An index replication scheme for wireless data broadcasting

Transcription

1 The Journal of Systems and Software 51 (2000) 191±199 wwwelseviercom/locate/jss An index replication scheme for wireless data broadcasting Yon Dohn Chung, Myoung Ho Kim * Department of Computer Science, Korea Advanced Institute of Science and Technology (KAIST), Kusong-dong, Yusong-gu, Taejon , South Korea Received 21 October 1998; received in revised form 27 January 1999; accepted 3 March 1999 Abstract In mobile distributed environment, data broadcasting has many applications because it has two desirable characteristics: energy e ciency and bandwidth e ciency There have been some researches on the indexing mechanisms for wireless data broadcasting in the past We rst describe the problematic issue in the conventional index replication scheme, and then propose various index replication methods based on three criteria: accessibility, energy e ciency and adjacency We evaluate the proposed scheme in analytic and experimental ways We show that the proposed index replication scheme reduces the data access cost of mobile clients in an energy e cient manner We also discuss the relaxation of the given criteria Ó 2000 Elsevier Science Inc All rights reserved Keywords: Index replication; Wireless data broadcasting; Mobile computing 1 Introduction Wireless technology gains its popularity and opens new elds of computing environment such as mobile distributed systems (Huang et al, 1994), wireless information systems (Imielinski and Viswanathan, 1994) and personal communication services (Imielinski and Badrinath, 1992) In wireless systems there are two major restrictions ie, bandwidth limitation and energy restriction (Acharya et al, 1995; Imielinski and Badrinath, 1993; Imielinski et al, 1994) Bandwidth limitation There is very narrow bandwidth that can be used for wireless communication and the capacity of wireless network is almost 1000 times less than that of wireline one Energy restriction The mobile computing devices usually use batteries as their main energy sources, which makes it very important how to use the limited energy e ciently Data broadcasting is a mechanism that can e ciently cope with the two limitations mentioned above The server sends data stream to a large number of unspeci- ed clients and the clients receive the broadcast data As clients do not send requests to the server and the energy consumed in sending data is much larger than that in * Corresponding author Tel: ; fax: address: mhkim@cskaistackr (MH Kim) receiving data, data broadcasting is energy-e cient It is also bandwidth-e cient because many clients share the broadcasting channel Mobile units provide two kinds of operating modes, ie, active and doze mode The energy consumption in doze mode is about 1000 times less than that in active mode (Argade et al, 1993) The index on wireless broadcast data stream enables the mobile unit to remain in doze mode when it need not read the broadcast data Without the index, all data stream must be read from the time the data access request is initiated to the time the required data are completely downloaded However, by using the index, the client reads only some index portions in the broadcast stream and recognizes the appropriate address of the target data After obtaining the address, ie, the temporal o set from the index to the data, the client can remain in doze mode until the target data are delivered The amount of time elapsed from the moment a client asks for data to the time it receives appropriate data is called the access time The tuning time is the amount of time for which the client actually listens to the channel Hence, the tuning time is determined by the amount of time spent being in active mode This will determine the power consumed by the client to retrieve the required data There have been some researches (Imielinski et al, 1994; Leong and Si, 1995) on data broadcasting techniques in mobile computing, such as indexing, caching, /00/$ - see front matter Ó 2000 Elsevier Science Inc All rights reserved PII: S (99)

2 192 YD Chung, MH Kim / The Journal of Systems and Software 51 (2000) 191±199 and cache-invalidation reporting In this paper we focus on the index replication scheme for indexing wireless broadcast data After pointing out the problem in the existing index replication scheme, we propose methods that can overcome the problem, with comprehensive performance evaluations The rest of the paper is organized as follows In Section 2 we explain the index replication concept We describe the problematic issue in the conventional index replication scheme and then propose energy e cient index replication approaches in Section 3 In Section 4 analytic evaluation and experimental results are presented Finally, we conclude this work with some relevant discussions 2 Background The major index replication schemes that have been developed so far are 1; M