Iso-Map: Energy-Efficient Contour Mapping in Wireless Sensor Networks

Transcription

1 Iso-Map: Eergy-Efficiet Cotour Mappig i Wireless Sesor Networks Yuhao Liu ad Mo Li Departmet of Computer Sciece ad Egieerig Hog Kog Uiversity of Sciece ad echology {liu, limo}@cs.ust.hk ABSRAC Cotour mappig is a crucial part of may wireless sesor etwork applicatios. May efforts have bee made to avoid collectig data from all the sesors i the etwork ad producig maps at the sik, which is prove to be iefficiet. he existig approaches (ofte aggregatio based), however, suffer from heavy trasmissio traffic ad icur large computatioal overheads o each sesor ode. We propose Iso-Map, a eergy-efficiet protocol for cotour mappig, which builds cotour maps based solely o the reports collected from itelligetly selected isolie odes i wireless sesor etworks. Iso-Map achieves high-quality cotour mappig while sigificatly reducig the geerated traffic from O() to O( ), where is the total umber of sesor odes i the field. he per-ode computatio overhead is also restraied as a costat. We coduct comprehesive trace-drive simulatios to verify this protocol, ad demostrate that Iso-Map outperforms the previous approaches i the sese that it produces cotour maps of high fidelity with sigificatly reduced eergy cost. 1. INRODUCION Recet advaces i wireless commuicatio ad micro system techiques have resulted i sigificat developmets of wireless sesor etworks (WSNs) [4, 6, 8]. A sesor etwork cosists of a large umber of low-power, cost-effective sesor odes that iteract with the physical world. he icreasig studies of wireless sesor etworks aim to eable computers to better serve people by usig istrumeted sesors to automatically moitor the physical eviromet. Cotour mappig has bee widely recogized as a comprehesive method to visualize sesor fields. A cotour map of a attribute (e.g. height) shows a topographic map that displays the layered distributio of the attribute value over the field. It ofte cosists of a set of cotour regios outlied by isolies of differet isolevels. Figure 1 plots a sectio of uderwater depth measuremet ad the correspodig isobath cotour map. For may applicatios, cotour mappig provides backgroud iformatio for the sik to detect ad aalyze evirometal happeigs i a global view of the features i the field. Such a view is ofte difficult to achieve by idividual sesor odes with costraied resources ad isufficiet kowledge. (a) (b) Fig. 1. Cotour mappig. (a) A sectio of uderwater depth measuremet; (b) he isobath cotour map of (a). A aïve approach for cotour mappig is to collect sesory data from all the sesors i the moitored field ad the costruct the cotour map at the sik. Obviously, deliverig a huge amout of data back to the sik icurs heavy traffic, which rapidly depletes the eergy of sesor odes. o address this problem, several aggregatio based protocols have bee proposed [9, 16, 17]. hese protocols aggregate data with similar readigs at itermediate odes, reducig the traffic overhead up to 4% [16]. We believe the aggregatio based protocols caot further improve the scalability of the etwork based o the followig observatios. First, as log as all sesors are required to report to the sik, the umber of geerated reports is always O(), where is the total umber of sesor odes. Secod, the aggregatio operatios isert a heavy computatio overhead to the itermediate odes. For example, INLR [16] requires each itermediate ode to carry out multiple itegrals i order to estimate the similarity of two cotour regios. I order to address the iheret limitatios of aggregatio based approaches, we propose Iso-Map. By itelligetly selectig a small portio of the odes to geerate ad report data, Iso-Map is able to costruct cotour maps with comparable accuracy while sigificatly reducig etwork traffic ad computatio overhead. Although the basic idea beyod Iso-Map is comprehesible, several challeges exist i its desig. For example, partial utilizatio of the etwork iformatio reduces the etwork traffic, but aturally leads to the degradatio of the mappig fidelity. hus careful ode selectio policies ad a effective algorithm to recover the cotour map from the partial iformatio are ecessary. We also eed to balace the tradeoff betwee the traffic savigs ad the mappig fidelity. I additio, we aim to avoid heavy computatioal overhead i the itermediate odes so that the desig is scalable for resource costraied 1

