A Routing Method for Top-k Query Processing in Mobile Ad Hoc Networks

Transcription

1 2013 IEEE 27th International Conference on Advanced Information Networking and Applications A Routing Method for Top-k Query Processing in Mobile Ad Hoc Networks Daichi Amagata, Yuya Sasaki, Takahiro Hara, Shojiro Nishio Department of Multimedia Engineering, Graduate School of Information Science and Technology, Osaka University {amagata.daichi, yuya.sasaki, hara, nishio}@ist.osaka-u.ac.jp Abstract In mobile ad hoc networks (MANETs), to acquire only necessary data items, it is effective that each mobile node retrieves data items using a top-k query, in which data items are ordered by the score of a particular attribute and the query-issuing mobile node acquires data items with k highest scores. In our previous works, we proposed top-k query processing methods for reducing traffic and also keeping high accuracy of query result. Those methods focus on the traffic reduction by not sending back unnecessary data items. However, queries are forwarded to all of nodes in the entire area by flooding, and thus, many nodes which do not contribute to the query result have to send redundant top-k queries and replies, which increases unnecessary traffic. In this paper, we propose a routing method for top-k query processing in MANETs. In this method, when each mobile node sends a top-k query, it refers to its own routing table consisting of the ranking of scores of data items in the network and identifiers of nodes to which queries are forwarded to obtain the necessary data items. Moreover, each node updates its own routing table when the link disconnection occurs and scores of data items are updated. Keywords-Top-k query; Routing; Mobile ad hoc networks; I. INTRODUCTION Recently, mobile ad hoc networks (MANETs)[5], [8] have been attracting increasing interests. Query processing for retrieving data items is one of the important issues in MANETs. Since the network bandwidth and batteries of mobile nodes are limited in MANETs, it is important for query processing to acquire only necessary data items in order to reduce data traffic. A possible and promising solution is that each mobile node acquires data items using a top-k query, in which data items are ordered by the score of a particular attribute and the query-issuing node acquires data items with the k-highest scores (top-k result). A naive manner to process a top-k query in a MANET is as follows. A query-issuing node floods all mobile nodes in the entire network with a query message, and then, each mobile node that receives the query message transmits its own data items with k-highest scores. By doing so, the query-issuing node can acquire all data items included in the top-k result if communication failures do not occur. However, many data items that are not included in the top-k result are sent back to the queryissuing node. This causes communication failures and large battery consumption. Figure 1 shows an application example of a top-k query assuming a rescue effort at a disaster site where the communication infrastructure, e.g., Internet, has been broken down. Let us assume that each rescuer manages Figure 1. Example of Top-k query processing in a MANET the information on his/her responsible sites, and a rescuer searches for sites with high damage to dispatch rescuers with a limited number of apparatuses. When the rescuer on the left side wants to find the two highest damaged sites in the entire area, he issues a top-k query where k is set to 2. Here, if each rescuer transmits the information on the two highest damaged sites in his/her responsible sites, the query-issuing rescuer acquires the information on more sites than necessary. In our previous works, we proposed query processing methods for top-k query for reducing traffic and also keeping high accuracy of query result [3], [9], [10]. In the methods in [3], [9], the query-issuing node floods the query message, and each node estimates the k-th score based on the scores of data items held by nodes on the query path, and sends back its own data items with scores higher than the estimated k-th score. In the method in [10], in the first phase, the query-issuing node collects the information of scores of data items held by each node (the size of a score is less than that of data items), and then determines the threshold as the k-th highest score. In the second phase, the query-issuing node transmits a query attached with the threshold, and each node that received the query sends back its own data items whose scores are equal to or larger than the threshold. However, those methods still have a problem. Those methods focus on traffic reduction by not sending unnecessary date items, but queries are forwarded to all nodes in the network by flooding. Thus, many nodes which do not contribute to the query result have to send redundant top-k queries and replies. As the result, unnecessary traffic increases, and thus, it causes extra battery consumption and communication failures. In this paper, to solve this problem, we propose a routing method for top-k query processing in MANETs. In this method, each node holds a routing table consisting of the ranking of scores of data items in the network and X/13 $ IEEE DOI /AINA

