SECTOR BASED MULTICAST ROUTING ALGORITHM FOR MOBILE AD-HOC NETWORKS

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1 SECTOR BASED MULTICAST ROUTING ALGORITHM OR MOBILE AD-HOC NETWORKS Murali Paramewaran 1 and Chittaranjan Hota 2 1 Department of Computer Science & Information Sytem, BITS-Pilani, Pilani, India 2 Department of Computer Science & Information Sytem, BITS-Pilani, Hyderabad, India ABSTRACT Multicat routing algorithm for mobile ad-hoc network have been extenively reearched in the recent pat. In thi paper, we preent two algorithm for dealing with multicat routing problem uing the notion of virtual force. We look at the effective force exerted on a packet and determine whether a node could be conidered a a Steiner node. The node' location information i ued to generate virtual circuit correponding to the multicat route. QoS parameter are taken into conideration in the form of virtual dampening force. The firt algorithm produce relatively minimal multicat tree under the et of contraint. We improve upon the firt algorithm and preent a econd algorithm that provide improvement in average reidual energy in the network a well a effective cot per data packet tranmitted. In thi paper, the virtual-force technique ha been applied for multicat routing for the firt time in mobile ad-hoc network. KEYWORDS Network Protocol, Wirele Network, Mobile Network, Routing Protocol, Multicating, 1. INTRODUCTION A mobile ad-hoc network (MANET) involve independent node that are rapidly deployed in an environment. Thee mobile node mut make the correct routing deciion in the preence of node mobility, tranient link failure and energy and other contraint. In the event of ending multiple copie of the ame information to multiple node, ue of multicat routing i the preferred option. Depending on how the ditribution path among multicat group member are created, multicat routing protocol can be claified into tree-baed, meh-baed and hybrid multicat routing protocol [1]. Tree-baed protocol can further be ub-divided into ource-tree and core-tree protocol. In our algorithm, we take the middle path by letting the multicat tree be created by the initial packet in tranit. The creation of multicat tree can be equated with the Steiner tree problem. Steiner tree problem for a graph G(V,E) i the problem of finding a tree panning all node in Q, where Q V, uch that the length of the reultant tree i minimized [2],[3]. The et of node S, where S V, S Q = ϕ, are known a Steiner node. A Steiner minimal tree contructed for a local ub-graph of a G need not be part of the minimal tree contructed for the entire graph [2]. Steiner tree problem i known to be NP-complete for planar graph. Approximation algorithm like the one given in [4] have been uggeted for the Steiner tree problem. A related notion i to claify a tree a relatively minimal Steiner tree. In a relatively minimal Steiner tree, the length of DOI : /ijwmn