2 sesor devices. he major cotributios of this work are as follows. (1) We desig a ovel algorithm to costruct cotour maps from a critical set of odes, which we call isolie odes. By restraiig the traffic geeratio withi the isolie odes, Iso-Map sigificatly reduces the etwork traffic while still costructig high-quality cotour maps that are comparable to the best oes ever achieved through existig protocols. Our aalysis proves that, Iso-Map reduces the traffic geeratio from O() of existig protocols to O( ). () By employig local measuremet o sesors, the per-ode computatioal overhead is costraied as a costat ad does ot grow with the etwork size. (3) We coduct a field study o a practical Iso-Map applicatio, ad based o the collected real world data, we coducted a trace-drive simulatio which cofirms the superior performace of Iso-Map compared with existig protocols. Aother stregth of this desig is that Iso-Map is orthogoal with may other desigs, eablig further traffic savigs to be achieved together with other approaches. he remaider of this paper is orgaized as follows. Sectio discusses the related work. Sectio 3 presets the Iso-Map desig, illustratig the flow of its operatios. I Sectio 4, we mathematically aalyze the commuicatioal ad computatioal overhead of Iso-Map ad compare with that of previous protocols. We preset simulatio results ad evaluate the performace of Iso-Map i Sectio 5. Sectio 6 itroduces our ivestigatio of a practical Iso-Map applicatio. Ad we coclude the work i Sectio 7.. RELAED WORK Cotour mappig has bee widely proposed as a comprehesive method for visualizig sesor fields. Much research o sesor etwork moitorig ca utilize cotour mappig to provide a global view of the moitored fields from which the occurrece ad developmet of eviromet chages ca be easily captured. Hellerstei et al. [4] propose the first framework for cotour mappig itegrated i the iydb system. I iydb, sesor odes are deployed ito grids. Each sesor ode builds a represetatio of its local cell ad delivers it back to the sik. he sik accordigly costructs a isobar cotour map based o the received represetative values of differet grids. Possible i-etwork aggregatio is suggested i this paper; differet isobars may be aggregated i the trasmissio if their attribute values are similar. However, there is o detailed descriptio for the aggregatio algorithm i this paper. Xue et al. [16] further develop a i-etwork aggregatio algorithm, INLR, for the isobar cotour mappig to reduce the traffic overhead. INLR makes cotour regios from close sesor reports of similar readigs ad delivers cotour regios back to the sik. A umerical data model is built for each cotour regio to describe the distributio of attribute values withi the regio. INLR aggregates cotour regios accordig to their data model durig the delivery. he sik costructs the cotour map from the received cotour regios. esca [17] is a similar work, that moitors the residual eergy of sesor odes by costructig cotour maps of the etwork. A esca is defied as a collectio of (VALUE, COVERAGE) tuples ad each tuple describes a regio of COVERAGE where each ode has its residual eergy withi VALUE = (mi, max). A tuple iitially cosists of oly a idividual sesor ode ad gets aggregated with other tuples with adjacet COVERAGE ad similar VALUE. he sik evetually collects differet tuples ad creates the esca cotour map based o them. Although the above protocols achieve cotour mappig with reduced traffic cost through i-etwork aggregatio, they do ot reduce the scale of the geerated traffic. he traffic geerated from all sesor odes is still high, ad the traffic geeratio oe the less scales proportioal to the ode umber of the etwork, O(). he recetly proposed protocol i [9] performs aggregatio from the data suppressio of sesor odes to reduce the traffic overhead. he sesor ode suppresses its data if there is aother sesor ode earby trasmittig similar data ad the trasmitted data is cosidered as a represetatio of the local field. Upo receivig a subset of sesor readigs, the sik performs iterpolatio ad smoothig to obtai the approximatio of the cotour map. he data suppressio protocol reduces the geeratio of sesor reportig ad thus reduces the traffic overhead. he fidelity of the resultig cotour map is highly related to the rate of data suppressio i the etwork. Limited data suppressio ca be performed to achieve a acceptable cotour map approximatio. As stated i the paper, the suppressio algorithm esures that the rage spaed by suppressed odes is bouded withi the -hop eighborhood, so the traffic geeratio is ideed lowered by a factor of the ode degree withi -hop eighborhood. Nevertheless, the traffic geeratio scales liearly with the umber of odes i the etwork. Isolie aggregatio [13] shares some similarities with our work. It proposes to reduce the traffic overhead by restrictig sesor reportig from odes ear the isolies. However, the paper either specifies how the sesor odes detect the isolies passig by or how the sik recovers the isolies from the discrete reports from sesor odes. 3. ISO-MAP DESIGN he basic idea of Iso-Map is to create the cotour map based o a selected set of odes, kow as the isolie odes. Isolie odes are the sesor odes residig o the isolies aroud cotour regios. A more formal defiitio of isolie ode will be give later. Ituitively, sice isolie odes correspod to the perimeter of cotour regios, the umber of reports from isolie odes ca be largely restricted compared with the etwork size. Later we mathematically show that the traffic geerated from isolie odes is at the level of O( ), where is the total umber of odes i the moitored field.