indexing and distributed indexing (Imielinski et al, 1994) 1; M indexing replicates the global index by M times This can reduce the tuning time for searching index buckets in the broadcast stream Distributed indexing organizes the index structure hierarchically and replicates some part of indexes appropriately It performs better than 1; M indexing with respect to the tuning time, ie, it is more energye cient A data bucket is the bucket whose contents are data A bucket whose contents are directory information is called an index bucket (The bucket is the basic unit of data manipulation on the air) The broadcast data stream, commonly called bcast, is composed of indexes and data Fig 1 shows an example of index tree with data at the bottom The index information is depicted as ellipses and the data as rectangles The top level index node I has index information for the second level index nodes a1, a2 anda3, and the node a1 has that for the third level index nodes b1; b2 and b3 The node b1 holds the index information for c1, c2 and c3 Finally, the lowest level index c1 contains the addresses of data 0; data 1 and data 2 In the gure we depict only data 0 in the rst rectangle due to the limited space In wireless data broadcasting an index node is composed of one or more buckets In this paper we assume, without loss of generality, an index node consists of one bucket and a data object consists of one or more buckets And we use the terms `index node' and `index bucket' interchangeably for the rest of our paper In Imielinski et al (1994) replicating some index buckets has been shown to reduce the tuning time that is important to energy e ciency The optimal level of index replication has also been studied in that work Fig 1 is based on replication level 2, where each node in the top level and the second level is replicated as many times as the fan-out of the tree The index nodes that are replicated are called control index nodes The index nodes that are not replicated are called non-control index nodes The conventional index replication scheme replicates control index buckets in front of their children when constructing bcasts Fig 2 shows two successive bcasts (here, rst three big rectangles are temporally contiguous and form one bcast) that are organized based on Fig 1 Note that each bcast represents an entire linearized sequence of information in Fig 1 The index bucket within the replication boundary is replicated three times because the number of children is 3 For instance, index bucket a1 has three replicas a1, a1 0, and a1 00 in front of b1; b2, and b3, respectively By replicating indexes we have more opportunities to follow down the tree without waiting for the next bcast The access protocol of a mobile client is as follows (Imielinski et al, 1994) The client remains in doze mode between index probes (1) Tune in bcast, obtain the temporal o set of the next control index bucket and go to doze mode (2) Tune in again at the time of the appropriate index Determine, on the basis of the address value in the control index and the target data id, whether to: Fig 1 An example index tree

3 YD Chung, MH Kim / The Journal of Systems and Software 51 (2000) 191± Fig 2 Broadcast data stream of Fig 1 (a) when the requested data had already passed over, go to doze mode again until the beginning of the next bcast and proceed as in (3) (b) otherwise, tune in again at the appropriate index (3) Following the sequence of index probes, obtain the data Example 1 Based on Fig 2, when a mobile client wants to access data 54 (which is under index bucket c19) and current tuning position is at data 36, the sequence of node accesses is: data 36! a2 00! I 00! a3! b7! c19! data 54 3 Proposed index replication scheme 31 Problem description In the conventional index replication scheme the control index buckets are replicated as many times as the fan-out of the index tree, where the replicated index buckets contain the same index information In Fig 1 (and also in Fig 2) the fan-out of the tree is 3 Thus for example, a1, a1 0 and a1 00 are the three replicas that have the same index information for fb1; b2; b3g By the way, in Fig 2, b1 andb2 had passed over at the moment when the client reads index a1 00 So the addresses of b1 and b2 in a1 00 cannot be used This is because a client can only read broadcast data that are or will be on the air In this paper we call the conventional index replication scheme mentioned in Section 2 as the blind index replication scheme (BIRS) When measuring the amount of index that is uselessly replicated in the BIRS, we can observe the following An index bucket contains n index slots, where n is the fanout of the index tree There are i 1 index slots that are uselessly replicated in the ith replicated control index bucket For example a1 0 (the second replica of a1) has one useless index slot (ie, b1) and a1 00 (the third replica of a1) has two useless