2 the tree i minimal for the pecific et of node choen to be part of the tree. The problem of multicating reduce to finding a minimal Steiner tree in a graph. The tak of a multicat routing problem i to determine the correct et of Steiner node S o that the tree can reach all terminal node in Q. or efficient communication, any multicat tree created mut at leat be relatively minimal. In our approach, we attempt to determine a relatively minimal Steiner tree with the help of virtual force approach. The notion of virtual force had been explored in deployment problem in wirele enor network [5],[6], and in routing in MANET [7]. In the virtual force approach (VA), the participating node and/or the packet in tranit are applied with ome electric charge. The electrotatic force are computed and the routing deciion i made baed on the magnitude and direction of the reultant force. Poduri, et al. [5] demontrated the ue of a combination of attractive and repulive force for olving enor deployment problem in wirele enor network. Liu, et al. [7],[8] ued the concept of virtual force in unicat routing for MANET. In the routing algorithm for MANET, the reultant force i ued only to make a deciion to move the packet forward. Our main contribution in thi paper i the ue of virtual force in multicat routing for MANET. The notion of virtual force i ued to guide the packet toward the detination. The effective force on the packet i a um of contributing force value from the detination, the ource node and the packet itelf. In addition to the forward guiding force, we ue dampener to limit choice of the next node in the path to accommodate QoS parameter. The combined reult of thee force will let the packet know whether it i currently in a Steiner node. The reultant force will be toward the node that will be in the path to the majority of the detination node in one direction of a branch in the multicat tree. In thi paper, we have ued the virtual force technique for multicating. While attempting to ue the technique for multicating, we identified everal new iue that were not preent in unicat routing algorithm. The firt algorithm propoed in thi paper deal with directly impoing the virtual force technique for MANET. We provide a refined algorithm that ue virtual force in a lightly different manner. We divide the region around the current node into ector and perform a virtual-force baed multicat routing on each of the ector. Multicat routing uing virtual force technique i attempted for the firt time in thi paper. A far a we know, no other paper ha uggeted the ue of ector of variable arc-length for performing multicat routing, in conjunction with the virtual force technique. The remainder of the paper i organized a follow: ection 2 decribe the related work for our algorithm. Section 3 provide overall decription of the technique, along with baic idea, aumption ued and the modelling detail. Section 4 decribe the firt algorithm propoed, viz. multicat routing algorithm uing virtual-force. Section 5 decribe the detail of the ector-baed virtual force-baed multicat routing algorithm. Section 6 contain the imulation reult, while ection 7 conclude the paper. 2. RELATED WORKS Gilbert, et al. in [2] had put forth the criteria that the angle between out-going edge at a branch node for a Steiner node i 120. A relatively minimal Steiner tree i a Steiner tree when thi angle i greater than or equal to 120 for all internal node. In their paper, they have uggeted an inductive property for contructing relatively minimal Steiner tree with the help of unit tenion force from the group node. However, in a real-world network, we do not have control over the location of variou node in the network. Thu, we hould ideally be chooing branching node uch that the angle between the out-going edge are exactly 120, but till be able to handle cae where appropriate node are not available in thoe poition. 50

3 Mauve, et al. uggeted a multicat routing algorithm uing geometric information in [9]. Their greedy algorithm ue a heuritic dependent on the normalized number of next hop neighbour to determine whether a branching node in multicat tree ha been reached. The parameter λ ued in their algorithm determine how late the plit of the multicat forwarding will take place, with λ = 0 indicating an early plit and λ 1 for a very late plit. otopoulou, et al. [10] uggeted the ue of geo-circuit for unicat routing. They computed the unicat path from ource to detination baed on greedy poition-baed trategy and aigned a virtual circuit number to uch path. Once a geo-circuit wa etablihed, they re-ued thi geocircuit to end future packet to the detination till the end of traffic or till the path i updated due to node mobility. The idea of uing geographic virtual circuit can be ued for multicating a well, with a few minor reviion in the route caching ytem. Liu, et al. uggeted two routing algorithm, SWING [8] and SWING+ [7], for unicat routing in MANET baed on the notion of mall world network. Thee algorithm expanded the notion of virtual circuit a decribed by otopoulou, et al. [10] to include long virtual logical link to the urrounding neighbourhood of the current node with the help of virtual force. Thee two protocol were the firt unicat routing protocol to ue virtual force to compute the path toward detination. By computing the repulive force exerted on the neighbour of the current node, the next hop neighbour wa choen a the node with the maximum repulive force from the ource node toward the detination node. They demontrated that their approach work efficiently in a 3-D environment, a well. In thi paper, we extend the notion of virtual-force uggeted by Liu, et al. for multicat routing. Rahman et al. [11] divided the region around the current node into quadrant, and conidered four cloet node in each quadrant for determining the next hop in the multicat tree. Their contention wa that a plit in multicat packet will occur when the detination node belong to multiple quadrant around the current node. They later expanded their algorithm in [12] ued an intelligent energy matrix to increae the average life of the node in the network. Their algorithm provide a very reaonable length of the multicat tree. However, we found that by tatically fixing the quadrant, their algorithm wa generating lightly longer multicat tree. The notion of virtual force a decribed in [7] cannot be ued directly for the multicat routing problem. If we apply electrical charge in only the ource node and the packet, a wa decribed in Liu, et al. [7], we found that we could not really accommodate for multiple detination typical in a multicating environment. Initially, when we attempted to apply the electrical charge in detination node and the packet in tranit, we found that the packet wa moving toward a forceequilibrium poition over and over again, increaing the likelihood of loop in the multicat tree. Alo, upporting QoS parameter in a multicat route i lightly different than adding it in a imple virtual circuit becaue of the nature of path etablihment. Intead of limiting the deciion into fixed quadrant around the current node, a decribed in Rahman, et al. [12], we dynamically divide the region around the current node into α ector baed on the direction of the effective force due to the node in the multicat group. In thi paper, we have devied imple mechanim to adapt the concept of virtual circuit into the multicat environment. 3. MULTICAST ROUTING USING THE VIRTUAL ORCE TECHNIQUE In thi ection, we tart with a dicuion on the aumption and baic working of our multicat routing algorithm with the help of the virtual force technique. We then introduce the ytem model ued. 51

