Mobility Control and Its Applications in Mobile Ad Hoc Networks

Transcription

1 Mobility Control and Its Applications in Mobile Ad Hoc Netorks Jie W and Fei Dai Department of Compter Science and Engineering Florida Atlantic Uniersity Boca Raton, FL 3331 Abstract Most existing localized protocols in mobile ad hoc netorks (MANETs), sch as data commnication and topology control, se local information for decentralized decision among nodes to achiee certain global objecties. These objecties inclde determining a small connected dominating set (CDS) for irtal backbone and topology control by adjsting transmission ranges of nodes. Becase of asynchronos sampling of local information at each node, delays at different stages of protocol handshake, and moement of mobile nodes, local ie captred at different nodes may be inconsistent and/or otdated and may not reflect the actal netork sitation. The former may case bad decisions that fail to keep the gien global constraint sch as global domination and connectiity, and the latter may incr broken links hich in trn ill ltimately case the failre of the constraint. In this paper, e reie some techniqes that handle inconsistent and otdated local ies. These techniqes are illstrated sing seeral ell-knon protocols in data commnication and topology control. Keyords: Connectiity, connected dominating set (CDS), mobile ad hoc netorks (MANETs), mobility management, simlation, topology control. This ork as spported in part by NSF grants CCR 32971, ANI 7373, and EIA 138. jie@cse.fa.ed Contact address:

2 1 Introdction In mobile ad hoc netorks (MANETs), all nodes cooperate to achiee a global task, sch as data gathering, commnication, and area monitoring. MANETs are characterized by nit disk graphs here to nodes are connected only if their geographical distance is ithin a gien transmission range (as shon in Figre 1 (a) here the transmission range is 2.). To design protocols that are simple and qick to conerge, many protocols in MANETs rely on localized algorithms. The localized algorithm rnning at each node makes its local decision based on local information ithin 1 or 2 hops. Collectiely, nodes rnning the localized algorithm achiee some desirable global objecties. To idely-sed applications of the localized algorithm are (1) determining a connected dominating set (CDS) for efficient roting [1, 3,, 1], and (2) selecting an appropriate transmission range of each node for topology control [2,,, 7]. A connected dominating set (CDS) is a sbset sch that each node in the system is either in the set or the neighbor of a node in the set. The CDS has been sed idely to spport the notion of irtal backbone in MANETs. Another application of CDS is in broadcasting, here nodes and only nodes in the CDS forard the broadcast message to redce message collision. Hoeer, finding a minimm CDS is NP-complete. Most practical approaches in MANETs se localized algorithms to find a small CDS. In a typical localized CDS protocol, each node ses local information to determine its stats, dominator or dominatee. Figre 1 (b) shos a CDS constrcted ia a localized algorithm [1]. In this diagram the connections beteen dominatees are not shon. As dominators (black nodes) form a backbone of the MANET, any dominatee (hite node) can sitch to the sleep mode for energy saing ithot casing netork partition. Most localized CDS algorithms rely on 2-hop information of the crrent node, hich incldes information of s neighbors and neighbors of s neighbors. In MANETs, in order to redce energy consmption and signal interference, it is important to select an appropriate transmission poer for each node, also called topology control, hile still satisfying certain global constraints, inclding connectiity and other reliability and throghpt related measres. In localized topology control, each node ses local information to select a sbset of physical neighbors, called logical neighbors, and its transmission range is redced to reaching only as far as the farthest logical neighbor. Figre 1 (c) shos the reslt of a localized topology control algorithm [2], here both the aerage nmber of neighbors and transmission range are redced significantly, hile the netork is still connected. Localized topology control algorithms sally rely on 1-hop location information of the crrent node, hich incldes information of s neighbors and their location information. Some algorithms reqire less information here distance or angle of arrial information of neighbors is sfficient. Compared ith their centralized conterparts, localized algorithms are lighteight, fast to conerge, and resilient to node moement. Hoeer, ithot a mobility control mechanism, global domination and connectiity may still be compromised by node moement. In most existing localized algorithms, each node in a MANET emits a periodic Hello message to adertise its presence and its position (if needed) at a fixed interal. Hello interals at different nodes are asynchronos to redce message collision. Each node ses receied Hello messages as samples to constrct a local ie of its 1- or 2-hop neighborhood. In a 1