slots (ie, b1 and b2) Since one P iˆn iˆ1 control index bucket generates i 1 =n ˆ n 1 =2 bucket(s) of bandwidth waste and the number of replicated control index buckets in level i is n i, we can derive the following formula for the amount of bandwidth waste (in terms of the number of buckets) in the BIRS Here, r denotes the replication level n 1 2 iˆr 1 X iˆ0 Fig 3 Bandwidth waste of BIRS n i ˆ nr 1 : 1 2 As shown in the formula and its graphical illustration in Fig 3, the bandwidth waste of the BIRS signi cantly increases with a large fan-out and more levels of replication The waste of index space on wireless channel means bandwidth ine ciency, which is not desirable in mobile computing systems 32 The criteria for index replication The bandwidth ine ciency of the BIRS is caused by the temporal property of the index information That is, an address in the index bucket indicates the time when the data (or index) to which the index points are delivered So when replicating an index bucket, the address of the data or index that had already passed over comes of no use To overcome the bandwidth waste, we propose a new index replication scheme that satis es the following criteria: 1 Accessibility Based on a given time, an address is called accessible if the bucket that the address indicates has not passed over but comes in the future In Fig 2,

4 194 YD Chung, MH Kim / The Journal of Systems and Software 51 (2000) 191±199 for example, the addresses of b2 and b3 ina1 0 are called accessible whereas that of b1 is not Inaccessible addresses are useless for accessing the target data 2 Energy efficiency An index pointer should provide good performance characteristics with respect to the tuning time For example, insertion of the address of a1 0 into I 0 does not give any kind of energy e ciency in the conventional distributed indexing This is because every bucket (regardless of index or data bucket) basically has an o set to the next-nearest upper-level control index and I 0 is that of a1 0 (Imielinski et al, 1994) 3 Adjacency We need to consider the locality (Bellady, 1966), especially spatial locality, in choosing index buckets to link Spatial locality means that storage references tend to be clustered so that once a location is referenced, it is highly likely that nearby locations will be referenced This will be e ective for processing rangequeries Therefore, we think it is more desirable to link the index bucket whose coverage is adjacent to that of the control index to be replicated Here, we say that the coverages of two index nodes are adjacent if the ranges of data in the subtrees rooted at the index nodexs are continuous Based on the three criteria mentioned above, we propose three index linking strategies The main di erences among them are the scopes of links In Figs 1 and 2, for example, a1 0 has the addresses of fb1; b2; b3g, but b1 is not accessible Therefore, an accessible, energy efficient and adjacent address needs to be used instead of b1 All the possible index nodes that are adequate to be linked with respect to the given three criteria are: (i) b1 in the next bcast, (ii) b4 and (iii) a2 All the others do not satisfy at least one of the three criteria Especially, these three nodes are the only candidates whose coverages are adjacent to that of a1 0 Fig 4 shows a control index a1 0 and its neighbor index nodes The coverage of a1 0 is data 9±data 26, the coverage of b1 isdata 1±data 8, the coverage of b4 is data 27±data 35 and the coverage of a2 isdata 27±data 53 Each shaded area represents a region that one index node covers and is adjacent to a1 0 s coverage One is on the left-hand side of a1 0 (Fig 4(i)) and the other two are on the right-hand side (Figs 4(ii) and (iii)) The adjacent index in the left means that it had already passed over so we have to link the same one in the next bcast (eg b1 in the next broadcast stream) 33 Forward link approach In the forward link (FL) approach, we use forward addresses instead of inaccessible ones The forward address means that it is the address in the next bcast rather than that in the current bcast Incontrol index a1 0 the address of b1 in the next bcast replaces the address of b1 in the current bcast Thus the index bucket a1 0 contains the addresses of b1 next ; b2; b3 instead of those of b1; b2; b3 We use the subscript next, like I next, to indicate that it is the bucket in the next bcast Let us look at the contents of index buckets when using the FL approach The notation ``Content W ˆ X ; Y ; Z '' means the index W contains the addresses of X, Y and Z: Content I ˆ a1; a2; a3 ; Content I 0 ˆ a1 next ; a2; a3 ; Content I 00 ˆ a1 next ; a2 next ; a3 ; Content a1 ˆ b1; b2; b3 ; Content a1 0 ˆ b1 next ; b2; b3 ; Content a1 00 ˆ b1 next ; b2 next ; b3 ; However, this approach requires that bcasts should be static In other words, two successive bcasts must be the same because otherwise some forward addresses may be dangling Example 2 In Fig 2, suppose a client asks for data 6 (which is under b1) when data 15 is on the air at this time Then each sequence of node accesses in the BIRS and the FL is as follows: BIRS: data 15! a1 00! I next! a1 next! b1 next! c3 next! data 6 next ; FL: data 15! a1 00! b1 next! c3 next! data 6 next : Fig 4 Neighborhood of control index a1 0 When a client asks for the data that is in the subtree rooted at b1, the client can remain in doze mode until b1 in the next bcast arrives by using the forward link in control index a1 00 In the BIRS, the client must traverse I next and a1 next additionally, which results in more energy consumption of the mobile unit