3 Fig.. Cotour mappig from isolie odes. (a) Dese deploymet of sesor odes leads to the isolies; (b) Sparse deploymet of sesor odes provides ambiguous iformatio; (c1) (c3) hree possible cotour maps of (b). It is ot, however, trivial to costruct the cotour map based solely o isolie odes reports. Ideally, as illustrated i Figure (a), whe sesor odes are desely deployed, the positios of isolie odes clearly outlie the cotour regios. I more practical scearios, however, sesor odes are usually deployed sparsely, as show i Figure (b), i which the positios of isolie odes provide oly discrete iso-positios. We caot deduce how the isolies pass through these positios. For example, based o the data illustrated i Figure (b), the sik ca iterpret ito differet cotour maps, such as the oes show i Figures (c1), (c) ad (c3). I this sectio, we will itroduce the major operatios of Iso-Map icludig buildig etwork architecture, query dissemiatio ad isolie ode appoitmet, isolie ode measuremet, ad cotour map geeratio. 3.1 Buildig Network Architecture Iso-Map first builds the routig structure i the sesor etwork, through which the sik isert queries ito the etwork ad collects reports. Although we do ot rely o ay particular uderlyig etwork architecture, for this work, we assume a tree-based routig scheme that is adopted i may systems [4, 7]. We believe that assumig a cocrete uderlyig etworkig strategy helps clearly state the idea, providig a fair platform for the compariso of performace of differet approaches. I the tree-based routig scheme, a spaig tree rooted at the sik is costructed over the commuicatio graph. Each ode is assiged a level, which specifies its hop cout distace from the sik. he paret ode is oe level lower tha its childre odes. Nodes i differet levels forward packets durig differet time slots. opology maiteace mechaisms ca be employed [7], which allow each ode to dyamically choose a paret from its eighborig odes based o commuicatio quality. MAC layer reliability of ode trasmissios ca be easily added ito this framework [1, 11]. 3. Query Dissemiatio ad Isolie Node Appoitmet Iitially, the sik dissemiates a query through the routig tree for cotour mappig over the targeted field. he query message specifies the data space [v L, v H ] ad the graularity of the cotour map, which specifies the desired isolies i the cotour map with the isolevels v i = v L + i [v L, v H ]. Upo receivig this query, each sesor ode accordigly determies whether it is a isolie ode. Defiitio 3.1: A sesor ode p (with sesig value v p ) is a isolie ode if ad oly if: (1) its sesig value is withi a predefied border regio of the isolevel v i specified i the query, i.e. [v i -ε, v i +ε], ad () oe of its eighborig odes q has a sesig value v q, where v i is betwee their sesig values, i.e. v p < v i < v q, or v q < v i < v p. he satisfyig ode has the isolevel of v i. Based o Defiitio 3.1, a ode icurs local operatios withi its eighborhood. he two coditios guaratee that the isolie ode is close to the isolie i terms of value ad space. 3.3 Isolie Node Measuremet Oce the isolie odes are appoited, they make local measuremets ad geerate reports to sed back to the sik. Each isolie ode geerates a 3-tuple report r = <v, p, d>, i which v represets the isolevel of the ode, p represets the positio of the sesor ode ad d represets the gradiet directio of the attribute value at the sesor ode. Clearly, the isolevel v ca be obtaied whe the ode determies that it is a isolie ode, ad the positio p ca be obtaied either from attached localizatio devices such as a GPS receiver or by oe of existig algorithms[3, 14]. However, as we metioed earlier, havig oly p ad v is ofte ot sufficiet for the sik to costruct the cotour map. o address this problem, we itroduce the ew parameter gradiet directio d. Each isolie ode performs local modelig o sesig values withi its eighborhood ad obtais a estimatio of the gradiet directio d. he spatial data value distributio is mapped ito the (x, y, v) space, where the coordiate (x, y) represets the