2 identifiers of nodes to which queries are forwarded (we call each of these identifiers the query address) to obtain the necessary data items. When each mobile node issues a query, it refers to its own routing table, and sends the query message to nodes which are the query addresses of these query. Nodes that received the query message behave in the same way. If the query-issuing node and relaying nodes cannot forward a query message to a query address due to a link disconnection, it searches another route to the query address and updates its routing table accordingly. Moreover, when a node updates the score of an its own data item, the node notifies other nodes of the update of the score in order to maintain their routing tables. We present simulation results to evaluate the performance of our proposed method. The contributions of this paper are as follows. We propose an effective routing method for topk query processing to reduce traffic and also keep high accuracy of the query result. To the best of our knowledge, this method is the first routing method for top-k query processing in MANETs. In our proposed method, each node holds a routing table to acquire the top-k result with small traffic. When link disconnections and updates of scores of data items occur, each node updates its own routing table accordingly. This procedure keeps high accuracy of the query result. The remainder of this paper is organized as follows: In Section II, we present some related works. In Section III, we present our proposed routing method for top-k query processing in MANETs. In Section IV, we show the results of the simulation experiments. Finally, in Section V, we conclude this paper. II. RELATED WORK There have been a large number of data-centric routing protocols. Since a data-centric routing protocol aims at retrieving data items with specific attribute values specified by the user, the approach to acquire data items could be similar to that in routing of top-k queries. We first survey some typical data-centric routing protocols. In [4], the authors have proposed a method called directed diffusion for wireless sensor networks. In this method, sinks disseminate a message with their interest of data items, and then, if nodes hold data items with the interest, they forward the data packets toward the sink by flooding. In this process, efficient paths between sinks and nodes are reinforced by a reinforcement mechanism. Messages and data packets are transmitted through reinforced paths with highest probabilities. This method can construct efficient path and achieve small traffic for data transmission. However, because the network topology changes dynamically in MANETs, this method is not effective in MANETs. In [6], the authors proposed a routing method for top-k query processing in wireless sensor networks. This method constructs a cluster for topk query whose size is determined based on the residual energy of the cluster head. This method can keep a balance between the energy consumption among sensor nodes in the network by changing the cluster head. However, the cost of cluster maintenance is too large in MANETs because of movement of nodes. A large number of strategies for processing a top-k query have been proposed in several research fields, such as unstructed P2P networks and wireless sensor networks. However there is no research which focuses on top-k query processing in MANETs except for our previous work and EcoTop [7]. Since the assumption in [7] is quite different with the assumption in this paper, we introduce our previous work, 2-phase top-k query processing [10], which can keep the highest accuracy of query result among our previous methods. 2-phase top-k query processing consists of two phases : search and data collection phases. In the search phase, the query-issuing node floods a query message, and then, collects the information on scores of data items held by all nodes in the entire MANET (the size of a score is smaller than that of data items). Then, it checks those scores and determines the k-th score as the threshold. In the data collection phase, the query-issuing node floods a query message attached with the threshold, and then, collects data items with scores equal to or larger than the threshold. This method can decrease the number of transmitted data items as much as possible. However, all nodes receive and forward queries (and replies) twice. This increases unnecessary traffic. Therefore, to solve this problems in our method in this paper, each node forwards a query message based on its own routing table to only nodes which contribute to the top-k result. As a result, our method can decrease traffic and also keep high accuracy of the query result. III. PROPOSED METHOD In this section, first, we describe the design policy of our proposed method and the assumed environment. Then, we describe the overview of our proposed method and how to process a top-k query in detail. A. Design Policy In MANETs, since mobile nodes consume the limited communication bandwidth for data transmission, a packet loss and packet retransmission may occur when the network is congested, i.e., some data items cannot be transmitted and extra overhead involved. Thus, the number of messages and data items sent by mobile nodes should be small as much as possible. For this aim, it is effective that each node holds the information on data items with k-highest scores and nodes to transmit a query message in order to acquire the top-k result. Thus, each node holds and maintains the information on data items as the routing table and forwards a query message based on the information. B. Assumption The system environment is assumed to be a MANET in which mobile nodes retrieve data items held by itself and other mobile nodes using a top-k query. The query-issuing 162

