Topic: Routing and Aggregation

1. International Computer Institute UBI 532 Wireless Sensor Networks • Topic: Routing and Aggregation • An Efficient Algorithm for Finding an Almost Connected Dominating Set of Small Size on Wireless Ad Hoc Networks (Li,Peng,Chu-IEEE,October 2006) • Sercan Demirci

2. Outline • Abstract of the Paper • Introduction of the Paper • Previous Work of the Paper • The Proposed Algorithm • Performance Analysis and Simulations • Concluding Remarks

3. Abstract of the Paper • In this paper, they propose an efficient,distributed and localized algorithm for finding an almost connected dominating set of small size on wireless ad hoc networks. • Additional information: A dominating set is a subset S of a graph G such that every vertex in G is either in S or adjacent to a vertex in S.Dominating sets are widely used in clustering networks[1].

4. Abstract of the Paper(cont.) • Connected Dominating Sets: A connected dominating set (CDS) is a subsetS of a graph G such that S forms a dominating set and S is connected[1]. • Figure 1 gives an example of a CDS. Black nodes 2 and 3 are connected and cover all nodes in the network.They form a CDS for this graph[2].

5. Abstract of the Paper(cont.) • Broadcast messages can be propagated to all nodes in theCDS because of the connectivity property[2]. • The efficieny of dominating-set-based broadcasting or routing mainly depends on the overhead in constructing the dominating set and the size of the dominating set.Their algorithm can find a CDS faster and the size of the found CDS is smaller than the previous algorithms proposed in the literature.

6. Abstract of the Paper(cont.) • Although their algorithm can not guarantee the set found is actually a CDS but from their simulation results, the probabilities that the found set is a CDS are higher than 99.96%.

7. Introduction of the Paper • A wireless ad hoc network is an interconnection ofmobile computing devices, where the link between twoneighboring nodes is established via radio propagation.Neighboring nodes can communicate directly when they are within transmission range. • Communication between non-neighboring nodes requires a multi-hop routing protocol. • Wireless networks consist of static or mobile hosts that can communicatewith each other over the wireless links. • Each mobile host has the capacityto communicate directly with other mobile hosts in its vicinity.

8. Introduction of the Paper(cont.) • Design of efficient broadcasting and routing protocolsis one of the challenging tasks in ad hoc networks. • Among various existing routing and broadcasting protocols,the ones based on dominating set are very promising. • A subset of vertices in a graph is a dominating set if every vertex not in the subset is adjacent to at least one vertex in the subset. The dominating set should be connected, called CDS, for ease of the broadcasting or routing.

9. Introduction of the Paper(cont.) • The main advantage of dominating-set-based approach is that it simplifies the broadcasting or routing processto the one in a smaller subnetwork generated from theCDS. Only the dominating vertices, called forwardingnodes, need to be active. • The efficiency of dominating-set-based approach dependslargely on the time complexity for finding and maintaining a CDS and the size of the corresponding subnetwork.

10. Introduction of the Paper(cont.) • The algorithm for constructing the CDS should be efficient, distributed,and based on local information only. Since finding aminimum CDS for most graphs is NP-complete, efficientapproximation algorithms are used to find a CDS of small size. • There are many existing algorithms in the literature for broadcasting/routing in ad hoc networks using dominating-set-based approach. • These algorithms can be evaluated by the efficiency in terms of the number offorwarding nodes, reliability in terms of delivery ratio,and running time for selecting the set of forwarding nodes.

11. Introduction of the Paper(cont.) • In general, if the number of forwardingnodes is large, there will be a rather high probability tocause contention and collision. In order to increase the delivery rate, the algorithm should try to reduce the sizeof the set of forwarding nodes. • In this paper, we propose a new algorithm for finding an almost CDS on ad hoc wireless networks.

12. Introduction of the Paper(cont.) • Their algorithm generates a smaller number of forwarding nodesand the time for selecting the set of forwarding nodesis shorter compared to other algorithms. • Although the full coverage of the set of forwarding nodes cannot beguaranteed, it is almost full coverage in the sense thatthe successful rate of broadcasting using our algorithmis higher than 99.96% in all cases in our simulations.

13. Previous Work of the Paper • We consider an ad hoc network as a graph G =(V,E), where V is a set of nodes and E is a set ofbidirectional links. For each node v, N(v) = {u|(u, v) ∈E} denotes its neighbor set. Let F ⊂ V. We say F isa CDS if F is connected and V − F ⊂ N(F). • A broadcasting or routing algorithmis full coverage if the set of selected forwarding nodes is a CDS. • The key issue on designing a distributedalgorithm for broadcasting or routing on wireless ad hocnetworks is to determine a set of forwarding nodes withits size as small as possible.

14. Previous Work of the Paper(cont.) • In previously known algorithms that select a set of forwarding nodes, for each node v in the network, all pairs of neighbors of v are checked in order to determineits forwarding status. Node v is marked as forwardingnode if it has two neighbors that are not connecteddirectly. They differ in the ways of pruning techniquesthat are used to reduce the number of forwarding nodes.