5 The FL approach covers the left-hand side region of a1 0 in Fig 4 The right-hand side regions are covered by the approaches in the subsequent sections 34 Nephew link approach YD Chung, MH Kim / The Journal of Systems and Software 51 (2000) 191± The nephew link (NL) approach adopts nephews as link pointers when replicating control index buckets The nephew of a control index is the children of its next sibling, eg b4 is a nephew of a1 Fig 5 illustrates the NL approach applied to Fig 1 The contents of index buckets in the gure are as follows: Content I ˆ a1; a2; a3 ; Content I 0 ˆ a2; a3; a1 next ; Content I 00 ˆ a3; a1 next ; a2 next ; Content a1 ˆ b1; b2; b3 ; Content a1 0 ˆ b2; b3; b4 ; Content a1 00 ˆ b3; b4; b5 ; Example 3 From the example in Fig 2, suppose a client asks for data 27 that is in the subtree rooted at b4 at the time when data 6 is on the air Then each sequence of node accesses in the BIRS and the NL is as follows: BIRS: data 6! a1 0! I 0! a2! b4! c10! data 27; NL: data 6! a1 0! b4! c10! data 27: In the NL approach the client can move directly to b4 after reading a1 0 because a1 0 has the pointer to b4 instead of b1 Therefore, two probes into index nodes I 0 and a2 are saved Note that bcasts need not be static in the NL approach 35 Sibling link approach The sibling link (SL) approach uses the pointers to the sibling nodes instead of inaccessible ones For instance, in Fig 4(iii), the node a1 0 contains the pointer to a2 that is a sibling of a1 An example of the SL approach is depicted in Fig 6 Note that since the root node has no sibling, the second level nodes are linked in the root node With this approach, the client can access a2 Fig 6 Sibling link approach without traversing I 0 when it tunes in a1 0 and accesses the data that is in the subtree of a2 The contents of index buckets in the SL approach are as follows: Content I ˆ a1; a2; a3 ; Content I 0 ˆ a2; a3; a1 next ; Content I 00 ˆ a3; a1 next ; a2 next ; Content a1 ˆ b1; b2; b3 ; Content a1 0 ˆ b2; b3; a2 ; Content a1 00 ˆ b3; a2; a3 ; When comparing the SL with the NL, the sibling index node has larger coverage than the nephew one but less bene t in the light of the tuning time The following example shows the relationship between the NL and the SL: Example 4 Consider the control index a1 0 in Figs 5 and 6 NL: a1 0 contains the pointers to fb2; b3; b4g From Fig 5 we can see that the NL approach reduces two tuning steps compared with the BIRS (ie, I 0 and a2) when a client accesses a data object under b4 SL: a1 0 contains fb2; b3; a2g From Fig 6 we can see that the SL approach reduces one tuning step compared with the BIRS (ie, I 0 ) when a client accesses the data under b4 (In fact this is true whenever a client accesses the data under a2) In the above example the coverage of b4 is three (ie, the fan-out of the tree) times less than that of a2 although the former gives more tuning time reduction More detailed comparisons and analyses are presented in the following sections Note that as in the NL approach the SL approach does not require static bcasts 4 Performance evaluations Fig 5 Nephew link approach We rst analyze the proposed approaches and then present performance results of simulation experiments Note that our evaluations are performed on the basis of the tuning time As for the access time, our approaches

6 196 YD Chung, MH Kim / The Journal of Systems and Software 51 (2000) 191±199 and the BIRS are the same because there is no modi cation in data locations and the amount of index information 41 Analytic evaluation We assume that the initial probe positions and the target data objects are uniformly distributed in the bcast Let r and n denote the replication level and the fan-out of the index tree, respectively Suppose that an index tree is balanced and each node has the same number of children For the purpose of analyses we de ne the concept of the segment as follows: De nition 1 A segment is the set of index and data buckets in the bcast, where all initial probes starting from that segment follow the same sequence of node accesses The segments of the bcast with n ˆ 3 and r ˆ 2 are labeled in Fig 7(a) and those of the bcast with n ˆ 3 and r ˆ 3 are labeled in Fig 7(b) by