3 node transmits a query message with the query condition and the number of requested data items, and acquires data items with the k-highest scores among all data items held by mobile nodes in the entire network. Each mobile node determines the number of requested data items, k, from 1 to k max. We assign a unique data identifier to each data item in the system. The set of all data items in the system is denoted by D= {D 1,D 2,,D n }, where n is the total number of data items and D i (1 i n) isa data identifier. Each data item is held by a specific node, and scores of data items are updated as time passes. For simplicity, all data items are of the same size and not replicated. The scores of data items can be calculated from the query condition and some scoring functions. We also assign a unique node identifier to each mobile node in the system. The set of all mobile nodes in the system is denoted by M= {M 1,M 2,,M m }, where m is the total number of mobile nodes and M i (1 i m) is a node identifier. Each mobile node moves freely. C. Overview In our proposed method, a top-k query is processed based on the routing table. Thus, it first needs to construct the routing table at each node. The query-issuing node which issues a query firstly in the network sends a message for constructing routing table, and then nodes that receive the message reply the information on scores of data items held by them. Through this procedure, the query-issuing node knows the ranking of scores (ranking table) and which nodes hold data items with high scores (data holders). Then, it floods a message attached with the ranking table and the information on data holders to all nodes in the network. Nodes that receive this message construct their own routing tables which consist of the ranking table, the identifiers of data holders, the identifiers of nodes to which a query is forwarded to acquire data items with high scores (query address), and time stamps. In top-k query processing, the queryissuing node sends a query message attached with ranks of data items that it requires to the query addresses. If nodes that receive the message hold required data items, they reply the data items. If a link disconnection occurs during processing a top-k query, the node that detects the disconnection searches another route and updates its own routing table accordingly. When the score of a data item is updated, the node that updated the score transmits a message to nodes which hold data items whose ranks have changed. Figure 2 shows an example of behavior of the proposed method when M 1 issues a top-k query for acquiring data items with the three highest scores (k =3). Table I shows the scores of its data items held by mobile nodes. In the figure, the table in each balloon denotes the routing table which each node holds, and q-a means query address. M 1 sends a query message to M 2 to request the 1st rank data item and M 4 to request the 2nd and 3rd rank data items. Then, for example, since M 4 knows that 2nd data Table I SCORES OF DATA ITEMS HELD BY EACH MOBILE NODE Node identifier Scores of data items M 1 89, 88, 82, 78, 70, 66, 49, 30, 21 M 2 99, 90, 80, 77, 72, 71, 69, 55, 42 M 3 81, 79, 53, 41, 33, 29, 19, 12, 11 M 4 96, 87, 76, 61, 58, 50, 44, 37, 10 M 5 92, 75, 60, 59, 56, 40, 30, 25, 22 Figure 2. Example of a behavior of the proposed method item s holder is itself, and 3rd one is not, it transmits a query message to request the 3rd data item to M 5. Nodes that hold required data items send them back. Finally, M 1 can collect data items with the three highest scores. D. Routing Table Construction In this section, we explain how to construct the routing table in detail. When the query-issuing node does not have its own routing table which corresponds to the query condition, the node starts constructing the routing table. First, the node floods all nodes in the network with a routing table message. Each node that received the message at the first time sets the sender node as its parent, and knows its neighbors. Through this process, a tree-network (the root node is the query-issuing node) is constructed. Leaf nodes in the tree-network start sending a reply message with the information on data items (the score, and the node identifier of the holder) with N(> k max )-highest scores to its parent. N is set larger than k max in order to adapt to a case that scores of data items with k max highest scores are updated as smaller scores. Intermediate nodes send back a reply when they received replies from all its children or the pre-determined time limit passes. If a node detects a link disconnection between the node and its parent, it sends a reply to its neighbor node with the information on the minimum hopcount to the queryissuing node. Each node that received a reply stores the information on data items with N-highest scores and the sender node of the reply, so it knows which data item is replied from which node (we call this information the node-data list). From this procedure, the query-issuing node can make the ranking table which consists of scores of data items, node identifiers of data holders, and time stamp. The time stamp is set as the time when the ranking table is made. The list of this information in the ranking table is sorted by score in descending order. Moreover, the node-data list is also made in order to use for constructing the routing table. Then, the query-issuing node floods a message attached 163

