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, Florida Atlantic Uniersity Abstract Most eisting localized protocols in mobile ad hoc netorks, 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 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, the 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 article 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. I n mobile ad hoc netorks (MANETs), all nodes cooperate to achiee a global task, sch as data gathering, commnication, or 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 Fig. a here the transmission range is.). 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 one or to hops. Collectiely, nodes rnning the localized algorithm achiee some desirable global objecties. To idely sed applications of the localized algorithm are: Determining a connected dominating set (CDS) for efficient roting [ ] Selecting an appropriate transmission range of each node for topology control [ ] A 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 a 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 b shos a CDS constrcted ia a localized algorithm []. In this diagram the connections beteen dominatees are not shon. As dominators (black This ork as spported in part by NSF grants CCR 9, ANI, and EIA. nodes) form a backbone of the MANET, any dominatee (hite node) can sitch to sleep mode for energy saing ithot casing netork partition. Most localized CDS algorithms rely on to-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 c shos the reslt of a localized topology control algorithm [], 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 one-hop location information of the crrent node, hich incldes information on 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 eisting localized algorithms, each node in a MANET emits a periodic Hello message to adertise its presence and position (if needed) at a fied 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 9-//$. IEEE IEEE Netork Jly/Agst

2 (c) Figre. Virtal netorks constrcted ia localized algorithms: a) the original netork; b) the connected dominating set; c) topology control. The original MANET has nodes and a transmission range of.. of its one- or to-hop neighborhood. In a 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 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: 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 [9], 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 pdate freqency and 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 global constraints 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 local information in a consistent ay We eamine to different approaches that address the consistency isse: enforcing consistent ies and making conseratie decisions. The first approach as initially proposed in [] to constrct consistent one-hop information for topology control. This approach can also be etended to spport the constrction of to-hop information. The second approach as originally proposed in [9] for CDS formation, bt the same principle can be sed in topology control. The main objectie of this article is to epose to the reader the challenging isse related to mobility control. Throgh discssion on the effects 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. The Link Aailability Isse and Its 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 eample, a preiosly sampled neighbor can moe ot of transmission range dring actal transmission. In order to apply eisting protocols ithot haing to redesign them, the notion of bffer zone is sed in [9], 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 t is defined as a bffered range depending on the moing speed t of mobile nodes and the maimm time delay d. To simplify the discssion, both Hello interals and moing patterns/ speeds are homogeneos; 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 [9] reeals that the orst case rarely happens. In MANETs ith ery high moing speed (t), it is either impossible or too epensie to se sch a large l. Both probabilistic analysis and simlation reslts in [9] sho that link aailability is presered in most cases ith a bffered range mch smaller than d t. 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: Select r = r for neighborhood information echange. Apply the selected localized CDS protocol to determine the stats of each node. Use r + l for each dominator in the actal transmission. The second step of the aboe process aries from protocol to protocol. Here e se W and Li s marking process and rles and [] to illstrate: At each node : Marking process: is marked tre (i.e., becomes a dominator) if there are to nconnected neighbors. Rle : is nmarked (i.e., becomes a dominatee) if its neighbor set is coered by another node ith a higher id. Rle : is nmarked if its neighbor set is coered jointly by to connected nodes ith higher ids. In rles and, 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 shos a sample ad hoc netork ith nine nodes. Node r is nmarked by the marking process becase its neighbors and z are directly connected. Node is nmarked by rle IEEE Netork Jly/Agst

