Pakitan Journal of Information and Technology 2 (3): 231-239, 2003 ISSN 1682-6027 2003 Aian Network for Scientific Information Heuritic Approach to Dynamic Data Allocation in Ditributed Databae Sytem 1 2 Tolga Ulu and Mithat Uyal 1 Management Information Sytem Department, Boaziçi Univerity, Bebek 34342 tanbul, Turkey 2 Computer Engineering Department, Dou Univerity, Kad köy 34722 tanbul, Turkey Abtract: In thi paper, a new dynamic data allocation algorithm for non-replicated ditributed databae ytem (DDS), namely the threhold algorithm, i propoed. The threhold algorithm reallocate data with repect to changing data acce pattern. The algorithm i analyzed for a fragment uing imulation. The threhold algorithm i epecially uitable for a DDS where data acce pattern change dynamically. Key word: Ditributed databae, fragmentation, data allocation, imulation Introduction Development in databae and networking technologie in the pat few decade led to advance in ditributed databae ytem. A DDS i a collection of ite connected by a communication network, in which each ite i a databae ytem in it own right, but the ite have agreed to work together, o that a uer at any ite can acce data anywhere in the network exactly a if the data were all tored at the uer own ite (Özu and Valduriez, 1991). The primary concern of a DDS i to deign the fragmentation and allocation of the underlying databae. Fragmentation unit can be a file where allocation iue become the file allocation problem. File allocation problem i tudied extenively in the literature, tarted by Chu (Chu, 1969) and continued for non-replicated and replicated model (Morgan and Levin, 1977; Azoulay- Schwartz and Krau, 2002). Some tudie conidered dynamic file allocation (Wah, 1979; Smith, 1981). Data allocation problem wa introduced when Ewaran (Ewaran, 1974) firt propoed the data fragmentation. Studie on vertical fragmentation (Navathe et al., 1984; Ceri et al., 1989); horizontal fragmentation (Ceri et al., 1983) and mixed fragmentation (Sacco, 1986; Zhang and Orlowka, 1994; Cheng et al., 2002) were conducted. The allocation of the fragment i alo tudied extenively (So et al., 1999; Bakker, 2000; Ahmad et al., 2002 and Chang, 2002). In thee tudie, data allocation ha been propoed prior to the deign of a databae depending on ome tatic data acce pattern and/or tatic query pattern. In a tatic environment where the acce probabilitie of node to the fragment never change, a tatic allocation of fragment provide the bet olution. However, in a dynamic environment where thee probabilitie change over time, the tatic allocation olution would degrade the databae performance. Initial tudie on dynamic data allocation give a framework for data reditribution (Wilon and Navathe, 1986) and demontrate how to perform the reditribution proce in 231
minimum poible time (Rivera-Vega et al., 1990). In (Bruntorm et al., 1995); a dynamic data allocation algorithm for non-replicated databae ytem i propoed, but no modeling i done to analyze the algorithm. Intead, the paper focued on load balancing iue. Thi paper propoe a new dynamic data allocation algorithm for non-replicated ditributed databae and analyze the algorithm uing imulation. In our tudy, horizontal, vertical or mixed fragmentation can be ued. Allocation unit can even be a mall a a record or an attribute. The ret of thi paper i organized a follow. Firtly, the optimal dynamic data allocation algorithm given in (Bruntorm et al., 1995) i reviited and it diadvantage are dicued. After that, a new algorithm (namely the threhold algorithm), which overcome the diadvantage of the optimal algorithm, i propoed for dynamic data allocation in ditributed databae. Next, the behavior of a fragment, in reaction to a change in acce probabilitie or to a change in threhold value, i invetigated uing imulation. Finally, concluding remark are given. Optimal algorithm In ditributed databae ytem, the performance increae when the fragment are tored at the node from which they are mot frequently acceed. The problem i to find thi particular node for each fragment. Counting the accee of each node to a fragment offer a practical olution. Having the highet acce value for a particular fragment, a node could be the primary candidate to tore the fragment. An m by n acce counter matrix S, where m denote the number of fragment and n denote the number of node, i hown below... 11 12 1n.. 21 22 2n S > > >> > m 1 m2.. mn + Every element of S, where 0Z c{0} (i.e. non-negative integer), how the number of ij ij accee to fragment I by node j. A row of S how the acce count of all node to a particular fragment, wherea a column of S how the acce count of all fragment for a particular node. S i updated after each acce to the fragment. To atify the minimum repone time contraint, each fragment hould be tored in the node with the highet acce count in it correponding row. In other word, if ix > iy for all y = 1,..,n, then the fragment I hould be tore in node x. For example let the following matrix be the acce counter matrix, S, of a DDS with three node and three fragment. A B C x y z 3 6 2 5 3 1 1 4 2 232