4 Table II M 1 S ROUTING TABLE with the ranking table. Nodes that received the message for the first time construct their own routing table. The process that a receiver of this message makes the routing table is as follows. 1) The receiver stores the information in the received ranking table into own routing table. 2) The receiver sets query addresses for all ranks in own routing table as the identifier of the node that sent the ranking table to it. 3) The receiver updates query addresses for ranks to its own identifier if it holds the corresponding data items. 4) The receiver further updates query addresses for ranks to the identifiers of nodes corresponding to data items in its node-data list. After the above procedure, each of nodes that hold data items with k max -highest scores floods a message attached with its node identifier to construct the shortest path to the data items. This process is important to reduce traffic in top-k query processing because without this process, the path depends on the position of the root node (i.e., the query-issuing node). Through all the above procedure, each node knows the next hop node to retrieve the data items with the required rank via the shortest path. Table II shows an example of the routing table of M 1 in Figure 2 in the case of N=20. For example, it knows that the next hop node is M 2 to retrieve the 1st rank data item. E. Top-k Query Processing In our proposed method, each node sends a query message based on its own routing table and nodes that received the query message send back only required data items. We explain the detail of top-k query processing. 1) Transmission of query: A query message consists of the following elements. Query-issuing node s ID: the node identifier of the query-issuing node. Query ID: the identifier of the query Number of requested data items: the number of data items, k, that the query-issuing node requests. Query condition: The query condition specified by the query-issuing node. Ranking list of requested data items: the list of ranks of data items requested by this query message. Sender node s ID: the node identifier of the node that sends this message. The behaviors of the query-issuing node, M p, and nodes that received the query message are as follows. 1) M p specifies the query condition and checks whether it has the routing table or not. If it does not have, it first performs the procedure in section III-D. 2) M p specifies the number of requested data items, k. Then, it unicasts a query message to each of query addresses corresponding to the ranks higher than k in its own routing table. In this message, the ranking list of requested data items is set as the list of ranks that this message targets. 3) Each mobile node, M q, that received the query message sends an ACK to its sender node. If M q received the query firstly, it sets the sender as its parent and stores the ranking list and query-issuing node s ID. Then, M q unicasts a query message to each of query addresses corresponding to the requested ranks in the query message (specified in the ranking list) except for data items that M q holds. In this message, the ranking list is set in the same way as step 2), and the sender s ID is set as M q. If M q received the same query message again and its requested ranks are different from that in the previous one, it unicasts a query message in the same way as described above. Otherwise, M q drops the message. 4) Each mobile node that received an ACK updates the time stamps of the ranks (as the current time) whose query address is the sender of the ACK. Through this procedure, a query message is forwarded to only necessary nodes for collecting data items included in the top-k result. If there are some data items whose query addresses are same, only one query is issued by aggregated by using the ranking list of requested data items, which is effective to reduce traffic. Moreover, each node can send back data items by only one reply message. 2) Transmission of Reply: In our proposed method, each mobile node sends back a reply message attached with data items requested by the query message, which can suppress unnecessary data items which are not included in the top-k result being sent back. A reply message consists of the following elements. Query ID: the identifier of the query Sender node s ID: the node identifier of the node that sends this message. Data list: the list of pairs of data items requested by the query and their scores. The behaviors of each mobile node that has completed the transmission of a query message are as follows. 1) Each mobile node, M r, that holds all data items corresponding to the ranking list in the received query message starts to transmit a reply message to its parent. In the reply message, the query ID is set as the query ID in the received query message, and data list consists of pairs of requested data items which M r holds and their scores. 2) When a mobile node, M s, receives a reply, it updates the time stamps (as the current time) for ranks corresponding to the data items in the data list 164