positio ad v = f(x, y) describes the distributio surface of the data value i this space. he gradiet directio d deotes the directio where the data value most degrades i the space. he vector of d is calculated by: f f d = grad( f) = f = (, ) 3.1 x y o estimate the gradiet directio d, a isolie ode first eeds to approximate the local data map. o build the local data map i this desig, each isolie ode seds queries to its eighborig sesor odes for their positios ad sesory values. he query scope ca be adjusted withi k-hop eighbors for differet sesor deploymet desities or to achieve differet levels of estimatio precisio. 3

4 Fig. 3. Liear regressio for spatial data modelig Upo receivig the <v, p> tuples from eighborig odes, the isolie ode approximates the local data map through regressio aalysis. Ideed, may regressio models ca be employed to costruct the approximated data value surface o the local data map, amog which liear regressio is a simple ad widely used oe. he computatioal simplicity of the liear regressio model makes it a atural choice for the resource costraied sesor devices. Figure 3 illustrates the ratioale of how the isolie ode performs the liear regressio ad approximates the data value surface with the regressio plae. Without loss of geerality, we assume the isolie ode positio is p (x, y ) ad the sesory value is v. he positios of its eighborig sesors are p 1 (x 1, y 1 ), p (x, y ),, p (x, y ) ad their sesory values are v 1, v,, v, respectively. A liear model v = L(x, y) = c + c 1 x + c y describes the regressio plae of the +1 poits i the data value space built o (x, y, v). With the +1 poits (x, y, v ), (x 1, y 1, v 1 ),, (x, y, v ), the isolie ode computes the coefficiets of the liear model by solvig the equatio: Aw = b 3. 1 xi yi 1 x y i= i= 1 x1 y1 A= V V xi xi xiyi, V =, i= i= i= 1 x y yi xiyi y i i= i= i= vi i= v c v1 b= V λ = xv i i, λ = ad w= c1. i= c v yv i i i= With the obtaied plae of liear model approximatio v = L(x, y), the isolie ode ca calculate its gradiet by itroducig this approximatio ito formula 3.1: L L d = (, ) p = ( c1, c) 3.3 x y Fig. 4. Gradiet directios of the isolie odes Figure 4 plots a example where the isolie odes are at the isolevel of 4. Each isolie ode calculates the gradiet directio from the regressio withi its eighborhood. We mark the calculated gradiet directios i the figure. he calculated gradiet directio of each isolie ode reflects the local tred of data spatial variatio ad it well approximates the ormal directio of the isolie passig by. 3.4 Cotour Map Geeratio Upo receivig isolie ode reports, the sik costructs the cotour map which is delieated by isolies of differet isolevels, say v i = v L + i [v L, v H ]. he sik separately costructs isolies of differet isolevels, ad the cotour regios reside betwee them. Whe costructig isolies of the isolevel v i, the sik utilizes the reports with isolevel v i from the isolie odes residig alog the isolies of v i. Sice the data gradiet directio d at each reported positio approximates the ormal directio of isolies, it helps to costruct local segmets of isolies. Figure 5(a) shows that isolie odes of the same isolevel report to the sik ad Figure 5(b) depicts the reported iso-positios ad correspodig gradiet directios. he sik first builds a Vorooi diagram for the set of iso-positios, as show i Figure 5(c). he Vorooi cell specifies the affectig area of each iso-positio, where the sik costructs the local isolie segmet accordig to the gradiet directio d at that iso-positio. For each cell, a straight lie passig the iso-positio ad perpedicular to its gradiet directio d is draw. It itersects with cell borders ad partitios the cell ito two parts. he part i the gradiet directio is the outer part ad the opposite oe is the ier part. he separatig lie acts as a local boudary i each Vorooi cell, which we call the type-1 boudary. he sik the merges the ier parts i differet Vorooi cells ad complemets the boudaries to separate cotour regios from outer area. he complemetary boudaries alog the cell borders are called type- boudaries. Figure 5(d) illustrates this step. As show, after this step, well-approximated cotour regios are outlied by the cocateated local boudaries, though it appears a bit rough. he sik the regulates the approximatio by smoothig the piacles based o the followig two rules. 4