3 (a) The original netork (b) Connected dominating set (c) Topology control Figre 1. Virtal netorks constrcted ia localized algorithms. The original MANET has 1 nodes and a transmission range of 2.. MANET ith mobile nodes, the limited sample freqency, asynchronos Hello interals, and delays at different stages of protocol handshake ill case a mismatch beteen the irtal netork constrcted from 1 the collection of local ies sampled at different nodes and the actal netork. This mismatch ill case the link aailability isse, here a neighbor in a irtal netork is no longer a neighbor in the actal netork, becase the irtal netork is constrcted from otdated information. Therefore, special mechanisms are needed to address the folloing isse: 2 3 Delay and mobility management: Ho protocols deal ith imprecise neighborhood information cased by node mobility and arios delays introdced at different stages of protocol handshake. One soltion in [8], as ill be discssed later in detail, ses to transmission ranges to address the link aailability isse. First, a transmission range r is determined based on the selected protocol. This transmission range is either the same as the Hello message range r as in the CDS protocol or shorter than r as in the topology control protocol. The actal transmission ses a long transmission range set to r + l. The difference, l, beteen these to ranges is based on the pdate freqency and the speed of node moement. The mismatch beteen the irtal netork and actal netork ill case a more serios problem: inconsistent local ies. Inconsistent local ies may case bad decisions that fail to keep the the global constraint sch as global domination and connectiity. Again, special mechanisms are needed to address the folloing isse: Node synchronization and consistent local ie: Ho each node knos hen to sample its local ie. Ho each node collects and ses the local information in a consistent ay. 2

4 We ill examine to different approaches that address the consistency isse: enforcing consistent ies and making conseratie decisions. The first approach as initially proposed in [9] to constrct consistent 1-hop information for topology control. This approach can also be extended to spport the constrction of 2-hop information. The second approach as originally proposed in [8] for CDS formation. Bt the same principle can be sed in topology control. The main objectie of this paper is to expose to the reader the challenging isse related to mobility control. Throgh discssion on the effect of mobile nodes on seeral important protocols, e present some problems, proide possible soltions, and discss seeral open isses. By this, e hope to stimlate more research in this important area. 2 Link aailability isse and soltion In MANETs, becase of asynchronos Hello messages and arios protocol handshake delays, neighborhood information and/or position sed in decision making may be otdated. For example, a preiosly sampled neighbor can moe ot of transmission range dring the actal transmission. In order to apply existing protocols ithot haing to redesign them, the notion of bffer zone is sed in [8], here to circles ith radii r and r + l are sed. r corresponds to the transmission range determined by a selected protocol, hereas r + l corresponds to the actal transmission range sed. l = d 2t is defined as a bffered range depending on the moing speed t of mobile nodes and the maximm time delay d. To simplify the discssion, both Hello interals and moing patterns/speeds are homogeneos, and hence, l is niform for each node. The aboe reqirement of bffered range garantees link aailability in the orst case sitation. Hoeer, probabilistic stdy in [8] reeals that the orst case rarely happens. In MANETs ith ery high moing speed (t), it is either impossible or too expensie to se sch a large l. Both probabilistic analysis and simlation reslts in [8] sho that link aailability is presered in most cases ith a bffered range mch smaller than d 2t. There is a ide range of potential trade-offs beteen efficiency and connectiity. Specifically, sppose r is the normal Hello message range. A typical CDS protocol orks as follos: 1. Select r = r for neighborhood information exchange. 2. Apply the selected localized CDS protocol to determine the stats of each node. 3. Use r + l for each dominator in the actal transmission. Step 2 of the aboe process aries from protocol to protocol. Here e se W and Li s marking process and Rles 1 and 2 [1] to illstrate: 3