5 in the received reply. If the query addresses for corresponding to those data items are not the sender of the reply message in its own routing table, M s updates those query addresses to the sender. 3) When a mobile node, M t, which is not the queryissuing node receives all data items which M t requested or the pre-determined time limit has passed, it transmits a reply message to its parent. In this message, the data list consists of pairs of requested data items which M t holds and all received data items and their scores. Here, if M t receives data items which are not recorded in its own routing table due to the updates of the scores of the data items., it updates its own routing table. We explain this procedure in section III-F2. 4) When a mobile node, M t, receives data items which it did not request in its query message, it does the same process as step 2). However, if M t has already transmitted the reply to its parent, it does not send data items which were already transmitted. Through this procedure, each mobile node sends back only data items which are requested by the query, so unnecessary data items are not transmitted. Moreover, each mobile node that received replies can update their routing table, which can keep accuracy of the routing table. F. Routing Table Maintenance In our proposed method, each node has to update its own routing table when a link disconnection occurs and scores of data items are updated in order to keep accuracy of the routing table. We explain how to maintain a routing table in this section. 1) Handling Link Disconnection: In MANETs, the network topology dynamically changes due to movement of nodes. If a mobile node cannot transmit a query to a query address or a reply to its parent because of a link disconnection between these nodes, the accuracy of query result decreases. Therefore, when a mobile node detects the link disconnection (we call the node the route request node), it searches another route to the query address or its parent (we call this node the destination node) by sending a route request message. A route request message consists of the following elements. Route request node s ID: the node identifier of the route request node. Sender node s ID: the node identifier of the node that sends this message. Query ID (only for reply transmission): the identifier of the query. TTL: the hopcount which represents the search range to find the destination node. Search list: the list of triples of a destination node s identifier, ranks corresponding to the node, and their time stamps in the route request node s routing table in the case of query transmission. The list of pairs of the destination node s identifier and query-issuing node s identifier in the case of reply transmission. A route reply message consists of following elements. Route request node s ID: the node identifier of the route request node. Sender node s ID: the node identifier of the node that sends this message. Query ID (only for reply transmission): the identifier of the query. Answer list (only for query transmission): the list of pairs of requested ranks and their time stamps in the destination node s routing table. The procedure is same in both query and reply transmission. A mobile node that detects a link disconnection broadcasts a route request message. If a node that received this message is the destination node or the query-issuing node (only for reply transmission), it starts to send back a route reply message. Otherwise, it decrements TTL and broadcasts the route request message if TTL is larger than 0. In the case of query transmission, if a node that received a route reply does not hold data items specifies in the answer list in its own routing table and the time stamps in the answer list are newer than that in its own routing table, it updates the query addresses corresponding to ranks as the sender of the route reply message as well as their time stamp as the current time. In this way, even if a link disconnection occurs, mobile nodes can continue to transmit a query or a reply by finding another route, and the accuracy of query result can be kept. 2) Score Update Announcement: If scores of data items are updated, the ranking of data items may change. In our proposed method, when the ranking of data items changes, a mobile node that updated the data items updates its own routing table, and sends a message to notify the change in rank of data items. There are three cases that need to maintain the routing table when updating the score of a data item held by a mobile node, M v. 1) The rank of the data item move to different rank in the routing table. 2) The data item is newly included in routing table (i.e., appear on the ranking list). 3) The data item is excluded from the routing table (i.e., disappear from the ranking list). In the following cases, we explain how to update the routing table in each of the three cases and how to notify the score updating. Case 1: If the score of the i(< N)-th data item in the routing table is updated and its rank becomes different ( N), M v updates its own routing table and resorts its records in descending order by score. M v also updates the time stamps for the moved ranks as the current time. Case 2: If the score of the data item newly becomes i(< N)- 165

6 Table III CONFIGURATION OF PARAMETERS Symbol Meaning Values(Range) k Number of requested data items 30 (1 50) d Size of data items 128 ( )[byte] T Score update interval 90 (15 300)[sec] th rank, M v inserts the information on the data items to its own routing table. Case 3: If the score of i(< N)-th data item becomes smaller than N-th score, M v deletes the information on the data item in routing table. Then, M v sends a score update announcement message to query addresses corresponding to data items whose ranks are changed. A score update announcement message consists of the following elements. Score update node s ID: the identifier of the score update node. Score update announcement ID: the identifier of the score update announcement. Sender node s ID: the identifier of the node that sends this message. Score update list: the list of pairs of the previous score and the new score of the data items. Each node that received a score update announcement message sends an ACK to its sender, and it updates its own routing table in the same way as M v, expect for that it sets query addresses for changed ranks