5 (a) (b) (c) (d) (e) (f) Fig.5. Illustratio of the process of cotour boudary deductio Rule 1. he type-1 boudary is prologed at the ed where it itersects with a type- boudary ad their iteral agle is withi (18º, 7º). If it itersects with the type-1 boudary i the adjacet Vorooi cell, the piacle area outside of it should be removed ad accepted as the ew boudary. Otherwise, o chage is made. Rule. he type-1 boudary is prologed at the ed where it itersects with a type- boudary ad their iteral agle is withi (9º, 18º). If it itersects with the type-1 boudary i the adjacet Vorooi cell, the cocave area iside of it should be icluded ad accepted as the ew boudary. Otherwise, o chage is made. Figure 5(e) illustrates how the two rules are applied to regulate the approximatio. he regulatio process uder the two rules substatially achieves better readjustmets o the affectig area of each iso-positio ad makes a tighter approximatio. he approximated isolies that are evetually obtaied are show i Figure 5(f). he sik iitially builds isolies of the lowest isolevel v L. hese isolies eclose all cotour regios above the isolevel v L. Isolies are the sequetially costructed accordig to their isolevels. 4. DISCUSSION Iso-Map utilizes the reports from isolie odes to costruct cotour maps. Compared with existig works which rely o the aggregatio of sesory readigs from all odes i the field, Iso-Map largely restrais the scale of sesor reportig. We will first coduct a theoretical aalysis o the icurred traffic scale ad prove that Iso-Map reduces the umber of reports from O() to O( ), sigificatly reducig the traffic cost over the etire etwork. We further show that Iso-Map cosiderably reduces the computatioal overhead itroduced to the odes. Ideed, Iso-Map outperforms existig approaches i terms of both commuicatioal ad computatioal complexity. 4.1 Network raffic o study the etwork traffic icurred by Iso-Map, we first simplify our aalysis to a cotiuous domai, where sesor odes cover the field with ifiite desity. he isolie odes are the represeted by cotiuous isolies. We prove that the total legth of a costat umber of isolies is O( 1/ ), give that all isolies are well behaved ad do ot itersect each other. It is atural that differet isolies do ot itersect each other due to the priciple of cotour mappig. We impose the costrait of well behaved curves as [1] did to exclude some pathologically-shaped moster curves such as Peao s space-fillig curves, which hardly emerge as cotour boudaries i practice [1]. Defiitio 4.1: A curve is well behaved if for ay square box of ay side x that itersects the curve, the legth of the curve iside the box is less tha cx for some costat c > 1. he defiitio is equivalet to observig that the curve has a Hausdorff dimesio of 1 []. I practice, most of the o-bizarre curves have Hausdorff dimesios of 1. heorem 4.1: For ay costat umber K isolies withi a 1/ 1/ square area, the total of their legths L is O( 1/ ). Proof: We first eumerate the K isolies ad assume that the boudig factors for the K well behaved curves are c 1, c,, c K. We the split the square area ito a r r grid, with sides d = 1/ /r for each cell (see Figure 6). he i-th isolie itersects with some of the cells ad the segmet i each cell is bouded by the factor c i. So: 1/ l < d c = r c 4.1 i i i r If we choose c = MAX (c 1, c,, c K ), formula 4.1 ca be reduced to l i < r c 1/. We sum up all isolies ad get: K L= l < Kcr i i= 1 1/ 4. Sice the costat factor of K c r is idepedet of, formula 4. leads to the fact that the sum of isolie legths is at the level of O( 1/ ). Now we exted our aalysis ito a more practical sceario, where sesor odes are uiformly deployed over the square field i a discrete maer. We