3 becase its neighbor set is coered by node. Here node id is higher than according to alphabetical order. Node is nmarked by rle becase its neighbor set is coered by to connected nodes, and z. Clearly, the marked nodes,, and z form a CDS of the sample netork. Originally, rles and 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 echange dominating set stats. Dai and W [] 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 ids. The nmber of coering nodes is alloed to be more than to. When the netork is static or local ies are consistent (say, all nodes see only a solid line) in Fig., both nodes and are marked after the marking process. ill be nmarked sing rle. A typical topology control protocol orks as follos: Select r to collect neighborhood information. Apply a selected localized topology control protocol to select r(), r() r, for node to coer its farthest logical neighbor. Use r() + l for actal transmission. We se Li, Ho, and Sha s topology control algorithm based on a local minimm spanning tree (MST) [] to illstrate the second of the aboe process. At each node : Bild a local MST sing Prim s algorithm based on one-hop location information. The resltant MST coers all one-hop neighbors of. Select neighbors in MST as logical neighbors of. 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 Fig. 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 Fig., the transmission range of each node is increased to maintain link aailability. For eample, if it is knon that the maimm relatie moement beteen to nodes dring one Hello interal is l =, the actal transmission range of nodes,, and are adjsted to,, and, respectiely. Therefore, link (,) is still aailable een if node moes pard, and the distance beteen and becomes. It is also obsered in r y Unmarked by marking process Unmarked by rle Figre. W and Li's CDS algorithm. Black nodes are marked (i.e., in the CDS). [9] that the bffer zone idth l = is conseratie and not alays necessary. The probability is high that all links can be maintained ith a smaller l. The Vie Consistency Isse t z s Unmarked by rle Marked nodes Again, e se to localized algorithms as eamples to demonstrate ho inconsistent local ies case bad decisions in MANETs: W and Li s marking process [] for CDS constrction, and Li, Ho, and Sha s topology control algorithm based on local MST []. In the CDS constrction eample (Fig. ) e assme that node moes sothard. Link (,) eists at time t and is broken at time t. We also assme t and t 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 eists. The local ie is shon in Fig. b. Based on rle, node is nmarked becase its neighbor set is coered by node. Hoeer, hen node decides its stats, it has the fresh informa- t t 's position at t and t 's decision as an nmarked node at t (c) 's decision as nmarked at t (d) 's conseratie local ie at t Figre. s node moes aay from node, 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 (,) (d). The dotted line represents a irtal link in 's ie. IEEE Netork Jly/Agst

4 t t Moement (c) (d) Figre. Node becomes nreachable from nodes and de to inconsistent local ies sampled at nodes and : a) s positions at t and t ; b) LMST() bilt at time t ; c)lmst() bilt at time t ; d) netork topology at time t. tion that link (,) is broken since it is adjacent to the link (Fig. c). Based on the marking process, the only to neighbors of, 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 eample (Fig. ), assme node s ie reflects the topology at t (as shon in Fig. b), hereas node s ie corresponds to the topology at t (Fig. c). This happens hen the recent Hello message from is sent at t, here t < t < t. 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 (,) eists after topology control (Fig. d). A netork partition occrs! In the aboe eamples, indiidal nodes make bad decisions based on inconsistent local ies. To ies are inconsistent if their common parts do not match. In the CDS eample, link (,) eists in node s ie bt not in node s ie. In the topology control eample, is closer to in s ie bt closer to in s ie. There are to soltions to this problem: Enforcing consistent local ies Making conseratie decisions that maintain the global property, as discssed in the net to sections Consistent Local Vies We first consider one-hop (location) information sed in topology control. Originally, each node receies Hello messages from its one-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 eample, if both nodes and make their decisions at t, they ill agree that is closer to ; at t 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, the to nodes hae inconsistent ies. This inconsistency cannot be aoided no matter ho small the asynchrony is. The traditional soltion to this problem is to bild local ies only once at the beginning of each Hello interal. As shon in Fig. a, each Hello interal is diided into three time periods, = h + s + d. 