to the sender node s ID in score update announcement message. After that, it further transmits a score update announcement message in the same way as M v. The node that received an ACK updates the time stamp for the rank whose query address is the sender of the ACK as the current time. If the node does not receive an ACK within the pre-determined time limit, it broadcasts a score update announcement message. In this way, a node that updates data items transmits a score update announcement message to only nodes which have to update their routing table soon, i.e., nodes holding data items whose ranks have been changed. Nodes which did not receive a score update announcement message can update their own routing table when they receive a reply message in a future top-k query. Therefore, the overhead of transmission of a score update announcement message is small. IV. SIMULATION EXPERIMENTS In this section, we show the results of simulation experiments regarding the performance evaluation of our proposed method. For the simulation experiments, we used a network simulator, QualNet4.0 [12]. A. Simulation Model The number of mobile nodes in the entire system is 100 (M 1,M 2,,M 100 ). These mobile nodes exist in an area of 800 [m] 500 [m] and move according to the random waypoint model [1] where the movement speed and the pause time are 0.5 [m/sec] and 60 [sec] respectively. Each mobile node transmits messages and data items using an IEEE b device whose data transmission rate is 11 [Mbps]. The transmission power of each mobile node is determined so that the radio communication range becomes about 100 [m]. We assume that packet losses and delays occur due to a radio interference. Each mobile node has 20 data items, and the size of data items is d [byte]. The score distribution in the entire network follows the normal distribution and the total range of scores are set as [1, 999]. A node which is randomly selected at every T [sec] updates scores of data items held by itself. In our proposed method, the number of rank orders, N, maintained in the routing table and k max are respectively set as 100 and 50. The TTL value of a route request message is set as 2. Table III shows the parameters and their values used in the simulation experiments. The parameters are basically fixed to constant values specified by numbers to the left of the parenthetic values. Each of them is varied in the range specified by the parenthetic element in a simulation experiment. We compare the performance of our proposed method with that of the method proposed in [10] and a naive method (denoted by Fixed k) in which each node replies k data items with highest scores among its own and received data item. In the above simulation model, we randomly determine the initial position of each mobile node and randomly determine a query-issuing node at every 3 [sec]. We evaluate the following criteria during 600 [sec]. Accuracy of query result: is MAP (Mean Average Precision) which is often used to calculate the accuracy with a ranking. MAP averages accuracy of each query result, AP (Average Precision). AP and MAP are determined by the following equations. AP i = 1 k MAP = k j=1 x j e (1) 1 querynum querynum i=1 AP i (2) AP i is accuracy of the i-th query result. x is the number of collected data items with j-highest score included within j-highest correct answer set. querynum is the total number of issued query. e is determined by the following equation. { 1 (j-th answer is included in top-k result) e = (3) 0 (otherwise) Thus, MAP gets higher as the query-issuing node gets data items with higher score. Traffic: is defined as the total volume of messages sent during the simulation. Search time: is defined as the average of the elapsed time after the query-issuing node issued a top-k query until it acquired the result. 166

7 (a) Accuracy of query result (a) Accuracy of query result (b) Traffic Figure 3. Effects of k (b) Traffic Figure 4. Effects of d (c) Search Time (c) Search Time B. Impact of Number of Requested Data Items We examine the effects of the number of requested data items, k. Figure 3 shows the simulation result. In this graph, the horizontal axis indicates k. The vertical axes indicate the accuracy of query result in Figure 3(a), the traffic in Figure 3(b), and the search time in Figure 3(c). From Figure 3(a), as k increases, the accuracy of query result decreases in all methods. This is because packet losses occur more often due to the increase of traffic. When k is large, the difference of accuracy of query result between our proposed method and the naive method is very large because a large number of unnecessary data items are sent back in the naive method. The accuracy of query result in our proposed method is also higher than that in the method in [10]. This is because in the method in [10], when the threshold is not set accurately due to packet losses in the search phase, traffic increases by sending back unnecessary data items. From Figures 3(b) and 3(c), as k increases, the traffic and the search time increase in all methods since the size of a reply message increases. Since in the method in [10], query processing requires two rounds of message transmissions, the search time is much longer than our proposed method. When k is small, the search time is short in our proposed method because the number of nodes which send a query message is very small. C. Impact of Data Size We examine the effects of the size of data items, d. Figure 4 shows the simulation result. In this graph, the horizontal axis indicates d. The vertical axes indicate the accuracy of