4 3.1. Aumption We aume that location information i available in all node in the network and that all node in the network will become eventually aware of location and mobility information. Mot off-thehelf product currently come with GPS facility. Our algorithm aume that there i an appropriate data tructure that can tore thi location information. Such a data tructure will allow look-up of node location from the node' addre. A far a proper working of the algorithm i concerned, the location information in the immediate vicinity of the current node need to be accurate. There can be light impreciion in the location value of farther node, a the algorithm only compute the bet likely member of the multicat route for the farther node. A the query for computing the multicat route reache cloer to the actual detination(), the intermediate node can divert the query appropriately a it i aumed that the cloer node will have more accurate information. All mobile node are aumed to be having omni-directional antenna, a i the cae with mot of the off-the-helf device. A our algorithm relie on the neighbourhood information derived from the Hello protocol, all mobile node need not be in the ame plane Baic Idea In thi algorithm, we aign poitive charge to ender, the multicat detination, and the packet. The packet i placed at a virtual point near the ender node, and will be guided by the effective repulive force to move toward the node in the multicat group. All the other node are given a tentative charge baed on QoS parameter. When a packet reache node u, we need to decide whether u i a branching node (a node at which the multicat tree branche) or not. If u i a branching node, we need to determine the number of branche to be taken, and the pecific neighbour that will become part of the branch. If u i not a branching node, then we need to determine which of the neighbour in the forwarding direction ha to be choen for the next hop. Let M be the et of node that are part of the multicat group. At the node u, we compute the effective force exerted on the packet due to node belonging to M, M. We take the direction of ˆ M a the forward direction. We compute the effective force on each of the k neighbouring node v 1, v 2,..., v k in neighbourhood et of the current node, N u, by taking into account the cumulative effect of dampening force( E ), u and M. By looking at the effective force on the neighbour, vi we determine the p neighbour w 1, w 2,..., w p which form part of the multicat route, and forward the query to them Sytem Model Liu, et al. [7] defined Equation 1 for computing the virtual force the current node v to the detination v d, where d max i the maximum ditance meaure, and d(v,v d ) i a meaure of ditance between v and v d. Thi equation i ufficient for dealing with a unicat tranmiion, and for the computation of imple, point-to-point force between any two node. However, for a multicat tranmiion, we need to expand the notion to incorporate all the multicat group node. det ( v v ) d d( v, v ), d max d = (1) 52

5 Alternatively, a definition of detination force a given in Equation 2 can alo be ued, where Q i a large contant charge value aigned for eae of computation. Thi i a minor modification of Equation 4 in [7]. det 2 Q, (2) d( v, v ) ( v vd ) =, v vd d At any node in the network, we compute the effective force on the node u due to the current et of detination, M, a hown in Equation 3. Here, i effective force on the node u exerted by all u, M the node in the et of current multicat detination, M. = u, M u, d d M (3) Apart from thi force acting on the packet, there i a force component from the ource node and a dampening force caued by other parameter determining the choice of the next node. The effective force on the packet p at node u i given in Equation 4. = + p, u u. M E u (4) The dampening force E produced by the node u depend on the variou QoS parameter that are u conidered. If k parameter are conidered, the weightage of the i th parameter i α i, the value of the parameter i in the node u i δ u i, the requeted value for the QoS parameter i δ req and the maximum value allowed for that parameter i λ max, then the value of the dampening force at node u i given by Equation 5. Here, for each parameter i, 0 β i 1 and β i = 1. E u ( ) i δ req δ i = u ˆ, u i max α (5) λ igure 1. A ample multi-cat plit node. 53

