Two Types of Broadcasting Database 

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... data broadcast is very suitable for disseminating public information to large number of mobile users. Generally, there are two major measures when evaluating the query efficiency in such environments. One is access time and the other is energy efficiency . The access time denotes the time interval between the moment a query starts to the moment all the requested data have been downloaded. Obviously, users prefer short access time . In addition, the power supply is finite for mobile devices, which means energy efficiency is also very important when design data retrieval method in mobile computing environments. In a general data broadcast network, a base station disseminates data to mobile users via one or multiple channels; so there are totally two entities: mobile client and base station . Fig. 1 shows a typical broadcast network. A base station can send information via radio waves to large number of mobile clients simulta- neously, and the cost at the server site will not change as the number of clients increases. For instance, the base station B 2 in Fig. 1 provide services to more users, but its costs is nearly the same as that of B 1 . Moreover, the mobile client may has two modes: active mode and sleep mode . With the help of index, clients can get the arriving time of their requested data in advance and “sleep” to save energy when there are no data of interests. Although, it is relatively easy for data retrieving if all the data are scheduled on one channel, users may prefer partition the data onto multiple channels to reduce the average expected access time. But it should be noticed that if a client is downloading a data from channel c i at time t 0 , then it cannot switch to channel c j , where j = i , to download another data at time t 0 + 1. The reason is that switching the channels takes time, and if a client want to download data from another channel, it needs one time slot for channel switching. Fig. 2 gives a typical process of data retrieval in multi-channel broadcast environments. The query data set is { d 1 , d 3 , d 5 } , and a user can download data object d 1 and d 3 from channel c 1 , and then switch to channel c 3 at time 6 to download data object d 5 at time 7. However, after time 5, the user cannot switch from channel c 1 to c 2 to download data d 5 at time 6. From Fig. 2, we also can get that the bandwidths of different channels are non-necessarily the same. Actually, the bandwidth of channel c 2 is twice as that of c 1 or c 3 , thus d 3 or d 5 , which take two time slots on c 1 or c 3 , can be broadcasted in one time slot by c 2 . In most situations, it is much more likely a client query a set of data instead of only one data at a time. After obtaining the locations of requested data items, we need to make a schedule to download the data one by one in some order. An unwise retrieving schedule may result in long access time and unnecessary energy consumption. Usually, the energy consumption is evaluated base on the following two metrics: 1) tune-in time and 2) the number of channel switchings. Assume the arriving time of each requested data item is already known from the index, then the energy consumption depends purely on the number of channel switching happens during the retrieval process. In this paper we propose a randomized algebraic algorithm to reduce the access time and channel switchings for data retrieval in multi-channel environments. It can be used in almost any data broadcast programs, in which the data access frequencies, data sizes, and channel bandwidths can all be non-uniform. The remainder of this paper is organized as follows. Section 2 presents the related works to wireless data broadcast. In section 3, we give an algebraic algorithm that considers both access latency and energy cost to get optimal solutions for data retrieving in multi-channel environments. Finally, in section 4, we conclude this paper. Scheduling is an important issue in the area of wireless data broadcast. Acharya et al. first proposed the scheduling problem for data broadcast [1], and Prabhakara et al. suggested the multi-channel model for data broadcast to improve the data de- livery performance [2]. After that, many works have been done for scheduling data on multiple channels to reduce the expected access time [5,6,12]. Besides, some re- searches began to study how to allocate dependent data on broadcast channels. (see e.g. [14,10,11]). With respect to index, many methods have been proposed to improve the search efficiency in data broadcast systems (see e.g. [8,3,9,10,11]). Furthermore, Jung et al. proposed a tree-structured index algorithm that allocates indices and data on different channels [7]. Lo and Chen designed a parameterized schema for allocating indices and data optimally on multiple channels such that the average expected access latency is minimized [4]. In terms of data retrieval scheduling, Hurson et al. proposed two heuristic algorithms for downloading multiple data items from multiple channels [15]. Shi et al. investigated how to schedule multiple processes to download a set of data items [16]. Both of them investigate the data retrieval problem by assuming that the data are allocated on multiple channels without replication. However, as shown in the prior studies [1,20,21,22], employing data replication in data broadcast programs will reduce the expected access time. Fig. 3 shows why disseminating replicative data by multiple channels can reduce both access time and energy consumption. The first program allocates data without replication. d 1 and d 2 are separately scheduled on channels c 1 and c 2 . we can download d 1 or d 2 in one time slot, but we need at least 3 time slots and 1 channel switching to download both d 1 and d 2 in such a system. If allocating data on channels like the way of program 2, we can still retrieve each datum in one time slot and we can retrieve both of them in 2 time slots without channel switching. In this paper, we develop an algebraic algorithm for solving the problem of retrieving multiple data from multiple channels, in which the data can be non-uniform length and are replication-allowed to be broadcasted via multiple channels. In this section we present an algebraic algorithm for the data retrieval problem in multi-channel environments. It can detect if a given problem has a schedule to download all the requested data before time t and with at most h channel switchings in O (2 k ( hnt ) O (1) ) time, where n is the number of channels and k is the number of required data items. We first give a problem definition in section 3.1, and then present the algorithm in section 3.2. Let’s consider a mobile user wants to query a set of data D = d 1 , d 2 , , d k , which are broadcasted via channels in C = { c 1 , c 2 , · · · , c n } . We assume the locations of all the data in D are known; and we also assume each channel is partitioned into discrete time slots and one time slot is the smallest unit for storing data. Let a tuple s = { i s , j s , t s , t s } denote the data d i s can be downloaded from channel c during the time span [ t , t ], then it is clear that a valid data retrieval schedule is a sequence of k intervals s 1 , s 2 , , s k , each tuple cor- responds to a distinct data item in D and there is no conflicts between any two of the k tuples. Given a data set D , a channel set C , a time threshold t and a switching threshold h , find a valid data retrieval schedule to download all the data in D from C before time t with at most h switchings. To solve the above decision problem, we developed a randomized algebraic algorithm. We present it in detail next. The basic idea of our algebraic algorithm is that for each data item d i D , where D is the query data set, we create a variable x i to represent it. Therefore, given D = { d 1 , d 2 , · · · , d k } , we construct a variable set X = { x 1 , x 2 , · · · , x k } . We then design a circuit H t,h,n such that a schedule without conflict will be generated by a multilinear monomial in the sum of product expansion of the circuit. A multilinear monomial is a monomial such that each variable has de- gree exactly one, for examples, x 3 x 5 x 6 is a multilinear monomial, but x 3 x 3 5 x 2 6 is not. The existence of schedules to download all the data items in D from the multiple channels of C is converted into the existence of multilinear monomials of H t,h,n . Replace each variable by a specified binary vector can remove all of the non-multilinear monomials by converting them to zero. Thus, the data retrieval problem is transformed into testing if a multivariate polynomial is zero. It is well known that randomized algorithms can be used to check if a circuit is identical to zero in polynomial ...