5 r z x nmarked by marking process y s nmarked by Rle 1 nmarked by Rle 2 marked nodes t Figre 2. W and Li s CDS algorithm. Black nodes are marked (i.e., in the CDS). At each node : Marking Process: is marked tre (i.e., becomes a dominator) if there are to nconnected neighbors. Rle 1: is nmarked (i.e., becomes a dominatee) if its neighbor set is coered by another node ith a higher id. Rle 2: is nmarked if its neighbor set is coered jointly by to connected nodes ith higher id s. In Rles 1 and 2, e say s neighbor set, N(), is coered by one or to coering nodes, if eery node in N() is either a coering node or a neighbor of a coering node. Figre 2 shos a sample ad hoc netork ith 9 nodes. Node r is nmarked by the marking process becase its neighbors and z are directly connected. Node is nmarked by Rle 1 becase its neighbor set is coered by node x. Here node id x is higher than according to the alphabetical order. Node is nmarked by Rle 2 becase its neighbor set is coered by to connected nodes x and z. Clearly, the marked nodes, x, and z form a CDS of the sample netork. Originally, Rles 1 and 2 se only marked nodes as coering nodes, and inole oerhead in commnicating dominating set stats. Stojmenoic et al [] shoed that nmarked nodes can also be coering nodes, and there is no need to exchange dominating set stats. Dai and W s [1] proposed a generalized rle (called Rle k) to constrct a smaller CDS. Based on the generalized rle, is nmarked if its neighbor set is coered by seeral connected nodes ith higher id s. The nmber of the coering nodes is alloed to be more than to. When the netork is static or local ies are consistent (say, all nodes see only solid line) in Figre 3, both nodes and are marked after the marking process. ill be nmarked sing Rle 1.

6 x t x x x t1 (a) s position at t and t1 (b) s decision as an nmarked node at t1 (c) s decision as nmarked at t1 (d) s conseratie local ie at t1 Figre 3. As node moes aay from node (a), both nodes and are nmarked de to inconsistent local ies sampled at nodes and (b,c). Based on the conseratie ie, node is still marked for a little hile after it detected the broken link (, ). The dotted line represents a irtal link in s ie. A typical topology control protocol orks as follos: 1. Select r to collect neighborhood information. 2. Apply a selected localized topology control protocol to select r(), r() r, for node to coer its farthest logical neighbor. 3. Use r() + l for the actal transmission. We se Li, Ho, and Sha s topology control algorithm based on local minimm spanning tree (MST) [2] to illstrate step 2 of the aboe process. At each node : 1. Bild a local MST sing Prim s algorithm based on 1-hop location information. The resltant MST coers all 1-hop neighbors of. 2. Select neighbors in MST as logical neighbors of. 3. Set the transmission range of to the distance to the farthest logical neighbor. When the netork is static or local ies are consistent (say, all nodes see only solid line) in Figre (a), the MST incldes to links (, ) and (, ). Node has one logical neighbor and sets its range to. Node has one logical neighbor and sets its range to. Node has to logical neighbors and and sets its range to to reach the farthest node. When the netork contains mobile nodes, sch as node in Figre, the transmission range of each node is increased to maintain the link aailability. For example, if it is knon that the maximm relatie

7 t1 t t moement (a) s positions at t and t1 (b) LMST() bilt at time t (c) LMST() bilt at time t1 (d) Netork topology at time t1 Figre. Node becomes nreachable from nodes and de to inconsistent local ies sampled at nodes and. moement beteen to nodes dring one Hello interal is l = 2, then the actal transmission range of nodes,, and are adjsted to 8, 7, and 8, respectiely. Therefore, link (, ) is still aailable een if node moes pard and the distance beteen and becomes. It is also obsered in [8] that the bffer zone idth l = 2 is conseratie and not alays necessary. The probability is high that all links can be maintained ith a smaller l. 3 Vie consistency isse Again, e se to localized algorithms as examples to demonstrate ho inconsistent local ies case bad decisions in MANETs: W and Li s marking process [1] for CDS constrction, and Li, Ho, and Sha s topology control algorithm based on local MST [2]. In the CDS constrction example (as shon in Figre 3), e assme that node moes sothard. Link (, ) exists at time t and is broken at time t 1. We also assme t and t 1 belong to to interals. Since link (, ) is to hops aay from node, hen node decides its stats, it ses the otdated information (lagging by one interal) that link (, ) still exists. The local ie is shon in Figre 3 (b). Based on Rle 1, node is nmarked becase its neighbor set is coered by node. Hoeer, hen node decides its stats, it has the fresh information that link (, ) is broken since it is adjacent to the link (as shon in Figre 3 (c)). Based on the marking process, the only to neighbors of, x and, are connected, so node is also marked false. As a conseqence, none of the nodes in the netork are marked! In the topology control example (as shon in Figre ), assme node s ie reflects the topology at t (as shon in Figre (b)) hereas node s ie corresponds to the topology at t 1 (as shon in Figre (c)). This happens hen the recent Hello message from is sent at t, here t < t < t 1. In this case, has only one logical neighbor, and has only one logical neighbor. Based on the protocol, a link is selected only if both end nodes select each other. As a reslt, only one link (, ) exists after the topology control (as shon in Figre (d)). A netork partition occrs! In the aboe examples, indiidal nodes make bad decisions based on inconsistent local ies. To ies are inconsistent if their common parts do not match. In the CDS example, link (, ) exists in node