6 4. MULTICAST ROUTING ALGORITHM USING VIRTUAL-ORCE In thi ection, we dicu the deign of the Multicat Routing Algorithm uing Virtual-force (MRAV) and it peudo-code A ample working of MRAV igure 1 how the node u that need to multicat to ix member of the multicat group M={D1,D2,D3,D4,D5,D6} repreented a circle. Other member of the MANET are indicated a black bubble. Viable communication link are indicated uing line. The node u ha five neighbouring node, namely A, B, C, E and. Let u conider the example of a multicat from node u to the et of detination node depicted in igure 1. The packet at node u experience virtual force a a reult of interaction with all the ix detination node. The direction of the force i indicated with the help of arrow in the figure. We firt compute the effective force on the packet that i currently at node u to each of the detination node. The arrow in the figure indicate the direction of the force vector due to the ix detination. By computing the effective force on the node, we can compute the general forward direction of the node. The igure 2(a) how the variou force value on the current node, u, of the network hown in igure 1. Here the reultant force at the node u i computed a vector addition of all force at the point correponding to node u. or the purpoe of illutration, let u aume that the forward direction, which i the direction of the reultant force, i toward D3. igure 2(b) how the cumulative um of force along the axe at node u. Since there are detination force affecting more than two direction in igure 2(b), it can be inferred that the node u i a branching node, alo termed a a plit node. It now ha to decide which among the node in it neighbourhood et (N u ) will form part of the multicat route. (a) igure 2(a). The virtual force exerted by the detination on node u. (b) Effecting force along axe. Let u have four ubet of the detination et M, named a M 1, M 2, M 3 and M 4, indicating the et of detination node that had contributed to the force vector upward, rightward, downward and leftward repectively. In igure 2(b), the element belonging to the ubet are indicated along with the force component to which they contribute. It can be een that D6 belong to the (b) 54

7 detination ubet M 3, M 2 contain {D4, D5} and M 4 contain {D1, D2}. M1 contain D2, D3, D4, and D5. rom igure 2(b), it can be inferred that only the detination D6 i contributing to the downward direction, which i the direction oppoite to the direction of the effective force at u. Alo, in a clockwie direction tarting from the left-ide, it can be oberved that the angle between D1 and D6 i greater than 180. Becaue of the factor that it i the only node in ubet M 3 a well a being more than 120, D6 i conidered eparate from the remaining et of detination node. To reach D6, the relevant neighbour of u are the node E and. If E i choen a a multicat forwarding node for u, then both detination D5 and D6 can be erved through it. In our algorithm, all node that are within ± 60 from the direction of the choen force vector are conidered to be part of the ame general path toward multicat et. The Query meage i forwarded to node E, with detination et a {D5, D6} When the multicat route query reache the node E, it identifie that D6 i it neighbour. So the node E directly communicate the query meage to D6. To communicate to D5, however, there i no path in the general direction toward it. Thu choice of E a the next node neighbour for communicating to D5 i a wrong one. To circumvent thi iue of wrongly identifying a neighbour to forward the multicat query, we firt evaluate all poibilitie firt, before deciding on the lit of mot uitable forwarding node. If the node till encounter a void, we chooe perimeter routing a dicued in Greedy Perimeter Statele Routing (GPSR)[13]. In thi cae, we firt try to combine D5 and D6 a wa dicued earlier, and then go on to determine the ret of the node to forward the query. The node D1 and D2 can be conidered together, a they form part of the et M 4. The effective force that act on the node B i the tronget among the neighbour of u. Hence, the forwarding node for thee two multicat detination will be B. The remaining node D3 and D4 can now be conidered. The cloet neighbour according to our force metric i node C. or the detination node D5, while comparing between the node C and the node E, it can be oberved that C feel a tronger force than E. The detination D5 i hence removed from the Query meage to node E and then attached to node C. The Query meage i going to be forwarded to the node B, C and E with the detination et marked a {D1, D2}, {D3, D4, D5} and {D6} repectively. Note that the node can be ued to replace E, a the effective force value on both E and due to node D6 i the ame The MRAV Algorithm In thi ection, we dicu the multicat routing algorithm uing virtual-force Data tructure Data tructure relevant for the algorithm are mentioned in thi ub ection. N u : Thi i typically implemented a a linked lit to tore the lit of neighbour of the current node. The lit i updated with the help of repone from the periodic Hello packet tranmitted a per the Hello Protocol. Ρ(M): Thi i the power et of M, uch that all node within each of the ubet created are reachable in increaing value of the angle. or example, in the ample network in igure 1, Ρ(M) may contain {D1, D2, D3}, but may not contain {D1, D3} a there exit a node D2 direction i in between D1 and D3. 55