query result in Figure 4(a), the traffic in Figure 4(b), and the search time in Figure 4(c). From Figure 4(a), as d increases, the accuracy of query result decreases in all methods. This is because packet losses occur more often due to the increase of traffic. When d is large, the difference of accuracy of query result between our proposed method and the method in [10] is large. This is because in the method in [10], if packet losses happen in the search phase, the threshold cannot be accurately set, and unnecessary data items are sent back, which further causes packet losses. Our method can suppress such unnecessary traffic by using the routing table. From Figures 4(b) and 4(c), as d increases, the traffic and the search time increase in all methods. The reason is the same as that mentioned in section IV-B. D. Impact of Score Update Interval We examine the effects of the score update interval, T. Figure 5 shows the simulation result. In this graph, the horizontal axis indicates T. The vertical axes indicate the accuracy of query result in Figure 5(a), the traffic in Figure 5(b), and the search time in Figure 5(c). Here, we omit the result of naive method from simulation results because the naive method shows much worse performance than other methods. From Figure in 5(a), the accuracy of query result is almost constant in the method in [10] since this method determines the threshold on demand when a query is issued, which is not affected by T. In our proposed method, when T is long, the accuracy is almost constant. However, as T gets very short, the accuracy of query result slightly decreases because a failure of score update announcement sometimes occurs, which causes an error in the ranking table in its routing table. 167

8 (a) Accuracy of query result (b) Traffic Figure 5. Effects of T (c) Search Time From Figures 5(b) and 5(c), the traffic and the search time are not significantly affected by T in both methods. The reason for the method in [10] is same as that for the result in Figure 5(a). In the proposed method, a score update announcement message is transmitted to only nodes which need to update its routing table soon, and thus, its overhead is not high. V. CONCLUSION In this paper, we propose a routing method for top-k query processing in MANETs. In this method, each mobile node holds the routing table consisting of the ranking of data items in the network and identifiers of nodes (query addresses) to which queries are forwarded. Each node sends a top-k query message by referring to its own routing table. Then, nodes which received a query message sends back required data items. In this way, our proposed method can reduce the traffic and also keep high accuracy of the query result. Moreover, when a mobile node detects a link disconnection during the transmission of query and reply message, it finds another route and updates routing table. In addition, when the score of a data item is updated, a score update announcement is forwarded efficiently. The simulation results show that our proposed method reduces traffic and achieves high accuracy of the query result compared with the method in [10] and the naive method. In our proposed method, a top-k query message is forwarded by using unicast and the route to each of data items with k-highest scores is single. Thus, the accuracy of the top-k result is expected to become lower in highly dynamic networks because link disconnections occur frequently. We plan to extend our method to solve this problem. ACKNOWLEDGMENT This research is partially supported by the Grant-in-Aid for Scientific Research (S)( ) and (B)( ) of MEXT, Japan. REFERENCES [1] T. Camp, J. Boleng, and V. Davies, A survey of mobility models for ad hoc networks research, Wireless Communications and Mobile Computing: Special issue on Mobile Ad Hoc Networking: Reserach, Trends and Applications, vol.2, no.5, pp , [2] J. Cecílio, J. Costa, and P. Furtado, Survey on data routing in wireless sensor networks, Wireless Sensor Network Technologies for the Information Explosion Era, vol.278, pp.3 46, [3] R. Hagihara, M. Shinohara, T. Hara, and S. Nishio, A message processing method for top-k query for traffic reduction in ad hoc networks, Proc. Int. Conf. on Mobile Data Management, pp.11 20, [4] C. Intanagonwiwat, R. Govindan, and D. Estrin, Directed diffusion for wireless sensor networking, IEEE/ACM Trans. Networking, vol.11, no.1, pp.2 16, [5] D. B. Johnson, Routing in ad hoc networks of Mobile Hosts, Proc. IEEE WMCSA 94, pp , [6] S. Mo, H. Chen, and Y. Lie, Clustering-based routing for top-k querying in wireless sensor networks, EURASIP Journal on Wireless Communications and Networking, vol.2011, no.1, p.1 13, [7] N. Padhariya, A. Mondal, V. Goyal, R. Shankar, and S. K. Madria, EcoTop: An Economic Model for Dynamic Processing of Top-k Queries in Mobile-P2P Networks, Proc. Int. Conf. DASFAA, pp , [8] C. E. Perkins, and E. M. Ooyer, Ad-hoc on-demand distance vecotr routing, Proc. ieee WMCSA 99, pp , [9] Y. Sasaki, R. Hagihara, T. Hara, and S. Nishio, A top-k query method by estimating score distribution in mobile ad hoc networks, Int. Workshop on Data Management for wireless amd Pervasive Communications, pp , [10] Y. Sasaki, T. Hara, and S. Nishio, Two-phase top-k query processing in mobile ad hoc networks, Proc. Int. Conf. on Network-Based Information Systems, pp.42 49, [11] X. Zhao, K. Mao, S. Cai, and Q. Chen, Data-centric routing mechanism using hash-value in wireless sensor network, Wireless Sensor Network, vol.2, no.9, pp , [12] Scalable Network Technologoes: Creaters of QualNet Network Simulator Software, <URL: 168