using the bold characters between control index buckets Here, we use the same notation as in Fig 1 to denote an index node ie, I's are the root nodes, a's are the nodes in the second level, b's are the nodes in the third level and c's are the nodes in the fourth level Fig 7 Segment labeling The elements of a few segments based on Fig 7(a) are given below Note that the control index node is included in its preceding segment, eg a1 0 is included in segment 1 in Fig 7(a) Segment 1 ˆfa1; b1; c1; c2; c3; data 0; data 1; ; data 8; a1 0 g; Segment 2 ˆfb2; c4; c5; c6; data 9; data 10; ; data 17; a1 00 g; Segment 3 ˆfb3; c7; c8; c9; data 18; data 19; ; data 26; I 0 g: There are n r segments in a bcast and the segment is the basic unit through which we measure the performance of the proposed approaches Although the segments are a little di erent in size, we assume them to be equal approximately We de ne the following terminology for the tuning bene t of the proposed index replication scheme against the BIRS: De nition 2 TB i; j is the reduction of the number of tuning steps in the proposed approach compared with the BIRS when a client tunes in segment i and accesses a data object under control index j Example 5 In Table 1, by using b1 0 in Fig 7(b), we describe its contents, TB value, the reduction of node accesses and the probability with which this event should occur for each approach In case of the FL, b1 0 contains the addresses of fc1 next ; c2; c3g Thus the NL approach reduces three tuning steps compared with the BIRS when a client accesses data that are under c1 next at segment 1 This is because the client must probe three additional index nodes, I next! a1 next! b1 next, to access c1 next when using the BIRS The initial probe falls into segment 1 with the probability of 1=n r ˆ 1=3 3 ˆ 1=27 and the client accesses a data object under c1 next with the probability of 1 the size of subtree rooted at c1 next : 27 the size of a bcast In case of the NL, b1 0 contains fc2; c3; c4g, so two tuning steps are reduced when a client accesses data under c4 at segment 1 The access probability of the data in the subtree rooted at c4 is1=27 and the probability of initial probing into segment 1 is 1=27 In case of the SL, b1 0 contains fc3; c4; b2g Thus one step of tuning is saved when a client accesses a data object under b2 with the probability of 1=27 1=9 Table 1 The use of TB ± an example for b1 0 Content b1 0 TB value Reduction Prob FL fc1 next ; c2; c3g TB 1; c1 next ˆ3 I next ; a1 next ; b1 next NL fc2; c3; c4g TB 1; c4 ˆ2 a1 0 ; b SL fc2; c3; b2g TB 1; b2 ˆ1 a

7 YD Chung, MH Kim / The Journal of Systems and Software 51 (2000) 191± Now we derive the general formula for the tuning time reduction of the proposed index replication scheme by summing up all TBs multiplied by their occurrence probability The di erence of the FL from the BIRS is the use of forward addresses in replicated control index nodes For instance, b2 00 contains the addresses of fc4 next ; c5 next ; c6g and a1 0 contains those of fb1 next ; b2; b3g Then TB(5,fc4; c5g) and TB(3,b1) of the FL are 3 and 2, respectively The total tuning time reduction of the FL is computed as follows Each replicated index slot in depth level k provides k steps of tuning time reduction and its coverage is 1=n k of a bcast The number of slots that are generated in replicating a control index and are not accessible is n n 1 =2, which is derived from P n iˆ1 i 1, and the number of control index nodes in level k is n k 1 with duplicates removed In addition each slot is accessed with the probability of 1=n r that is the access probability of a segment Therefore, we can derive the following formula for the performance improvement (tuning time reduction in terms of bucket) of the FL approach that is obtained in a single data access 1 Xkˆr n r kˆ1 n n 1 2 n k 1 1 n k k n 1 r r 1 ˆ : 2 4n r The general formula for the tuning time reduction of the NL are obtained as follows by computing all the TBs in the bcast: n 1 n r 1 n2 r 1 n 2n 2r 2n 2r n 1 2n2 1 n 2r 1 3 n 2r 2 n 1 n 2 1 ' 1 with large n r : 4 n 1 Formulas (5) and (6) represent the tuning time reduction of the SL compared with the BIRS in case that the replication level(r) is greater than 2 If the replication level is less than or equal to 2, its tuning bene t is analyzed as n r n r 1 =2n 2r bucket(s) per one data access By asymptotic transformation we can obtain 05 bucket of average tuning time reduction per data access The full set of TB values of Figs 5 and 6, and the detailed steps for obtaining the formulas are described in Chung and Kim (1998): n r 1 n r 3 n r n 2 n r 2 n r 1 2n 5 n 2 1 n r 1 n 1 n r 2 1 r 3 n r 3 6 2n 2r ' 1 with large n: 7 2 We illustrate formulas (2), (3), (5) and (6) graphically in Fig 8 Among the three proposed approaches, the tuning time reduction of the FL and the NL decreases with large n or r while that of SL is independent