assume that the desity of odes is p, ad each isolie triggers a stripe of isolie odes alog it with a small width of ε (ε correspods to the ode commuicatio radius, which is small eough compared with the size of the field). I fact, the cotiuous sceario discussed above is a extreme case of this whe p ad ε. heorem 4.: For ay costat umber K cotour regios withi a square area of sesor odes, the umber of isolie odes is O( 1/ ). Proof: he side of the square area is calculated to be (/p) 1/. We the satch the K isolies from the K cotour regios. As show i heorem 4.1, the total legth L of the K isolies is O((/p) 1/ ) = O( 1/ ). he area of the stripe is approximated by the path itegral through these isolies: K S = εds= ε L = εl K i= 1 L i= 1 i i 4.3 5

6 1/ 1/ } d = 1/ /r Fig. 6. he square field split ito grids ABLE 1: Overhead Compariso Approach raffic Network Sesor Deploymet Geeratio Computatio iydb [4] O() O() Grid esca [17] O() O( 4 ) Free INLR [16] O() Ω( 1.5 ) Grid Suppressio [9] O() Ω(d) Grid Iso-Map O( ) O() Free Accordig to formula 4.3, the umber of isolie odes scattered i the stripe is thus p S = O( 1/ ). From heorem 4., the geerated traffic from isolie odes is thus limited to O( 1/ ). 4. Computatioal Overhead We aalyze the computatioal overhead of (1) the isolie odes for local measuremets o the 4-tuple parameters ad () the itermediate odes which carry out i-etwork filterig to reduce the traffic of reports. he local measuremets coducted by each isolie ode require oly local iformatio withi the eighborhood. he computatioal overhead is bouded by the ode degrees. From the calculatig process described i Sectio 3.3, we observe that the mai computatioal workload comes from solvig the regressio equatio of formula 3. which ideed icurs O(deg) calculatios, where deg is the average degree of each ode i the etwork. herefore, the total computatioal overhead amog all isolie odes is bouded by O(deg 1/ ). he itermediate odes which forward the isolie ode reports ormally simply relay the reports without ay computatioal workload. hus the computatioal overhead withi the forwardig etwork is bouded by O(). Combiig the above two parts, the computatioal overhead withi the etire etwork is O(deg 1/ + ) = O(). able 1 summarizes ad compares Iso-Map with 4 existig approaches. Iso-Map icurs the lowest traffic cost ad etwork computatio whe performig cotour mappig. Note that amog the 5 approaches, oly the Iso-Map ad esca protocols have o requiremet o the sesor deploymet. he iydb, INLR ad Data Suppressio protocols basically rely o a regular deploymet of sesor odes ito grids. hey use sik iterpolatio to deal with irregular ode deploymet, which potetially degrades the fidelity of the resultig cotour map. 5. PERFORMANCE EVALUAION We implemeted the Iso-Map protocol ad coducted trace drive simulatios to evaluate its performace. We utilized a real map of uderwater depth as our testig data which is obtaied from soar measuremets i H.H. Harbor (see Sectio 6). Basically, sesor odes are uiformly deployed to moitor the depth values over a ormalized 1/ 1/ surveillace field with a desity of 1. he radio rage of sesor odes determies the average degree of each ode. Experimetally, we fid that to keep a coected commuicatio graph, the radio rage should be o less tha 1.5, which results i a average ode degree of 7. his correspods to a reasoable deploymet of oe ode per 4 m i practice, if we set up a 3 m radio rage for the MICA motes [5]. Perfect lik layer is assumed i this simulatio, i which the data delivery is guarateed through performace based routig dyamics [7, 15] ad MAC layer retrasmissios [1, 11]. We first evaluate the produced fidelity of Iso-Map uder various settigs. he we study the etwork overhead icurred by Iso-Map o the costructio of the cotour map, icludig commuicatioal overhead as well as computatioal overhead. 