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. 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 based on these local ies. This scheme can be etended to bild to-hop information. As shon in Fig. b, each Hello interal is diided into fie periods, = h + s + h + s + d. Normally h = h and s = s. Again, e assme the clock difference is bonded by both s and s. Each node first adertises its -hop information (i.e., its id and/or location) in period h, bilds one-hop information at the end of period s, and then adertises the nely constrcted one-hop information in period h. At the end of period s, eery node constrcts its consistent local ie, hich is ready for se in period d. The draback of this scheme is that to Hello messages are sent dring each interal, and the effectie commnication period d is frther redced. h s d h s h s d t t t t Figre. Bild consistent local ies at the beginning of each Hello interal; dotted lines represent Hello messages, solid lines data packets: a) consistent one-hop information; b) consistent to-hop information. IEEE Netork Jly/Agst

5 The traditional soltion relies on the assmption that the maimal 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 eist to adjst clock ales, freqent clock synchronization is costly. When maintaining a (partially) synchronos Hello interal becomes too epensie 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 corresponding to a recently sed timestamp. Similarly, seeral logic topologies coeist 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 Fig., sppose the first Hello message from node has timestamp, and the second has timestamp. When the aboe method is applied, to parallel logic topologies eist. The logical topology corresponding to timestamp incldes to bidirectional links, (,) and (,). The logic topology corresponding to timestamp 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, it is sent to directly ia logical link (,). In both cases, p arries safely at its destination. Conseratie Local Vies Both soltions for enforcing consistent local ies reqire a certain degree of internode synchronization, hich introdces etra oerhead. When maintaining consistent local ies becomes too epensie or impossible, another approach called the conseratie local ie [] can be applied, hich makes conseratie decisions based on inconsistent ies. No synchronization is necessary. A conseratie decision is one that maintains the global property ith the penalty of loer efficiency. This 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 eample to illstrate the conseratie approach. In W and Li s marking process, a node may be nmarked incorrectly if: no longer ies a node as its neighbor 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 periodic 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 the aboe conditions 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 Vie c () of node is constrcted from k most recent local ies Vie (), Vie (),, Vie k () based on the folloing rle: a link (,) eists in Vie c () if and only if () (,) eists in the most recent local ie Vie (), or () = and (,) eists in at least one recent local ie Vie i () for 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 Fig. 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 earlier. The irtal link stays in s ie ntil all other nodes hae remoed this link from their ies. When to-hop information is sed, link (,) eists in local ies of s onehop neighbors and s one-hop neighbors, hich ill remoe link (,) from their local ies after receiing a Hello message from or. Node ill send its net 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. 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 eample, 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 Vie (), Vie (),, Vie k (), hich contain distance ales d i (,) ( i k) beteen any to nodes and ithin s transmission range (inclding ), their distance in the conseratie ie is: ma i d i (,), if and 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 Fig., both nodes and select as a logical neighbor, and netork connectiity is presered. Simlation Reslts We illstrate sample reslts from simlations of the mobility control mechanisms. For more reslts, the readers can refer to [9, ]. All simlations are condcted sing ns-, ith nodes, a 9 9 m deployment area, normal transmission range r = m, s Hello interal, and a random aypoint mobility model. 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 Dai and W s original CDS algorithm [], the connectiity ratio drops rapidly as the aerage moing speed increases. When a small ( m) bffer zone is sed to tolerate broken links, the deliery ratio improes significantly nder lo ( m/s) to moderate ( m/s) mobility. With a m bffer zone, the algorithm has almost percent connectiity ratio nder ery high ( m/s) mobility. Figre a shos the connectiity ratio of Li, Ho, and Sha s topology control algorithm []. When there is no bffer zone IEEE Netork Jly/Agst