of them The formulas are based on the case when an index node consists of one bucket When an index node is composed of m buckets, the tuning time reduction becomes m-times of the formula in each, for one step of tuning reduction equals to m buckets of tuning time reduction 42 Experimental evaluation We perform experimental simulation Our simulation model is composed of a broadcasting server process, a client process, and a le whose role is the wireless media The server generates the broadcast data stream with appropriate index information and writes it into a le on the disk The client process accesses the data in the le according to the data access protocol in Section 2 We count the number of node accesses in the client process in terms of bucket In the experiment the initial probe positions and the target data objects are uniformly distributed in the bcast Varying the fan-out (n), the replication level (r) and the height (h) of the index tree, the tuning time reduction of the proposed index replication scheme is measured We consider only point-queries in the experiment In the next section we will give brief comments on Fig 8 Tuning time reduction of the proposed scheme

8 198 YD Chung, MH Kim / The Journal of Systems and Software 51 (2000) 191±199 Table 2 Experimental results Cases n±r±h processing range-queries We have used various sizes for the data object, but similar results have been obtained Table 2 shows the tuning time reduction (in terms of bucket) that is obtained per single data access when using the proposed index replication approaches When the replication level increases, the tuning reduction of the SL comes close to 05 while those of the NL and the SL decrease In the result we also observe that the height of the index tree has little e ects on the performance improvement, which is found in our analytic results According to the analytic and experimental results, the SL approach shows the best performance in most cases except that the parameter values are very small It also provides almost constant tuning time reduction, 05 bucket per each data access with large n 43 Practical implication Average tuning reduction FL NL SL 2±2± ±2± ±3± ±3± ±2± ±2± ±3± ±3± ±2± ±2± ±3± ±3± We have applied the SL method into a real world wireless system, called Quotrex (Imielinski et al, 1994), that periodically broadcasts stock market information (about 160 KB) with 10 Kbps on FM band The result is shown in Table 3 The AT-opt method has no index but only data, so it gives optimal access time but the worst tuning time The TT-opt method replicates the global index (ie, the index is organized in at structure) at every possible positions, so it provides optimal tuning time but the worst access time The 1; M method reduces the access time by replicating the global index by M times compared with the TT-opt method The DI (distributed indexing) method uses hierarchical index structure and blind index replication policy As shown in the table, the SL method reduces the tuning time by 05 bucket with a near optimal access time 5 Discussion 51 Processing range-queries Let us consider the way a mobile client retrieves a set of data objects bounded by a range One straightforward method is to nd the beginning of the range and sequentially read the broadcast stream until all the required data are obtained This method is very simple but it consumes too much tuning energy, for index buckets are intermixed with data buckets in the broadcast stream and hence all of them are read unnecessarily An ad hoc solution for avoiding this problem is to chain either the leaf index nodes or data buckets as in B -tree Another method for sequential data retrieval is to generate a set of threads (or processes) retrieving data Example 6 shows this method using the BIRS based on Figs 1 and 2 Example 6 Suppose a client accesses a set of data (data 24 ±data 27 ) at the time data 6 is on the air Because a1 0 contains the addresses of b1, b2, and b3 (ie, it covers data 0 ±data 26 ), and a part of the target range (data 27 )is not covered by a1 0, the client generates a new thread for accessing data 27 after probing data 6 and a1 0 That is, two threads process each of the split target data ranges (`data 24 ±data 26 ' and `data 27 ') in parallel as in Fig 9 When using this sequential processing method, the proposed approaches still gives tuning time reduction For example, if applying the SL approach to the above example, we can nd that two tuning steps I 0 and a2 is reduced because a1 0 informs the client to move to b4 This reduction is depicted as dotted area in Fig 9 The FL and NL approaches are also e ective for this kind of range-query processing This is because that our approaches are based on the adjacency criterion Table 3 Implication result Indexing method Access time (buckets) AT-opt TT-opt ; M DI SL Tuning time (buckets) Fig 9 Using multiple threads for range-query processing