8 t h s d1 t 1 t h1 s1 h2 s2 d 2 t 1 (a) consistent 1 hop information (b) consistent 2 hop information Figre. Bild consistent local ies at the beginning of each Hello interal. Dotted lines represent Hello messages. Solid lines represent data packets. s ie bt not in node s ie. In the topology control example, is closer to in s ie bt closer to in s ie. There are to soltions to this problem: (1) enforcing consistent local ies, or (2) making conseratie decisions that maintain the global property, as ill be discssed in the next to sections. Consistent local ie We first consider 1-hop (location) information sed in topology control. Originally, each node receies Hello messages from its 1-hop neighbors, and pdates its local ie pon the arrial of eery Hello message. If all nodes hae synchronized clocks, this scheme actally orks. In the topology control example, if both nodes and make their decisions at t, they ill agree that is closer to ; at t 1, they ill agree that is closer. Here e omit the propagation delay and assme that a Hello message is receied by all neighbors at the same time. Hoeer, it is impossible to hae totally synchronized clocks in a MANET ithot centralized control. If makes its decision slightly earlier than, and s Hello message arries after s decision and before s decision, then the to nodes hae inconsistent ies. This inconsistency cannot be aoided no matter ho small the asynchrony is. The traditional soltion for this problem is to bild local ies only once at the beginning of each Hello interal. As shon in Figre (a), each Hello interal is diided into three time periods = h + s + d 1. Becase of asynchronos clocks, different nodes may start their Hello interals at different times. That is, some nodes hae faster clocks than other nodes. Hoeer, e assme the difference beteen to clocks is bonded by s. In the constrction of consistent ies, each node sends its Hello message dring period h, aits for a period s, and condcts normal actiities (e.g., sending data packets) in period d 1. As the h period of the sloest node ends before the s period of the fastest node, eery node receies all Hello messages before the end of its s period. Local ies bilt in the end of s are consistent. It is safe to rote data packets in period d 1 based on these local ies. This scheme can be extended to bild 2-hop information. As shon in Figre (b), each Hello interal is diided into fie periods = h 1 + s 1 + h 2 + s 2 + d 2. Normally h 1 = h 2 and s 1 = s 2. Again, e assme 7

9 the clock difference is bonded by both s 1 and s 2. Each node first adertises its -hop information (i.e., its id and/or location) in period h 1, bilds 1-hop information at the end of period s 1, and then adertises the nely constrcted 1-hop information in period h 2. At the end of period s 2, eery node constrcts its consistent local ie, hich is ready for se in period d 2. The draback of this scheme is that to Hello messages are sent dring each interal, and the effectie commnication period d 2 is frther redced. The traditional soltion relies on the assmption that the maximal difference among local clocks, s, is predictable and s. In a totally asynchronos system, s = and the aboe simple approach cannot be applied. Note that een if s < at a particlar netork, delays accmlate nless some clock synchronization protocol is applied. Althogh arios soltions exist to adjst clock ales, freqent clock synchronization is costly. When maintaining (partially) synchronos Hello interal becomes too expensie or impossible, e propose sing timestamped asynchronos Hello messages to enforce application specific consistent local ies. The basic idea is to maintain a seqence nmber i at each node, and attach the seqence nmber to each Hello message from this node. The seqence nmber seres as a timestamp. Consistent local ies are obtained from Hello messages ith the same timestamps. This can be done by carrying a timestamp in each data packet (inclding control packets from a higher leel protocol). The timestamp is chosen by the originator of the data packet, and all nodes relaying this packet mst determine their logical neighbors based on information of the same ersion (i.e., ith the same timestamp). In this scheme, each node keeps seeral local ies, each local ie corresponding to a recently sed timestamp. Similarly, seeral logic topologies co-exist in the same netork. Each logic topology corresponds to a timestamp and is connected. The logic time (i.e., the timestamp of the latest local ie) of the originator of the data packet is sed as a selector. It indicates in hich logical topology this data packet is traelling. This approach can tolerate a larger time ske among different local ies and, therefore, inoles less synchronization oerhead. In Figre, sppose the first Hello message from node has timestamp, and the second one has timestamp 1. When the aboe method is applied, to parallel logic topologies exist. The logical topology corresponding to timestamp incldes to bidirectional links (, ) and (, ). The logic topology corresponding to timestamp 1 incldes (, ) and (, ). When a data packet p is sent from to, the sorce node selects a recent timestamp and forards p on the corresponding logical topology. If p has timestamp, it is first forarded to. Based on s local ie ith timestamp, is a logical neighbor of, and p is forarded along the logical link (, ). If p has timestamp 1, it is sent to directly ia logical link (, ). In both cases, p arries safely at its destination. Conseratie local ie Both soltions for enforcing consistent local ies reqire a certain degree of internode synchronization, hich introdces extra oerhead. When maintaining consistent local ies becomes too expensie or impossible, another approach called conseratie local ie [9] can be applied, hich makes conseratie decisions based on inconsistent ies. No synchronization is necessary. A conseratie decision is one 8