8 Π : Thi i a priority queue that tore the ubet of node with highet force value on the front of the queue. It i aumed that thi queue alo ha eparate lookup function implemented that can retrieve the force value for any ubet given a input to the function. Thi can be achieved by including an auxiliary data tructure in the form of a hah table along with Π. v : The et of poible neighbour to chooe from, while marking a plit node. Thi lit tore the next node a well a the lit of detination that are reachable from it Algorithm The algorithm for ending a Query meage i hown in Algorithm 1. Once the Query meage ha reached the detination or a plit node, a virtual circuit linking the detination and the previou plit node or the ource node hall be contructed a the acknowledgement to the Query travel back to the ource node. Algorithm 1: Multicat routing Algorithm uing Virtual-force 1: procedure SendQuery(u,M) 2: if u M then // The current node i itelf a multicat detination 3: M M {u} 4: end if 5: for each v N v M do u // A neighbour of the current node i a multicat detination 6: Call SendQuery ( v, M ) 7: end for 8: Let M = M 9: Repeat 10: for each Ρ(M) do 11: calculatevirtualorce ( u, ) 12: Add, to Π(M) 13: end for 14: Let M be front(π(m)) 15: o o Compute w N,. t. uw, Mˆ 60 Mˆ, uw u 60 16: if = M then // all node are in the ame general direction M 17: Call SendQuery ( w, M ) and exit 18: end if 19: Add (w, M ) to v 20: Remove all entrie from Ρ(M) which contain the detination node M 21: M = M - M 22: while M ϕ 23: Mark u a plit node 24: for each v do v 25: if ϕ then v v max 26: elect w = max w, M E w w v 27: Check for other detination in the direction of uw and verify whether they can alo 56

9 be addreed by the ame neighbour, w. 28: SendQuery ( w, M ) 29: end if 30: end for 31: end procedure 5. SECTOR-BASED MULTICAST ROUTING ALGORITHM In thi ection, we dicu the ector-baed virtual-force-baed multi-cat routing algorithm Motivation Though MRAV ue virtual force technique to correctly identify the et of neighbour to whom the query meage need to be forwarded, the meage complexity for making the computation i on the higher ide. One of the reaon for higher overhead and energy conumption derive from the fact that the algorithm compare all the node in the neighbourhood for making the routing deciion. However, mot of the node queried are not in the general direction of communication. The number of node that need to be enquired about the effective force value can hence be reduced. At each node u, we need to identify the ubet of N u that are leat likely to be part of the multicat route. The primary challenge while trying to decide which node can be excluded for path computation come from the uncertainty regarding the ret of the network Baic working Unlike MRAV and [12], we divide the node around u into α ector, with each ector covering an angle of θ = 2 π. Here, α varie from 3 to 6 depending on the denity of the region α containing u. or α = 4, we haveθ = π. or each of the α ector containing ome detination 2 node, we elect the appropriate neighbour in that ector to forward the packet. We compute the effective force on each of the k neighbouring node v 1, v 2,..., v k in the ector, by taking into account the cumulative effect of dampening force( E ), u and M, where M M, M contain vi all the detination node in ector. Once the appropriate forwarding node v for the ector i determined, the packet i communicated to v along with M, which i the et of detination node to be handled in ector. When a ource node i intereted in tranmitting a packet to a multicat group M, it firt end a Query meage to etablih the multicat route. Thi Query meage contain a pointer to indicate the multicat group and the et of node in M repreented uing bit array. The algorithm for ending the Query meage i given in Algorithm 1. When a node u decide on forwarding a packet to the detination, it determine whether it ha to plit the multicat packet or not. The node determine whether all detination are in the ame general direction or not by computing the effective force from detination,. If u, M and u, M are in oppoing direction, then the node determine the appropriate neighbour in the, u forward direction to route the Query packet. The bet way to determine whether all node are in 57