9 YD Chung, MH Kim / The Journal of Systems and Software 51 (2000) 191± Fig 10 Tuning time reduction of the new approach 52 Relaxing the criteria Comparing the NL and the SL, we observe that there is a trade-o between the coverage of an index slot and its tuning bene t For example consider TB(1,c4) ˆ 2 in the NL and TB(1,b2) ˆ 1 in the SL in Table 1 While the coverage of the upper-level index (b2) is bigger than the lower-level one (c4) as many times as the fan-out, the tuning bene t of the latter is usually bigger than the former by one tuning step Therefore, we can deduce that linking to upper-level index is more energy-e cient because the pro t from the larger coverage compensates the loss from the less tuning bene t Following this way, we devise a new approach that links the most upper level index, ie, a1; a2 and a3 when replicating the control index buckets The root index is the most upper-level one, but it has no tuning bene t because every control index has the address of I next That is, it does not satisfy the energy efficiency criterion Although this approach will not be e ective for sequential processing, it gives the best tuning performance as in Fig 10 The graph shows that this approach gives better performance with more replication level When broadcasting a lot of data, the index tree becomes large, so this approach gives signi cant tuning time reduction for point queries In addition, when using this approach, we can see that an index tree with small fan-out and high depth is more energy e cient than that with large fanout and low depth 6 Conclusion In this paper we have proposed three energy-e cient index replication approaches, FL, NL and SL, that are based on three criteria: accessibility, energy efficiency and adjacency They use the index slots in replicated index nodes for linking useful pointers, which are the forward pointers to the next bcast, the nephew pointers and the sibling pointers, respectively We have evaluated the performances of the proposed approaches in analytic and experimental ways, and have shown that the SL approach provides better performance than the other two in most cases Also we have discussed the relaxation of the criteria (ie, not considering adjacency) and have addressed another index replication approach whose tuning e ciency is signi cantly better than the SL approach for point queries As a future work, we are investigating the extension of the proposed index replication scheme for multichannel environment When there are many broadcasting channels through which data are delivered and the data objects between channels have some semantic relationships, the linkable candidates can be on other channels E ective usage of this knowledge can provide another kind of optimization strategy References Acharya, S, et al, 1995 Broadcast disks: data management for asymmetric communication environments In: Proceedings of ACM SIGMOD, pp 199±210 Argade, PV, et al, 1993 Hobbit: a high-performance low-power microprocessor Proceedings of COMPCON, pp 88±95 Bellady, LA, 1966 A study of replacement algorithms for virtual storage computers IBM Systems Journal 5 (2), 78±101 Chung, YD, Kim, MH, 1998 Energy-e cient indexing for wireless broadcast data Technical Report, KAIST, Taejon, South Korea Huang, Y, et al, 1994 Data replication for mobile computers In: Proceedings of ACM SIGMOD, pp 13±24 Imielinski, T, Badrinath, BR, 1992 Querying in highly mobile distributed environments Proceedings of VLDB, pp 41±52 Imielinski, T, Badrinath, BR, 1993 Data management for mobile computing SIGMOD RECORD 22 (1), 34±39 Imielinski, T, Viswanathan, S, 1994 Adaptive wireless information systems In: Proceedings of SIGDBS Imielinski, T, et al, 1994 Energy e cient indexing on air Proceedings of ACM SIGMOD, pp 25±36 Leong, HV, Si, A, 1995 Data broadcasting strategies over multiple unreliable wireless channels In: Proceedings of CIKM, pp 96± 104 Yon Dohn Chung received his BS degree in Computer Science from Korea University, Seoul, South Korea, in 1994, and his MS degree in Computer Science from Korea Advanced Institute of Science and Technology (KAIST), Taejon, South Korea in 1996 He is currently a PhD student of Computer Science at KAIST His current primary research interests include mobile distributed computing, multimedia communication and multimedia database systems Myoung Ho Kim received his BS and MS degrees in Computer Engineering from Seoul National University, Seoul, South Korea, in 1982 and 1984, respectively, and his PhD degree in Computer Science from Michigan State University, East Lansing, MI, in 1989 In 1989 he joined the faculty of the Department of Computer Science at KAIST, Taejon, South Korea, where currently he is a professor His research interests include database systems, data mining, information retrieval, OLAP, mobile computing and distributed processing He is a member of the ACM and the IEEE Computer Society