In the example, A, B, C denote fragment and x, y, z denote node. Fragment A i acceed 3, 6 and 2 time by node x, y and z, repectively. For fragment B and C, the acce count are 5, 3, 1 and 1, 4, 2, repectively. According to S, fragment A and C hould be tored in node y; and fragment B hould be tored in node x. The torage node of S i an iue of the algorithm. To tore it in a central node create an extra network traffic overhead. It alo lead to a reliability problem in cae of central node failure. The bet olution would be to decompoe the matrix into row and tore each row together with it aociated fragment in the ame node. In thi way, whenever the fragment migrate, it aociated counter migrate a well. Fig. 1 how fragment I with it aociated counter, through. 0 n Fragment... i 0 1 2 n Fig. 1: Any fragment I in optimal algorithm Initially, all fragment are ditributed to the node according to any method. Afterward, any node j, run the optimal algorithm given in Fig. 2 for every fragment I, that it tore. Step 1. For each (locally) tored fragment, initialize the acce counter row to zero. (S = 0 ik were k = 1,..,n) Step 2. Proce an acce requet for the tored fragment Step 3. Increae the correponding acce counter of the acceing node for the tored fragment. (If node x accee fragment I, et ix = ix +1) Step 4. If the acceing node i the current owner, go to tep 2. (i.e.. Local acce, otherwie it i a remote acce) Step 5. If the counter of a remote node i greater than the counter of the current owner node, tranfer the ownerhip of the fragment together with the acce counter array to the remote node. (i.e. fragment migrate) (if node x accee fragment I and ix > ij, end fragment I to node x) Step 6. Go to tep 2. Fig. 2: Optimal algorithm There are two inherent propertie introduced by the optimal algorithm. Firt one i the ownerhip property, that i, for each fragment; the node with highet acce counter value i the current owner node of the fragment, in which cae the fragment i tored in thi node. The econd one, namely migration property, dictate that for any fragment the ownerhip i tranferred to a new node, if the acce counter value of the new node exceed the acce counter value of current owner node. In thi cae, thi particular fragment migrate and i tored in thi new owner node. In other word, the owner node of the fragment change. 233
An advantage of the optimal algorithm i the central node independence. That i, ince each node run the algorithm autonomouly, there i no central node dependence. Every node i of equal importance. Whenever one node crahe, the algorithm may continue it operation without the fragment tored in the crahed node. There are two drawback aociated with the optimal algorithm. Firt one i the potential torage problem. A the fragment ize decreae and/or the number of node increae, the ize of acce counter matrix increae, which in turn reult in extra torage pace need for the acce counter matrix. For intance, if the fragment ize i one record and the number of node i 500, then for each record an array of 500 acce counter value hould be tored. In ome cae, thi acce counter array ize may exceed the record ize. The econd drawback i the caling problem for the data type that tore the acce counter value. Since acce counter value are continuouly increaing, thi problem may reult in anomalie. For example, if one byte i choen to tore the counter value, then a value greater than 255 cannot be tored in thi data type. A potential timing problem, which may caue back and forth migration of a fragment, deerve explanation. Think of a cae where there are two node denoted by Y and Z. Suppoe at an intant, Y ha the highet acce counter for a fragment wherea Z counter i one le than Y'. Conider Z perform two ucceive accee to the fragment, cauing a tranfer of the fragment from Y to Z. Later on, Y perform two ucceive accee to the fragment, cauing again the tranfer of the fragment from Z to Y. If thee ucceive two accee of Y and Z continue in turn, the fragment will migrate back and forth between Y and Z after every two accee. Thi can alo be generalized to multiple node where fragment migrate in a circular fahion. The threhold algorithm In ome cae, due to extra torage pace need, it could be very cotly to ue the optimal algorithm in it original form. For a le cotly algorithm, the olution i to decreae the need for extra torage pace. The heuritic threhold algorithm in thi paper erve thi purpoe. Let the number of node be n and let x denote the acce probability of a node to a particular fragment. Suppoe the fragment i tored in thi particular