5.1 Fidelity of Cotour Mappig We utilize a 4m 4m sectio of the uderwater depth measuremet as our testig data (refer to figure 1 for the measuremet ad its cotour map). We compare the resultig fidelity of Iso-Map with that of iydb, which achieves the best fidelity compared with all other existig approaches. Sice the iydb protocol requires a grid deploymet of sesor odes, whe simulatig the iydb protocol, we deploy the sesor odes ito grids istead of radomly. For both approaches, ode desity is the domiatig factor affectig the fidelity of the cotour mappig. hus, we simulate differet ode desities of deploymet to reflect the impact. We study the cases with 4 odes,,5 odes ad 1, odes separately. If we ormalize the field size to be 5 5 uits, the ormalized ode desities are.16, 1 ad 4, respectively. I practice, all three cases correspod to reasoable ode desities for differet applicatios requirig more or less surveillace precisio. Figures 7(a) (c) depict the resultig cotour maps of iydb uder the above ode desities. Figures 7(d) (f) depict the resultig cotour maps of Iso-Map. he isolie reports received at the sik are 11, 89 ad 49. Clearly, both approaches degrade i precisio as the ode desity decreases, but both still produce acceptable fidelity maps. 6

7 (a) (b) (c) (d) (e) (f) Fig. 7. Performace of isobath cotour mappig. (a) (c): he cotour maps created by iydb algorithm, uder differet ormalized desities of sesor odes (4, 1 ad.16); (d) (f): he cotour maps created by Iso-Map, uder differet ormalized desities of sesor odes (4, 1 ad.16). Mappig Accuracy (%) iydb Iso-Map raffic Overhead (KB) iydb INLR Iso-Map Computatioal Itesity per Node (ormalized) INLR iydb Iso-Map Node Desity (Normalized) Network Diameter (hops) Network Diameter (hops) Fig. 8. (a) Cotour mappig accuracy agaist ode desity; (b) Network traffic overhead agaist etwork diameter; (c) Computatioal itesity agaist etwork diameter. Figure 8(a) plots how the mappig accuracy is affected by the deployed ode desity. Here the mappig accuracy is measured as the ratio of the accurately mapped area i the resultig cotour map to the whole area. he ormalized desity of 1 correspods to deployig,5 odes i the 4m 4m field. he mappig accuracy of both iydb ad Iso-Map rapidly jumps to a high level above 8% as the deployed ode desity icreases. I all cases, Iso-Map is slightly below iydb but with comparable accuracy. 5. Network raffic Overhead It is well kow that the etwork traffic cosumes the largest portio of the sesor eergy ad is cosidered the most importat metric used to evaluate the eergy efficiecy of a WSN. I this sectio, we cotrast Iso-Map with the most recet work INLR [16], as well as with the well-kow iydb protocol. We vary the etwork diameter so that three protocols are simulated over the fields of differet sizes. With a costat ode desity of 1, the etwork diameter varies from 1 to 5 hops. Each parameter i a report uses two bytes, such as the sesory value, positio, gradiet, etc. Figure 8(b) plots the traffic overhead of the three protocols i terms of kilobytes. Cosistet with the theoretical aalysis, the traffic overhead icurred by iydb ad INLR grows rapidly while Iso-Map maily relies o the isolie ode reports, imposig much less traffic. 5.3 Node Computatioal Overhead I the aggregatio based protocols, itermediate odes coduct heavy computatios to aggregate differet map segmets. O the other had, i the o-aggregatio protocols, such as iydb, etc., reports are delivered to the sik without aggregatio, which meas the itermediate odes simply store ad forward packets. hus, iydb actually gives a lower boud o the average computatioal overhead of each ode. We compare the computatioal overhead per ode i iydb, INLR ad Iso-Map. Figure 1 plots the ormalized computatioal itesity of the three protocols uder differet etwork sizes. As show i Figure 1(a), iydb ad Iso-Map costrai the computatioal itesity at a low level, while INLR itroduces a relatively huge amout of computatios o each sesor ode, ad such overhead grows with the etwork size. Compared with INLR, the differece betwee iydb ad Iso-Map becomes egligible. 6. APPLICAION SCENARIO We coducted a field study o H.H. Harbor, which is curretly the secod largest harbor of coal trasportatio i Chia. It has experieced rapid developmet over the past 5 years, ad its coal trasportig capability has icreased from 1.6 millio tos per year i to 6.7 millio tos 7