15. Previous Work of the Paper(cont.) • In Wu and Li’s algorithm, two pruning rules are used to reduce the size of the resultant CDS . In rule 1, a forwarding node becomes non-forwarding if all of its neighbors are also neighbors of another node that has higher priority value. In rule 2, a forwarding node can be nonforwarding if its neighbor set is covered by two other nodes that are directly connected and have higher priority values.

16. Previous Work of the Paper(cont.) • Dai and Wu extended the Wu and Li’salgorithm by using a more general rule called Rule kin which a forwarding node becomes non-forwarding ifits neighbor set is covered by k other nodes that areconnected and have higher priority values . • Three types of priority were defined in : 0-hop priority (node id), 1-hop priority (node degree), and 2- hop priority (NCR - neighborhood connectivity ratio), and the authors concluded that sing node id as priority is more efficient and more reliable than node degree andNCR . In this paper, they use node id as the node priority value.

17. Previous Work of the Paper(cont.) • Chen proposed an algorithm, called Span, toconstruct a set of forwarding nodes, called coordinators. A node v becomes a coordinator if it has twoneighbors that cannot reach each other by either directlyconnected, indirectly connected via one intermediatecoordinator, or indirectly connected via two intermediatecoordinators. Span uses 3-hop information and cannot ensure a CDS.

18. Previous Work of the Paper(cont.) • Rieck proposed an algorithm that can be viewedas the enhanced Span . In Rieck’s algorithm, a nodev is a forwarding node if it has two neighbors thatcannot reach each other by either directly connectedor indirectly connected via one intermediate node withhigher priority than v. Rieck’s algorithm requires only2-hop information. Checking every pair requires O(d2)running time, where d is the maximum node degree of anetwork. Rieck’s algorithm also checks an intermediatenode that needs O(d) running time. Therefore, the time complexity of Rieck’s algorithm is O(d3).

19. Previous Work of the Paper(cont.) • The algorithm proposed in this paper differs withall previous algorithms by that the algorithm doesn’tcheck all pairs of its neighbors in order to determinethe forwarding status. The algorithm only check certainpairs of neighbors. So the running time of the algorithmis shorter. Furthermore, the number of forwarding nodesfound by their algorithm is significantly smaller than other algorithms.

20. The Proposed Algorithm • Full coverage of a broadcasting algorithm in ad hocnetwork can be achieved theoretically by selecting a CDSas the set of forwarding nodes. However, practically, thedelivery ratio in most of cases is lower than 100%due to collision, contention, and mobility. Therefore, it isdesirable to design a distributed broadcasting algorithmthat is efficient in selecting a small set of forwardingnodes and the running time for the selection is fastalthough the set of selected forwarding nodes might notbe a CDS with a very small probability. This is especially important for real-time applications.

21. The Proposed Algorithm(cont.) • The existing algorithms for deciding forwarding ornon-forwarding status for a node v need to check everypair of neighboring nodes of v. If there is any pairof neighboring nodes of v that are not directly connected then v will be included in the initial set of theforwarding nodes. Therefore, the initially selected CDSmight contain too many redundant nodes for forwardingthe message in broadcasting or routing. Although somepruning techniques are used to reduce the size of the selected CDS in many algorithms, the overhead is high, especially when the size of the initially selected set is large.

22. The Proposed Algorithm(cont.) • For deciding forwarding or non-forwarding status for a node v, their algorithm does not check all pairs of v’s neighbors. The number of pairs checked by the algorithm is O(d log d), where d is the maximum degree of nodes in the network.

23. The Proposed Algorithm(cont.) • The coverage rates of the networks from thesimulations were not completely satisfied. For ad hocnetworks with 40 - 200 nodes in 2000m × 2000m area,the coverage rates are between 97% and 99% in average. • To increase the coverage of the network, we shouldincrease the connectivity among the neighbors. Thisleads to the proposed algorithm in which for a node v, every neighbor of v checks log r other neighbors, wherer = deg(v) is the degree of node v.

24. The Proposed Algorithm(cont.) • The algorithm first provides acircular array of the set N(v), and then the indices ofthe neighbors are selected in an exponentially increasingfashion. If all pairs of the selected neighbors have directlinks then v is set as a non-forwarding node. • Their algorithm extends the direct links to 2-hop links as in Rieck’s algorithm. • It works as follows:

25. The Proposed Algorithm(cont.) • For each node v that has more than one neighbor, the algorithm firstarranges its neighboring nodes in a total order, for example,an increasing order of node_ids. Let the neighboringnodes of v listed in this order be v0,v1,.......,vr-1,where r = deg(v). The algorithm checks the pairs of nodes (vi,v(i+s)mod r), where i = 0, 1, . . . r − 1 and s = 2j , j = 0, 1, . . . , .If there exists a pair of nodes that are neither connected directly nor connectedvia a node u that has a higher priority than v then v is marked as forwarding node.

26. The Proposed Algorithm(cont.) • The distributed algorithm runs in O(d log d) time for 1-hop connectedness and O(d2logd) for 2-hop connectedness,respectively. Previous algorithms for 1-hop and2-hop connectedness run in O(d2) and O(d3), respectively.