10 that maintains the global property ith the penalty of loer efficiency. That means selecting more logical neighbors in a topology control algorithm, hich in trn generates a larger aerage transmission range, and marks more nodes as dominators in a CDS formation process. We se W and Li s marking process as an example to illstrate the conseratie approach. In W and Li s marking process, a node may be nmarked incorrectly if (1) no longer ies a node as its neighbor, and (2) another node still ies as s neighbor and nmarks itself based on this ie. As the broken link (, ) is first detected by and then propagated to ia periodical Hello messages, local ies of nodes and are inconsistent for a short period. Dring that period, and may be nmarked simltaneosly, and the CDS is temporarily compromised. In order to preent conditions (1) and (2) from happening together, each node mst se a conseratie local ie, instead of its most recent local ie, to make conseratie decisions. In this case, the conseratie local ie V ie c () of node is constrcted from k most recent local ie V ie 1 (), V ie 2 (),..., V ie k () based on the folloing rle: a link (, ) exists in V ie c () if and only if (1) (, ) exists in the most recent local ies V ie 1 (), or (2) = and (, ) exists in at least one recent local ie V ie i () for 1 i k. That is, a broken link is presered longer in the conseratie ies of its to end nodes than in those of all other nodes. As shon in Figre 3 (d), after node detects a broken link (, ), it ill keep a irtal link corresponding to the broken link in its local ie for a short time period. Based on this conseratie ie, is still a dominator. Note that the irtal link (, ) is still aailable dring this time period, if ses a large actal transmission range to create a bffer zone, as discssed in Section 2. The irtal link stays in s ie ntil all other nodes hae remoed this link from their ies. When 2-hop information is sed, link (, ) exists in local ies of s 1-hop neighbors and s 1-hop neighbors, hich ill remoe link (, ) from their local ies after receiing a Hello message from or. Node ill send its next Hello message ithin a Hello interal ( ). Node may detect the broken link and send its Hello message later than, bt the difference is bonded by. Therefore, it is safe to remoe the irtal link (, ) for s local ie after 2. This approach can also be applied to other localized CDS and topology control algorithms. Hoeer, the conseratie decisions are different from algorithm to algorithm, and the constrction of conseratie ies depends on the specific algorithm. For example, in Li, Ho, and Sha s local MST algorithm, a conseratie ie of node can be defined as follos: gien k most recent local ies V ie 1 (), V ie 2 (),..., V ie k (), hich contain distance ales d i (, ) (1 i k) beteen any to nodes and ithin s transmission range (inclding ), their distance in the conseratie ie is (1) max i d i (, ), if and, and (2) min i d i (, ) otherise. That is, the irtal distance beteen and a neighbor in its conseratie ie may be smaller than the actal distance, and the irtal distance beteen to neighbors may be larger than the actal distance. When conseratie local ies are sed in Figre, both nodes and select as a logical neighbor, and the netork connectiity is presered. 9