node (i.e. it i the owner node). For the ake of implicity, let x denote the acce probability of all the other node to d thi particular fragment. The owner doe local acce, wherea the remaining node do remote acce to the fragment. The probability that the owner node doe not acce the fragment i (n - 1)x d. The 2 probability that the owner node doe not perform two ucceive accee i [(n - 1)x d]. Similarly, the probability that the owner node doe not perform m ucceive accee i [(n - m 1)x d]. Therefore; the probability that the owner node perform at leat one acce of m m ucceive accee i 1-[(n - 1)x d]. Table 1 how the probabilitie that the owner node perform at leat one acce out of m ucceive accee, where x range from 0.1 through 0.9 and where m i 5, 10, 25, 50 and 100. The value in the table are truncated to five decimal digit. 234
Table 1: The probability that at leat one local acce occur in m accee x m=5 m=10 m=25 m=50 m=100 0,1 0,40951 0,65132 0,92821 0,99485 0,99997 0,2 0,67232 0,89263 0,99622 0,99999 1,00000 0,3 0,83193 0,97175 0,99987 1,00000 1,00000 0,4 0,92224 0,99395 1,00000 1,00000 1,00000 0,5 0,96875 0,99902 1,00000 1,00000 1,00000 0,6 0,98976 0,99990 1,00000 1,00000 1,00000 0,7 0,99757 0,99999 1,00000 1,00000 1,00000 0,8 0,99968 1,00000 1,00000 1,00000 1,00000 0,9 0,99999 1,00000 1,00000 1,00000 1,00000 Fragment i Fig. 3: Any fragment I in threhold algorithm According to the table, the probability that the owner node with the acce probability of 0.1 perform at leat one acce of ten ucceive accee i 0.65132. It i trivial from the table that a the acce probability of owner node increae, o a the probability that at leat one local acce occur in m accee. Applying the ame idea, a new threhold baed algorithm (or threhold algorithm) can be propoed. In threhold algorithm, only one counter per fragment i tored. Fig. 3 how fragment I together with it counter. Comparing it to the optimal algorithm, thi radically decreae the extra amount of torage pace to jut one value compared to an array of value in the optimal algorithm. In the threhold algorithm, the initial value of the counter i zero. The counter value i increaed by one for each remote acce to the fragment. It i reet to zero for a local acce. In other word, the counter alway how the number of ucceive remote accee. Whenever the counter exceed a predetermined threhold value, the ownerhip of the fragment i tranferred to another node. At thi point, the critical quetion i which node will be the fragment' new owner. The algorithm give very little information about the pat accee to the fragment. In fact, throughout the entire acce hitory only the lat node that acceed the fragment i known. So, there are two trategie to elect the new owner. Either it i choen randomly, or the lat acceing node i choen. In the former, the randomly choen node could be one that ha never acceed the fragment before. So picking the latter trategy i heuritically more reaonable. Initially, all fragment are ditributed to the node according to any method. A threhold value t i choen. Afterward, any node j, run the threhold algorithm given in Fig. 4 for every fragment I, that it tore. Threhold algorithm overcome the volley of a fragment between two node provided that a threhold value greater than one i choen. The algorithm guarantee the tay of the fragment for at leat (t+1) accee in the new node after a migration. In other word, it delay the migration of the fragment from any node for at leat (t+1) accee. 235
Step 1. For each (locally) tored fragment, initialize the counter value to zero. (Set = 0 for i every tored fragment I) Step 2. Proce an acce requet for the tored fragment. Step 3. If it i a local acce, reet the counter of the correponding fragment to 0 (If node j accee fragment I, et = 0). Go to tep 2. i Step 4. If it i a remote acce, increae the counter of the correponding fragment by one. (If fragment I i acceed remotely, et i = i + 1) Step 5. If the counter of the fragment i greater than the threhold value, reet it counter to zero and tranfer the fragment to the remote node. (If, i > t, et i = 0 and end the fragment to remote node) Step 6. Go to tep 2. Fig. 4: Threhold algorithm An important point in the algorithm i the choice of threhold value. Thi value will directly affect the mobility of the fragment. It i trivial that a the threhold value increae, the fragment will tend to tay more at a node; and a the threhold value decreae, the fragment will tend to viit more node. Another point in the algorithm i the ditribution of the acce probabilitie. If the acce probabilitie of all node for a particular fragment are equal, the fragment will viit all the node. The ame applie for two node when there are two highet equal acce probabilitie. Simulation reult In the imulation, it i aumed that there are n node; x i the acce probability of the owner node; x