© Yamacraw, 2001 Selecting Forwarding neighbors in Wireless Ad Hoc Networks A. Zelikovsky GSU G. Calinescun, Illinois IT I. Mandoiu, Ga Tech P-J. Wan, Illinois IT

© Yamacraw, 2001Outline Broadcasting in ad hoc mobile networks Flooding mechanism Broadcast storm Problem formulation Algorithm –analysis Fast Implementation Conclusions

© Yamacraw, 2001 Broadcasting in Ad Hoc Mobile 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.

© Yamacraw, 2001 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

© Yamacraw, 2001 = These nodes receive redundant messages sent at nearly the same time which may cause collision 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. = The close proximity of these nodes may cause contention for space in the wireless channel

© Yamacraw, 2001 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 = 2-hop neighbors = 1-hop neighbors = origin of message = Minimum Forwarding Set

© Yamacraw, 2001Algorithm Algorithm 1: Refine Disk Covering Input: Unit-disk A, set of unit disks D centered inside A, set of points P outside A such that P   {D  D } Output: Subset F  D such that P   {D  F } 1. Partition the exterior of A into four quadrants Q 1 - Q 4 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 D q = { D 1, …, D |D q | } of D which have a non-empty intersection with the interior of Q q. For each D j  D d find the two points of intersection, l j and r j, of the boundary circle of D j with J q, the boundary of Q q. We assume that l j < r j in a fixed orientation of J q. (b) Renumber the disks in D q such that either l j < l j+1 or l j = l j+1 and r j < r j+1 for every j = 1, …,. |D q | - 1. Let F q be the list of disks in D q enumerated in this order. (c) Remove from the list F q each disk D j for which there is another disk D k  F q such that l k  l j < r j  r k. (d) While there is a disk D j  F q whose points in Q q are covered by the disks, D p and D s, that precede, respectively succeed D j in F q, remove disk D j from F q (points of D j in F q are covered by D p and D s if D j  P  Q q  D p  D s ). 3. Output F = F 1  F 2  F 3  F 4

© Yamacraw, 2001Algorithm Q1Q1 Q3Q3 Q4Q4 Q2Q2 1: Partition in 4 quadrants 2(c): Drop fully covered 2(d): remove covered by two neighbors 2(a-b): sort wrt intersection points l1l1 l2l2 r2r2 r1r1 l1l1 l2l2 r2r2 r1r1

© Yamacraw, 2001 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(n 2 ), n = # of points + neighbors Q1Q1 Q3Q3 Q4Q4 Q2Q2

© Yamacraw, 2001 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

© Yamacraw, 2001Conclusions 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(n 2 ) 3-approximation algorithm