11 Connectiity ratio (%) Aerage moing speed (m/s) 1m 1m 1m m (a) With inconsistent local ies Connectiity ratio (%) Aerage moing speed (m/s) (b) With consistent local ies 1m 1m 1m m Figre. Connectiity ratio of a topology control algorithm nder different bffered ranges. Simlation Reslts We illstrate sample reslts from simlations of the mobility control mechanisms. For more reslts, the readers can refer to [8, 9]. All simlations are condcted sing ns-2, ith 1 nodes, a 9 9m 2 deployment area, normal transmission range r = 2m, 1s Hello interal, and a random aypoint mobility model. The netork connectiity is measred in terms of the connectiity ratio, hich is defined as the ratio of pairs of connected nodes to the total nmber of pairs. In the original Dai and W s CDS algorithm [1], the connectiity ratio drops rapidly as the aerage moing speed increases. When a small (2m) bffer zone is sed to tolerate broken links, the deliery ratio improes significantly nder lo (1m/s) to moderate (m/s) mobility. With a 1m bffer zone, the algorithm has almost 1% connectiity ratio nder ery high (1m/s) mobility. Figre (a) shos the connectiity ratio of Li, Ho, and Sha s topology control algorithm [2]. When there is no bffer zone (m), the connectiity ratio is ery lo (1%) nder an aerage moing speed of 1m/s. The connectiity ratio increases significantly after a ery small (1m) bffer zone is sed. On the other hand, 1% connectiity ratio is not achieed nder lo mobility. Moderate and high mobility cases lo connectiity ratio. Figre (b) shos the effect of sing consistent ies. When sing a 2m bffer zone in MANETs ith a 1m/s aerage moing speed, the connectiity ratio is % ithot consistent ies, and 7% ith consistent ies. When sing a 1m bffer zone nder a m/s aerage moing speed, the connectiity ratio reaches 98% ith consistent ies, hile the original connectiity ratio ithot consistent ies is only 7%. Oerall, simlation reslts confirm that the global connectiity can be compromised by both link aailability and ie consistency isses. Both isses can be oercome ith mobility control mechanisms, and the global property can be presered ith high probability and relatiely small oerhead. 1

12 7 Conclsion We hae addressed isses related to mobility control in mobile ad hoc netorks. To illstrate the importance of the negatie impact of mobile nodes on arios protocols, e focs on to types of protocols, one for CDS constrction and the other for topology control. It has been shon that most existing protocols on CDS constrction and topology control ill generate incorrect reslts in the presence of mobile nodes. We discss to major problems cased by mobility control: link aailability and ie consistency, and proide seeral soltions. Mobility control in MANETs is still in its infancy. Many open isses exist: Ho does mobility affect protocols at other layers? Can approaches for ie consistency in distribted systems be applied in mobile ad hoc netorks? Ho shold arios kinds of cost and efficiency trade-off be done? More efforts are needed to address these isses before arios protocols can be applied in MANETs ith mobile nodes. References [1] F. Dai and J. W. Distribted dominant prning in ad hoc ireless netorks. In Proc. of ICC, page 33, May 23. [2] N. Li, J. C. Ho, and L. Sha. Design and analysis of an MST-based topology control algorithm. In Proc. of INFOCOM, olme 3, pages , Mar./Apr. 23. [3] A. Qayym, L. Viennot, and A. Laoiti. Mltipoint relaying for flooding broadcast message in mobile ireless netorks. In Proc. of HICSS-3, Jan. 22. [] V. Rodopl and T. H. Meng. Minimm energy mobile ireless netorks. IEEE Jornal of Selected Areas in Commnications, 17(8): , Ag [] I. Stojmenoic, M. Seddigh, and J. Znic. Dominating sets and neighbor elimination based broadcasting algorithms in ireless netorks. IEEE Transactions on Parallel and Distribted Systems, 13(1):1 2, Jan. 22. [] Y. Wang, X. Li, P. Wan, and O. Frider. Distribted spanners ith bonded degree for ireless ad hoc netorks. International Jornal of Fondations of Compter Science, 1(2):183 2, 23. [7] R. Wattenhofer, L. Li, V. Bahl, and Y. M. Wang. Distribted topology control for poer efficient operation in mltihop ireless ad hoc netorks. In Proc. INFOCOM, pages , Apr. 21. [8] J. W and F. Dai. Mobility management and its applications in efficient broadcasting in mobile ad hoc netorks. In Proc. of INFOCOM, Mar

13 [9] J. W and F. Dai. Mobility-sensitie topology control in mobile ad hoc netorks. In Proc. of IPDPS, Apr. 2. accepted to appear. [1] J. W and H. Li. On calclating connected dominating set for efficient roting in ad hoc ireless netorks. In Proc. of DiaLM, pages 7 1,