d i the acce probability of the other node; O i the probability that the fragment i in owner node and O d i the total probability that the fragment i in the other node. Since, O + O d = 1, invetigating only O i ufficient. The following formula how the relation between n, x and x d. x + (n-1) x d = 1 Now, let u find how a change in the acce probabilitie and the threhold value effect the probability that the fragment i in any node. Change in acce probability When n i held contant, x and x d are inverely proportional. So, it i ufficient to invetigate only the change in x of O. Fig. 5 how the behaviour of O a a function of x in a five-node ytem. Fig. 5 i drawn for three different threhold value, 0, 3 and 10. For the threhold of 0, O i a linear function of x with a lope of 1. Thi mean that when the threhold i 0, the acce probability of a node directly give the probability that the fragment i in the correponding node. 236
Fig. 5: O a a function of x in a five-node ytem for threhold 0, 3 and 10 For threhold value of 3 and 10, notice the change in teepne of the curve. Change in threhold value Threhold t can take only non-negative integer value. Fig. 6 how the behaviour of O a a function of t in a five-node ytem. Fig. 6 i drawn for five different acce probabilitie x of 0.28, 0.24, 0.2, 0.16 and 0.12. For 0.28 and 0.24, O converge to one. Thi i becaue x > x. Noticing the change in d teepne of two curve, it converge fater for greater acce probabilitie. For 0.2, O i contant at 0.2. Thi i becaue x = x. In thi cae, the acce probability of d a node directly give the teady-tate probability that the fragment i in the correponding node. Fig. 6: O a a function of t in a five-node ytem for x value of 0.28, 0.24, 0.2, 0.16 and 0.12 237
For 0.16 and 0.12, O converge to zero. Thi i becaue x < x. Noticing the change in d teepne of two curve, it converge fater for maller acce probabilitie. In thi paper, a new dynamic data allocation algorithm, namely threhold algorithm, for nonreplicated DSS i introduced. In the threhold algorithm, the fragment, previouly ditributed over a DDS, are continuouly reallocated according to the changing data acce pattern. The behavior of a fragment, in reaction to a change in acce probabilitie or to a change in threhold value, i invetigated uing imulation. It i hown that the fragment tend to tay at the node with higher acce probability. A the acce probability of the node increae, the tendency to remain at thi node alo increae. It i alo hown that a the threhold value increae, the fragment will tend to tay more at the node with higher acce probability. Threhold algorithm can be ued for dynamic data allocation to enhance the performance of non-replicated DDS. For further reearch, the algorithm can be extended to ue on the replicated DSS a in (Wolfon and Jajodia, 1997; Sitla et al., 1998). Reference Ahmad, I., K. Karlapalem, Y. K. Kwok and S. K. So., 2002. Evolutionary Algorithm for Allocating Data in Ditributed Databae Sytem, Ditributed and Parallel Databae, 11: 5-32. Azoulay-Schwartz, R. and S. Krau, 2002. Negotiation on Data Allocation in Multi-Agent Environment, Autonomou Agent and Multi-Agent Sytem, 5: 123-172. Bakker, J.A., 2000. Semantic Partitioning a a Bai for Parallel I/O in Databae Management Sytem, Parallel Computing, 26: 1491-1513. Bruntrom, A., S.T. Leutenegger and R. Simha, 1995. Experimental Evaluation of Dynamic Data Allocation Strategie in a Ditributed Databae With Changing Workload, in Proceeding of the 1995 International Conference on Information and Knowledge Management, Baltimore, MD, USA, pp: 395-402. Ceri, S., S.B. Navathe and G. Wiederhold, 1983. Ditribution Deign of Logical Databae Schema, IEEE Tranaction on Software Engineering, 9:487-503. Ceri, S., B. Pernici and G. Wiederhold, 1989. Optimization Problem and Solution Method in the Deign of Data Ditribution, Information Sytem, 14: 261-272. Chang, C.T., 2002. Optimization Approach for Data Allocation in Multidik Databae, European J. Operational Re., 143: 210-217. Cheng, C.H., W.K. Lee and K.F. Wong, 2002. A Genetic Algorithm-Baed Clutering Approach for Databae Partitioning, IEEE Tranaction on Sytem Man and Cybernetic Part C-Application and Review, 32: 215-230. Chu, W.W., 1969. Optimal File Allocation in a Multiple Computer Sytem, IEEE Tranaction on Computer, C-18: 885-889. Ewaran, K.P., 1974. Placement of Record in a File and File Allocation in a Computer Network, in Proceeding of IFIP Congre on Information Proceing, Stockholm, Sweden, pp: 304-307. Morgan, H.L. and K.D. Levin, 1977. Optimal Program and Data Location in Computer Network, Communication of ACM., 20: 315-321. Navathe, S.B., S. Ceri, G. Wiederhold and J. Dou, 1984. Vertical Partitioning Algorithm for Databae Deign, ACM Tranaction on Databae Sytem, 9: 680-710. 238
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