Selecting Forwarding neighbors in Wireless Ad Hoc Networks

1. Selecting Forwarding neighbors in Wireless Ad Hoc Networks A. Zelikovsky (alexz@cs.gsu.edu), GSU G. Calinescun, Illinois IT I. Mandoiu, Ga Tech P-J. Wan, Illinois IT

2. Outline • Broadcasting in ad hoc mobile networks • Flooding mechanism • Broadcast storm • Problem formulation • Algorithm • analysis • Fast Implementation • Conclusions

3. Broadcasting in Ad HocMobile Networks • Wireless ad hoc networks often need to simultaneously send the same message to everyone on the network; this operation is broadcasting. Unlike wired networks, ad hoc networks have no backbone infrastructure. Messages must be relayed in a single transmission or through intermediate nodes. • Broadcasting may be used to page a particular host, send an alarm signal, find a route to a particular host, and other similar network tasks. • A simple broadcasting method is flooding.

4. Flooding Mechanism • Each node retransmits the message to its 1-hop neighbors. Message is broadcast from the origin Message is repeated; note that some nodes receive the message three times. Message is flooded outward as outlying nodes receive and echo the message. = Origin of message = Recipients of message, 1-hop adjacent to origin = Recipients of message, 2-hop adjacent to origin = Recipients of message, 3-hop adjacent to origin

5. Broadcast Storm • Retransmissions are redundant for recipients covered by many nodes. • Heavy contention from close proximity of retransmitting nodes. • Timing of retransmissions is closely correlated and can result in collisions. When the message is first transmitted, there is no is no redundancy. = These nodes receive redundant messages sent at nearly the same time which may cause collision = The close proximity of these nodes may cause contention for space in the wireless channel

6. Problem Formulation • We can avoid broadcast storm with beaconing. • A subset of 1-hop neighbors is selected to be beacons. We want to minimize this subset = forwarding set. • Minimum Forwarding Set Problem • Given the origin of a message, there is a set of 1-hop neighbors and a set of 2-hop neighbors. • Find the Minimum Forwarding Set from the set of 1-hop neighbors such that every 2-hop neighbor is within the coverage of a Minimum Forwarding Set 1-hop neighbor = origin of message = 1-hop neighbors = 2-hop neighbors = Minimum Forwarding Set

7. Algorithm Algorithm 1: Refine Disk Covering Input:Unit-diskA, set of unit disksDcentered insideA, set of pointsP outside Asuch thatP  {D  D} Output:SubsetFDsuch thatP   {DF} • 1. Partition the exterior of A into four quadrants Q1 - Q4 by two orthogonal lines through the center of A, • such that no point in P or center of disk in D belongs to any of the lines. 2. For q = 1, … , 4, do • (a) Find the set of disks Dq = {D1, … , D|Dq|} of D which have a non-empty intersection with the interior • of Qq. For each DjDd find the two points of intersection, lj and rj, of the boundary circle of Dj with Jq, the boundary of Qq. We assume that lj < rj in a fixed orientation of Jq . • (b) Renumber the disks in Dq such that either lj < lj+1 or lj = lj+1 and rj < rj+1 for every j = 1, …, . |Dq| - 1. • Let Fq be the list of disks in Dq enumerated in this order. (c) Remove from the list Fq each disk Dj for which there is another disk Dk Fq such that lklj < rjrk. • (d) While there is a disk DjFq whose points in Qq are covered by the disks, Dp and Ds, that precede, • respectively succeed Dj in Fq, remove disk Dj from Fq (points of Dj in Fq are covered by Dp and Ds if Dj P QqDp Ds). 3. Output F = F1F2F3F4

8. l1 r2 l2 r1 l1 r2 r1 l2 Algorithm 1: Partition in 4 quadrants 2(a-b): sort wrt intersection points Q1 Q2 Q4 Q3 2(d): remove covered by two neighbors 2(c): Drop fully covered

9. Q1 Q2 Q4 Q3 Algorithm Analysis • Theorem: Algorithm Refined Disk Covering finds at most 3 times more disks than the optimum • Fact 1: in each quadrant the algorithm finds the optimum number of disks covering all points • Fact 2: Each disk may cover points in at most 3 quadrants. • Runtime: O(n2), n = # of points + neighbors

10. Faster Algorithm • Algorithm: combinatorial refinement  geometric refinement • Theorem: Algorithm Geometric Refinement finds at most 6 times more disks than the optimum • Runtime: O(n log n),n = # of points + neighbors

11. Conclusions We presented a practical algorithm for selecting forwarding neighbors in wireless ad hoc networks: • improved runtime and quality of the best previously known algorithm • O(n log n) 6-approximation algorithm • O(n2) 3-approximation algorithm