8 per year i 6. However, H.H. Harbor curretly suffers from the icreasigly severe problem of the silted sea route. H.H. Harbor has a sea route that is 19 autical miles log ad 8m wide at the etrace, icludig a ier route ad a outer route. he sea route is desiged to have a water depth of 13.5m to allow for the passage of ships that weigh over 5 thousad tos. Sice the sea route has bee i operatio, it has always bee threateed by the movemet of silt from the short sea area withi 14 autical miles outside the route etrace. I the evet that the sea route is silted up, ships of large toages must wait to prevet groudig, ad ships of small toages eed be piloted ito the harbor. Moitorig the extet of siltatio reliably is critical i order to esure the safe operatio of H.H. Harbor. he ucertaity ad the high istataeous itesity of the siltatio make moitorig the extet of siltatio extremely expesive ad difficult. he amout of siltatio i H.H. Harbor is affected by may factors, amog which tide ad wid blow are the most domiatig. While the tide produces a periodical ifluece o the movemet of silt, the sudde blowig of wid brigs more icidetal ad itesive iflueces. We propose to deploy a echolocatio sesor etwork o the sea surface to cotiuously moitor the water depth of the sea route. he precise depth measuremet at each spot is ot eeded. Istead, Iso-Map ca be utilized to build a isobath cotour map to visualize the depth level of the sea area. he cotour map depicts the cotour sea zoes above differet depth levels. Based o this cotour map, we ca easily guide ships of differet toages. With the map, we ca also clearly locate the dagerous areas where the water depth is uder alarm thresholds. 7. CONCLUSIONS AND FUURE WORK We propose Iso-Map, which achieves eergy-efficiet cotour mappig by collectig reports from isolie odes oly. Our theoretical aalysis shows that Iso-Map outperforms previous protocols i terms of commuicatioal ad computatioal cost i the etwork. Iso-Map reduces the geerated traffic from O() of existig protocols to O( ). We also use trace-drive simulatios to compare Iso-Map with existig protocols, ad the results show that Iso-Map achieves high fidelity maps with sigificatly reduced overhead. he scalability of Iso-Map is superior, which makes Iso-Map feasible for the large-scale deployed sesor etworks. We coducted a field study at H.H. Harbor ad ivestigated the practical applicatio sceario of moitorig the siltatio of the sea route. We aalyze the advatages ad feasibility of deployig a echolocatio sesor etwork for this sceario. We show that it will be of great beefit to utilize Iso-Map to costruct cotour maps over the sesor etwork i order to moitor the siltatio. Our future work icludes buildig a prototype system at H.H. Harbor ad testig our Iso-Map protocol o this prototype. We hope the implemetatio experiece helps us further uderstad the efficiecy ad scalability of the Iso-Map desig. ACKNOWLEDGEMEN his work is supported i part by the Hog Kog RGC grat HKUS615/6E, the HKUS Digital Life Research Ceter Grat, the Natioal Basic Research Program of Chia (973 Program) uder grat No. 6CB33, ad NSFC Key Project grat No REFERENCES [1] C. Buragohai, D. Agrawal ad S. Suri, "Distributed Navigatio Algorithms for Sesor Networks," i Proceedigs of IEEE INFOCOM, 6. [] L. Evas ad R. Gariepy, Measure heory ad Fie Properties of Fuctios: CRC Press, 199. [3] D. Goldeberg, P. bihler, M. Gao, J. Fag, B. Aderso, et al., "Localizatio i Sparse Networks usig Sweeps," i Proceedigs of ACM MobiCom, 6. [4] J. M. Hellerstei, W. Hog, S. Madde ad K. Staek, "Beyod Average: oward Sophisticated Sesig with Queries," i Proceedigs of IPSN, 3. [5] J. Hill ad D. Culler, "Mica: A Wireless Platform For Deeply Embedded Networks," IEEE Micro, vol., pp. 1-4,. [6] M. Li ad Y. 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