10 the ame general direction i to check whether the direction of force from each detination, d i, where d i M, are within ± angle from. u, M θ 2 igure 3 how a imple illutration on how the force vector are ued in our algorithm. irt, by uing Equation 3, the effective repulive force on the node u due to the detination in multicat group M, given a, i computed. The next tep i to divide the region around the node u into u, M α ector. Here α i the plit parameter that we ue. or dividing the region into ector, we firt look at the unit vector correponding to the effective detination force, ˆ. rom the direction u, M of the unit vector, we take all node within angle θ ± a the firt ector, where π θ = 2. In the 2 α example in igure 3, α=4 and π θ =. The node within the next θ radian form part of the econd 2 ector. Thu, α ector will be marked around the current node u. The four ector in igure 3 are divided by the dotted line a illutrated. Now, we divide the neighbour of u into α et (V 1, V 2,..., V α ), uch that all neighbouring node in ector are put inide the et. We apply the ame procedure to divide the node in M into v (M 1, M 2,..., M α ), where each et M indicate the et of detination node in the current detination et M. In the example in igure 1, the et M i divided into two et M 1 = {d 1 } and M 2 = {d 2, d 3, d 4 } correponding to ector 1 and 2. Similarly, the neighbour of u are divided into two et; V 1 V i =N u, where N u i the et of neighbouring node of = {v n1, v n2 } and V 2 ={v n3, v n4, v n5 }. Here, U i the current node u. Alo, U i M i = M. igure 3. Virtual orce acting on node u with α=4. Once the ubet of M, M, ha been computed, we can eaily determine whether any ector i having detination or not by checking for the condition: M = ϕ. If the condition hold true, then 58

11 we don't have to explore that ector. If M ϕ, then we have to determine appropriate neighbour to forward the packet in that ector. To chooe the appropriate neighbour in ector, firt we have to determine whether v = ϕ. If o, then we have encountered a void in that ector. The implet way to overcome void in the network i to follow the approach taken by Liu, et al. in [7]. Virtual force i ued to cro acro the void if poible, or ele the perimeter rule of greedy perimeter tatele routing (GPSR) algorithm [13] i applied. If v ϕ, then the effective force on the packet a given in Equation 4 i computed for each neighbour in v. The neighbour w w v with the maximum force on the packet i choen a the next hop neighbour Algorithm The algorithm that ue the notion of ector and virtual force, ector-baed virtual force-baed multicat routing algorithm (VM), i hown in Algorithm 2. Algorithm 2: Virtual orce-baed Multicat routing algorithm 1: procedure SendQuery(u,M) 2: if u M then 3: M M {u} 4: end if 5: for each v N v M do u 6: Call SendQuery ( v, M ) 7: end for M u. m 8: calculatevirtualorce( u, ) 9: Divide region into α ector centred at u, each of angle θ uch that firt ector lie within θ ± of 2 ˆ u. M 10: for each ector do 11: ϕ v 12: for each v N do u 13: if = ector( v) then 14: v v v 15: end if 16: end for 17: end for 18: for each ector do 19: ϕ M 20: for each d M do 21: if = ec tor( d) then 22: d 23: end if 24: end for 25: end for M M 59