6 9 m m m m m m m m Connectiity ratio (%) Connectiity ratio (%) Aerage moing speed (m/s) Aerage moing speed (m/s) Figre. The connectiity ratio of a topology control algorithm nder different bffered ranges: a) ith inconsistent local ies; b) ith consistent local ies. ( m), the connectiity ratio is ery lo ( percent) nder an aerage moing speed of m/s. The connectiity ratio increases significantly after a ery small ( m) bffer zone is sed. On the other hand, percent connectiity ratio is not achieed nder lo mobility. Moderate and high mobility case lo connectiity ratio. Figre b shos the effect of sing consistent ies. When sing a m bffer zone in MANETs ith a m/s aerage moing speed, the connectiity ratio is percent ithot consistent ies and percent ith consistent ies. When sing a m bffer zone nder a m/s aerage moing speed, the connectiity ratio reaches 9 percent ith consistent ies, hile the original connectiity ratio ithot consistent ies is only percent. Oerall, simlation reslts confirm that 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. 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 eisting 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 eist: 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-offs be done? More efforts are needed to address these isses before arios protocols can be applied in MANETs ith mobile nodes. References [] F. Dai and J. W, Distribted Dominant Prning in Ad Hoc Wireless Netorks, Proc. ICC, May, p.. [] A. Qayym, L. Viennot, and A. Laoiti, Mltipoint Relaying for Flooding Broadcast Message in Mobile Wireless Netorks, Proc. HICSS-, Jan.. [] I. Stojmenoic, M. Seddigh, and J. Znic, Dominating Sets and Neighbor Elimination based Broadcasting Algorithms in Wireless Netorks, IEEE Trans. Parallel and Distribted Sys., ol., no., Jan., pp.. [] J. W and H. Li, On Calclating Connected Dominating Set for Efficient Roting in Ad Hoc Wireless Netorks, Proc. DiaLM, 999, pp.. [] N. Li, J. C. Ho, and L. Sha, Design and Analysis of an MST-based Topology Control Algorithm, Proc. INFOCOM, ol., Mar./Apr., pp.. [] V. Rodopl and T. H. Meng, Minimm Energy Mobile Wireless Netorks, IEEE JSAC, ol., no., Ag. 999, pp.. [] Y. Wang et al., Distribted Spanners ith Bonded Degree for Wireless Ad Hoc Netorks, Int l. J. Fondations of Comp. Sci., ol., no.,, pp.. [] R. Wattenhofer et al., Distribted Topology Control for Poer Efficient Operation in Mltihop Wireless Ad Hoc Netorks, Proc. INFOCOM, Apr., pp. 9. [9] J. W and F. Dai, Mobility Management and Its Applications in Efficient Broadcasting in Mobile Ad Hoc Netorks, Proc. INFOCOM, Mar.. [] J. W and F. Dai, Mobility-sensitie Topology Control in Mobile Ad Hoc Netorks, Proc. IPDPS, Apr.. Biographies JIE WU [SM] (jie@cse.fa.ed) is a professor at the Department of Compter Science and Engineering, Florida Atlantic Uniersity. He has pblished oer papers in arios jornal and conference proceedings. His research interests are in the area of mobile compting, roting protocols, falt-tolerant compting, and interconnection netorks. He sered as a program ice chair for the International Conference on Parallel Processing and IEEE International Conference on Distribted Compting Systems. He is a program co-chair for the IEEE st International Conference on Mobile Ad Hoc and Sensor Systems. He as a cogest editor of a special isse of IEEE Compter on Ad Hoc Netorks. He as editor for seeral special isses of the Jornal of Parallel and Distribting Compting and IEEE Transactions on Parallel and Distribted Systems. Crrently, he seres as an Associated Editor of IEEE Transactions on Parallel and Distribted Systems and three other international jornals. He as a recipient of the 99-9 and - Researcher of the Year Aards at Florida Atlantic Uniersity. FEI DAI (fdai@fa.ed) is a Ph.D. candidate at the Department of Compter Science and Engineering, Florida Atlantic Uniersity. His crrent research focses on the design and application of localized algorithms in ireless ad hoc and sensor netorks. Other research areas inclde interconnection netorks, falt-tolerant roting, and softare architectre. He receied his B.S. and M.S. degrees in compter science in 99 and 99, respectiely, from Nanjing Uniersity, China. He orked as a senior programmer at Greatall Compter, China, from 99 to 99, and as a softare architect and team leader in J&A Secrities, China, from 99 to. IEEE Netork Jly/Agst