27. The Proposed Algorithm(cont.)

28. The Proposed Algorithm(cont.) • The proposed distributed algorithm for each node v is shown in Algorithm 1.They use my_id and my_degree to denote node v and deg(v), respectively. In the algorithm,my_neighbor_id, an array of length deg(v), stores theids of v’s neighbors. The output of the algorithm is my_status that will be “forwarding” or “nonforwarding”.

29. The Proposed Algorithm(cont.) dd Figure 1 shows an example marked by their algorithm. The nodes with bold cycles, nodes 4,5, and 7 are forwarding nodes; the rest are non-forwarding nodes. Their algorithm marks node 0 as a non-forwarding node:

30. The Proposed Algorithm(cont.) • Node 0 has 6 neighbors: nodes 1, 2, 4, 5, 6, and 7. Their algorithm first checks whether these 6 nodes forma circular link (either 1-hop or 2-hop) in the increasingorder of node_id or not. As shown as in Table I, it does.

31. The Proposed Algorithm(cont.)

32. The Proposed Algorithm(cont.) In this figure, in addition to the circular link,the algorithm also checks the log links (the links between two nodes of distance 2j in the circular array ). Since r=deg(0)=6,only the nodes of distance 2 need to be checked.This is also listed in Table I.

33. The Proposed Algorithm(cont.) • Since all log links exist, we mark node 0 as a nonforwarding node. Notethat Rieck’s algorithm marks node 0 as a forwardingnode because nodes 2 and 6 are not connected. • For 1-hop checking, since only up to d log d links arechecked, the computing time is O(d log d). In practice,to reduce the size of the forwarding node set, we alsocheck 2-hop connection between a pair of neighbors, thatis, connected via an intermediate node. In this case, thecomputing time of the algorithm is O(d2 log d).

34. Performance Analysis and Simulations • They had done some simulations on their algorithm and Rieck’s algorithm for broadcasting on wireless ad hoc networks. Their interests here are on evaluating efficiency(the number of forwarding nodes), coverage rate (thepercentage of the forwarding nodes forming a CDS), andredundancy (the number of packets received per node).

35. Performance Analysis and Simulations(cont.) • All simulations were conducted on static networkswith a collision-free MAC layer. Each ad hoc networkis generated by randomly placing n, 100 ≤ n ≤ 400, nodes in a restricted 2000m × 2000m area. Thetransmission ranges are set to be 250m, 350m, and450m. Both algorithms check 2-hop connectedness anduse node id as priority. • For each configuration, we test 10,000 networks.

36. Performance Analysis and Simulations(cont.) Figure 4 shows the number of forwarding nodes for randomly generated ad hoc networks of node ranges from 100 to 400, and the transmission range is set to be 350m.From the figure,it is clear that their algorithm out-performs Rieck’s algorithm by reducing the • number of forwarding nodes.

37. Performance Analysis and Simulations • For other transmission ranges (250mand 450m), the results are similar to that in Figure 4.Table II lists the details.

38. Performance Analysis and Simulations(cont.)

39. Performance Analysis and Simulations(cont.) • Table III gives the coverage rate, the percentage of theforwarding nodes forming a CDS. These are obtained bydividing the number of full coverages by the total numberof trials. The worst case is that, in 10000 trials, thereare only 3 times in which the forwarding nodes do notforward packets to all nodes in the network. • They conclude that the set of forwarding nodes generatedby their algorithm is almost a CDS practically.

40. Performance Analysis and Simulations(cont.)

41. Performance Analysis and Simulations(cont.) • Figure 5 shows the broadcast redundancy, which isdefined as the average number of duplicated packetsreceived at each node when a node broadcasts a packetto all the other nodes. They only test the broadcast redundancywhen the forwarding nodes form a CDS. • In such a case, any node can act as the initial node to broadcast apacket to all the other nodes and selecting different initialnode does not affect the broadcast redundancy. Node 0was assigned as the initial node in this simulation. They can see that their algorithm has lower redundancy (higher efficiency) than Rieck’s algorithm.

42. Concluding Remarks • A new distributed algorithm for finding an almost connecteddominating set on ad hoc network was proposedand the performance was evaluated through simulations. • Although the performance is compared only to Rieck’s algorithm, it is clear that their algorithm will producesmaller set of forwarding nodes than the other CDSalgorithms under the same requirement of neighborhood information.

43. Concluding Remarks (cont.) • They did not perform pruning techniques on the generatedset of forwarding nodes in their algorithm. • It is quite obvious that the size of the resulting forwarding set willbe smaller than using the original initial-set. • Their future work includes combiningsome self-pruning techniques in their algorithm to reducefurthermore the size of the forwarding set.

44. References • [1] D.Cokuslu,K.Erciyes, and O.Dagdeviren. A Dominating Set Based Clustering Algorithm for Mobile Ad Hoc Networks. ICCS 2006,Part I,LNCS 3991,pp. 571-578,2006. • [2]T.Lin,S.Midkiff, and J.Park. Minimal Connected Dominating Set Algorithms and Application for a MANET Routing Protocol. IEEE 2003.

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