12 M 26: for each ector uch that ϕ do 27: if ϕ then v v max 28: elect w = max w, M E w v 29: SendQuery ( w, M ) 30: end if 31: end for 32: end procedure w 6. SIMULATION RESULTS We have performed imulation of our algorithm uing a imulator written in Python language. The imulator ue the ame energy model and Two Ray propagation model a implemented in n-2. or the imulation run, we have placed node in a fixed area of 2000m x 2000m with maximum tranmiion range et a 250m. We have compared MRAV and VM with the QBIECRA algorithm propoed by Rahman, et al. [11]. While comparing with the ector-baed VM algorithm, we have taken α value a 3, 4 and 6. We have choen QBIECRA ince it ue a notion of quadrant for computing the multicat tree. Though Rahman, et al. alo propoed another verion of their quadrant baed algorithm in [12], while performing imulation we didn t perceive a major difference between the reult of QBIECRA and 4-N Intelligent routing. Thi i may be due to the fact that thee algorithm only differ on the bai of which four neighbour are going to be choen for computing the next forwarding node in the multicat path. The imulation reult obtained are dicued in the ret of thi ection. igure 4. Average normalized reidual energy over time Average normalized reidual energy i computed a the average reidual energy of all node in the network normalized in percentage term to account for variation in initial energy value of variou node. We have computed the average of reidual energy in each of the node after completing one cycle of packet tranmiion for a ender node in each epoch, and are howing the normalized value in percentage term after each epoch. The reult for normalized average 60

13 reidual energy are hown in igure 4. MRAV perform lightly better than QBIECRA. We oberved that in the initial period, the choice made by QBIECRA and MRAV were ame in many cae. But the choice began to diverge only later, when there wa ignificant difference between the choice made, primarily due to the effect of the dampening force. or VM, we oberved that for all value of α, it performed a ame a or better than QBIECRA and MRAV. igure 5. Normalized cot per data packet over time Normalized cot per data packet i computed a the overall cot for ending a data packet from ource node to detination that i normalized in term of percentile energy cot for the ake of comparion acro multiple imulation run with varying network ize. The reult for thi metric are hown in igure 5. We oberved that VM perform better than QBIECRA primarily by optimizing the effective energy pent on optimal path computation. Due to the number of comparion made, MRAV wa performing wore than VM. We couldn t tatitically etablih a clear difference between MRAV and QBIECRA baed on normalized cot per data packet. igure 6. Average length of multicat tree with repect to number of node 61

14 We alo oberved the effective length of the multicat tree generated a hown in igure 6. We oberved a variation in the general trend of length of the multicat tree for 20 node for both of our algorithm. We attribute thi variation to the choice of multicat et, preence of void and other apect pecific to the tet graph ued for imulation. Even with thi variation, both MRAV and VM provided horter length for multicat tree a compared to QBIECRA. MRAV performed conitently better than QBIECRA a far a thi metric i concerned for a larger network. or very mall network, there wa no major difference between the two algorithm. We oberved that 120 i the bet angle between the branche for getting relatively minimal Steiner tree a defined by Gilbert, et al.[2]. A expected, the length of the multicat tree wa nearing the optimal value for α=3. We urpriingly found that we were getting good reult for α=4 a well. Thi wa primarily due to the fact that we were not having many out-going edge in the oppoite direction of the forward path. When it came to α=6, our algorithm performed wore a expected, a we were generating too many out-going edge in ome node reulting in a ub-optimal multicat tree. However, the performance of VM algorithm wa till better than QBIECRA a een from the figure. 7. CONCLUSIONS We have applied the notion of virtual force for energy efficient multicat routing in MANET. We have preented two algorithm centred on the virtual-force technique. Our algorithm generate relatively minimal Steiner tree for ue in multicat routing. The imulation reult indicate that our algorithm perform better than other quadrant/ector baed multicat routing algorithm. We have evaluated appropriate choice for the number of ector to be ued, and have found that α = 3 or 4 can be ued to generate energy efficient multicat path. While we were applying the notion of virtual force for multicating, we oberved that the approach a a whole provide good reult. We haven t yet explored the relationhip between the value of α and network denity and pread. However, we believe that there i till cope in fine tuning the force model ued. Though we had only ued life of the network for QoS, the dampening force can eaily be extended to include other parameter a well. The propoed algorithm have hown that the virtual force approach can be uccefully ued in MANET. To our knowledge, thi i the firt paper that perform multicat routing algorithm uing the virtual force approach in mobile ad-hoc network. Thi i alo the firt paper to perform virtual-force computation on the bai of ector. REERENCES [1] Luo Junhai, Ye Danxia, Xue Liu, and an Mingyu. A urvey of multicat routing protocol for mobile ad-hoc network. Communication Survey Tutorial, IEEE, 11(1):78 91, quarter [2] E. Gilbert and H. Pollak. Steiner minimal tree. SIAM Journal on Applied Mathematic, 16(1):1 29, [3] Marhall Bern and Paul Plamann. The Steiner problem with edge length 1 and 2. Information Proceing Letter, 32(4): , [4] Glencora Borradaile, Philip Klein, and Claire Mathieu. An o(n log n) approximation cheme for teiner tree in planar graph. ACM Tran. Algorithm, 5(3):31:1 31:31, July [5] S. Poduri and G.S. Sukhatme. Contrained coverage for mobile enor network. In Robotic and Automation, Proceeding. ICRA IEEE International Conference on, volume 1, page Vol.1, april-1 may

