is within in-band Λ its status is i_band  receiver sends a conflict msg to the cand 3.candidate hears a conflict msg  candidate becomes o_band for respective cluster 4.candidacy period Δ expires  cand becomes c_head, and bcasts c_head message 5.idle Λ c_head message is heard  become i_band or o_band resp. 6.receiver of c_head msg is within in-band Λ is o_band  receiver joins cluster as i_band

15. 15 FLOC is fast Assumption: atomicity condition of candidacy is observed by T Theorem: Regardless of the network size FLOC produces the partitioning in T+ Δ time. Proof:  An action is enabled at every node within at most T time  Once an action is enabled at a node, the node is assigned a clusterhead within Δ time  Once a node is assigned to a clusterhead, this property cannot be violated  action 6 makes a node change its clusterhead to become an i-band member, action 2 does not cause clusterhead to change

16. 16 Selection of T To achieve atomicity of elections, ensure (with a high probability) that for a node j whose idle-timer expires, the idle timers of none of the nodes within 2 units of j expire within next Δ time The probability of atomicity of elections is (1- Δ/T) w  w is the maximum number of nodes within 2 units of a node As seen from the formula T is independent of network size

17. 17 Self-stabilization of FLOC Invariant of FLOC For all j,k 1. j.idle \/ j.cand ≡ j.cluster_id= ┴ 2. j.c_head ≡ j.cluster_id=j 3. j.i_band Λ j.cluster_id=k  k.c_head Λ j in i-band of k 4. j.o_band Λ j.cluster_id=k  k.c_head Λ j in o-band of k 5. k.c_head Λ j in i-band of k  j.i_band Λ j.cluster_id=k

18. 18 Stabilization actions 1.I1 is locally corrected 2.I2 is locally corrected 3.Clusterhead send heartbeats for detecting any violation of I3 & I4 4.For correcting I3 & I4 leases are used, on expiration node returns to idle state 5.Violation of I5 is detected when node receives a c_head_msg as an i-band; a demote message is sent to both clusterheads 6.Upon receiving demote, the clusterheads return to idle state

19. 19 FLOC is fault-locally stabilizing I1 and I2 are locally detected and corrected Correction of I3 and I4 are local to the node A violation of I5 is reduced to violation of I3 and I4 for the nodes that are at most m+1 distance to j Once the invariant is satisfied due to locality of clustering reclustering is achieved locally

20. 20 FLOC is locally-healing… Node failures  inherently robust to failure of non-clusterhead members  clusterhead failure dealt via S3 and S4  effects contained within at most m Node additions  either join existing cluster, or  form a new cluster without disturbing immediate neighboring clusters, or  if the new node is within i-band of multiple clusterheads, S5 and S6 ensure stabilization

21. 21 Extensions to basic FLOC algorithm The extended FLOC algorithm ensures that solid-disc property is satisfied even when atomicity of candidacy are violated occassionally Insight: Bcast is an atomic operation  The candidate that bcasts first locks the nodes in the vicinity for Δ time  The later candidates become idle again by dropping their candidacy when they find some of the nodes are locked 4 additional actions to implement this idea

22. 22 Simulation for determining T Prowler, realistic wireless sensor network simulator  MAC delay 25ms Tradeoffs in selection of T  Short T leads to network contention, and hence, message losses  Tradeoff between faster completion time and quality of clustering Scalability wrt network size  T depends only on the node density  In our experiments, the degree of each node is between 4-12  a constant T is applicable for arbitrarily large-scale networks Code is at www.cse.buffalo.edu/~demirbas/floc

23. 23 Tradeoff in selection of T

24. 24 Constant T regardless of network size

25. 25 Implementation Mica2 mote platform, 5-by-5 grid Confirms simulation

26. 26 Sample clustering with FLOC

27. 27 Related work LEACH does not satisfy solid-disc clustering FLOC complements LEACH  FLOC addresses network contention problem at clusterheads  LEACH style load-balancing readily applicable in FLOC  via probabilistic rotation function for determining the waiting-times for candidacy announcements FLOC is the first time the solid-disc property is achieved

28. 28 Concluding remarks FLOC is  Fast : clustering is achieved in constant time, T+Δ  Locally self-healing : changes and faults are confined within the immediate cluster

29. Energy-efficient communication protocol for WSN Wendi Rabiner Heinzelman, Anantha Chandrakasan, and Hari Balakrishnan

30. 30 Model The base station is fixed and located far from the sensors  Communication with the base station is expensive All nodes in the network are homogeneous and energy constrained  No high-energy nodes Transmit and receive costs are approximately equal  the energy to power the radio dominates both costs

31. 31 Adaptive clustering:  Nodes take turn to be cluster-heads.  After a fixed period (round) cluster heads are changed. Dynamic clusters for different rounds  Some nodes become the cluster head.  Other nodes choose a cluster to join. LEACH protocol

32. 32 Percentage of clusterheads Optimal percentage of clusterheads is determined empirically

33. 33 LEACH Algorithm Each round is divided into 4 phases –Advertisement phase –Cluster set up phase –Schedule Creation phase –Data transmission phase Multiple Clusters problem –Transmission in one cluster may corrupt transmission in a nearby cluster. –Use CDMA to solve. – But CDMA is unavailable in almost any of the platforms.

34. 34 Advertisement Phase Cluster Set up Phase Schedule Creation Phase Data Transmission Phase “ Me Head !!!” (CSMA-MAC) “I am with you” (CSMA-MAC) “Here’s your time slot” “ Thanks for the time slot, Here’s my data” (TDMA) After decide which cluster it joins, each node informs the cluster-head Based on the number of nodes in the cluster, the cluster-head node creates a TDMA schedule telling each node when it can transmit. This schedule is broadcast back to the nodes in the cluster. To reduce energy consumption non- cluster-head nodes: Use minimal amount of energy chosen based on the strength of the cluster-head advertisement. Can turn off the radio until their allocated transmission time. Every node chooses a random number (R) and compute a threshold T(n). T(n) = P/(1-P*(r mod(1/P)) if n element of G, = 0 else P – desired percentage of cluster heads (e.g. 5%) r – the current round G – set of nodes that have not been cluster head in the last 1/P rounds It elects itself as a cluster-head if R < T(n) Every cluster-head broadcast an advertisement message, with the same transmit energy. Non-cluster-head node decide which cluster it joins in this round based on the received signal stregth. Largest strength  closer  minimal enery needed for communication.

35. 35 Simulation results

36. 36 Simulation results… DirectMTELEACH