15 [6] Y. Zou and Krihnendu Chakrabarty. Senor deployment and target localization baed on virtual force. In INOCOM Twenty-Second Annual Joint Conference of the IEEE Computer and Communication. IEEE Societie, volume 2, page vol.2, march-3 april [7] Cong Liu and Jie Wu. Virtual-force-baed geometric routing protocol in manet. Parallel and Ditributed Sytem, IEEE Tranaction on, 20(4): , april [8] Cong Liu and Jie Wu. Swing: Small world iterative navigation greedy routing protocol in manet. In Computer Communication and Network, ICCCN Proceeding.15th International Conference on, page , oct [9] Martin Mauve, Holger üler, Jörg Widmer, and Thoma Lang. Poition-baed multicat routing for mobile ad-hoc network. SIGMOBILE Mob. Comput. Commun. Rev., 7(3):53 55, July [10] S. otopoulou-prigipa and A.B. McDonald. Gcrp: geographic virtual circuit routing protocol for ad hoc network. In Mobile Ad-hoc and Senor Sytem, 2004 IEEE International Conference on, page , oct [11].M. Rahman and M.A. Gregory. Quadrant baed intelligent energy controlled multicat algorithm for mobile ad hoc network. In Advanced Communication Technology (ICACT), th International Conference on, page , feb [12].M. Rahman and M.A. Gregory. 4-n intelligent manet routing algorithm. In Autralaian Telecommunication Network and Application Conference (ATNAC), 2011, page 1 6, nov [13] Brad Karp and H. T. Kung. Gpr: greedy perimeter tatele routing for wirele network. In Proceeding of the 6th annual international conference on Mobile computing and networking, MobiCom 00, page , New York, NY, USA, ACM. Author Murali Paramewaran: i currently puruing hi PhD in Computer Science and Engineering from Birla Intitute of Technology & Science, Pilani. Hi reearch interet include: Ditributed Algorithm, Wirele Ad hoc Network, and Network Security. He i a member of IEEE, ACM and IETE. Chittaranjan Hota: did hi PhD in Computer Science and Engineering from Birla Intitute of Technology & Science, Pilani. He wa the founding head at BITS Hyderabad and currently he i the aculty In-charge of Information Proceing Center. He ha been a viiting reearcher and viiting profeor at everal univeritie abroad over pat few year. He ha current reearch funding from organization like UGC, DIT, Intel, and TCS. He ha guided PhD tudent and currently guiding PhD tudent in the area of P2P Overlay, Information Security, Wirele Network, and Ditributed Scheduling. He i a member of IEEE, ACM, IE, and ISTE. 63