A Novel Timestamp Ordering Approach for Co-existing Traditional and Cooperative Transaction Processing

Transcription

1 A Novel Timestamp Ordering Approah for Co-existing Traditional and Cooperative Transation Proessing Author Sun, Chengzheng, Zhang, Y., Kambayashi, Y., Yang, Y. Published 1998 Conferene Title Proeedings of Third IFCIS Conferene on Cooperative Information Systems DOI Copyright Statement 1998 IEEE. Personal use of this material is permitted. However, permission to reprint/ republish this material for advertising or promotional purposes or for reating new olletive works for resale or redistribution to servers or lists, or to reuse any opyrighted omponent of this work in other works must be obtained from the IEEE. Downloaded from Griffith Researh Online

2 A Novel Timestamp Ordering Approah for Co-existing Traditional and Cooperative Transation Proessing Yanhun Zhang Yahiko Kambayashi Yun Yang Chengzheng Sun Dept of Math & Comp. Dept of Information Si. Shool of Comp. & Math Shool of Comp. & IT University of Southern Qld Kyoto University Deakin University Griffith University TWB, Q4350, Australia Kyoto , Japan Geelong, 3217, Australia Brisbane, 4111, Australia Abstrat In order to support both traditional short transation and long ooperative transations, we propose a novel timestamp ordering approah. With this timestamp ordering method, short transations an be proessed in the traditional way, as if there are no ooperative transations, therefore not be bloked by long transations; ooperative transations will not be aborted when there is a onflit with short transations, rather, it will inorporate the reent updates into its own proessing; and the serialisabilities, among short transations, and between a ooperative transation (group) and other short transations, are all preserved. 1. Introdution In traditional database systems, user appliation programs are pakaged as transations and the onurrent data aess is synhronised using onurreny ontrol algorithms suh as optimisti onurreny ontrol (OCC), two-phase loking (2PL), and timestamp ordering (TO) [2, 3, 15]. The traditional database transation model is suitable for onventional database appliations, suh as banking and airlines reservation systems. Transations for these appliations are generally simple, and are haraterised as short duration that they will be finished within minutes or muh shorter. The traditional transation onept has limited appliability in many of advaned appliations suh as ooperative work. In those environments, transations tend to be very long, and need to ooperate with eah other. For example, in ooperative environments, several designers might work on the same projet. Eah designer may start up a ooperative transation. Those ooperative transations joinly form a transation group. Cooperative transations in the same transation group may read or update eah others unommitted objet versions. Therefore, ooperative transations may be interdependent. The long transations in traditional database systems may be aborted due to onflit operations or deadloks. Aborting long transation means the inreased proessing ost[25]. Cooperative transations have been reently addressed in several researh areas suh as advaned database systems, groupware and CSCW, and workflow. [7] offers a omprehensive review and a olletion of works on advaned transation models from the database point of view. Saga[11], Cooperative Transation Hierarhy[17], Cooperative SEE Transation[13], DOM Transations[4], Multilevel Transations[14] and other transation models [7] have been disussed, where all of them need some degrees of transation ooperation and different orretness riteria from serialisability exept Split Transation model[19] (as Split Transation model tries to reorganise a long transation into independent and serialisable transations). Other ooperative works have been onduted in the areas suh as groupware and workflow systems, where the transation ooperation is more evident [1, 8, 20, 21]. The major ahievements in these areas are the models and some tehniques to synhronise or oordinate the ooperative operations and to resolve the onflits between ooperative transations. So far, it seems there is no work addressing the oexistene of both traditional transations and ooperative transations. In an envrironment with both traditional transations and ooperative transations, ooperative transations should not be aborted due to onflit operations with short transations. On the other hand, as the quik response is often required or preferred for short transations, ooperative transations should not blok the short transations. In this paper, we will fous on the synhronisation and onurreny ontrol between traditional transations and ooperative transations. As a long and ooperative transation, it may take days even months to finish. It is rea-

3 sonable for this long transation to see the results of other short transations, no matter whether those short transations start earlier or not. Therefore, we aim at developing a new timestamp approah to support both traditional transations and ooperative transations. Figure 1 shows a lientserver system struture with both long and short transations. We divide transations into short transations (T s ) and ooperative (or long) transations, where long transations are grouped to a ooperative group. Ts Ts Ts Server DB T l group... T l loal spae... Clients Figure 1. A system struture with both short transations and ooperative transations The proposed method has the following features: (1) it allows both short (traditional) and ooperative transations o-exist; (2) short transations an be proessed in the traditional way, as if there were no ooperative transations, therefore not be bloked by long transations; (3) ooperative transations will not be aborted when there is a onflit with short transations, rather it will inorporate the reent updates into its own proessing; and (4) the f-onflit serialisability, a general orretness riteron for advaned transation proessing between a ooperative transation (group) and other short transations is preserved. Based on these features we believe this method is very suitable for advaned database appliations to support both short transation and ooperative work. The paper is organised as follows. In setion 2, we review some onepts and tehniques on traditional transation proessing, inluding transations, onflit serialisability and onurreny ontrols, espeially the timestamp ordering approah. Setion 3 develops a ooperative transation model and a general orretness theory for ooperative transation proessing. Setion 4 proposes a novel timestamp ordering method to deal with the interation between traditional transations and ooperative transations. In setion 5, we give some proofs on onsisteny and serialisability theorems. Conlusions and future work are inluded in setion Traditional transation proessing The database system refers to a database and the aess failities (database management system) to the database. One of the ommon objetives of database management systems, entralised or distributed, is the ontrol and oordination of the exeution of onurrent database transations. The onepts of database transations, onurreny ontrol and serialisability are the ommon notions in the transation management of entralised and distributed database management systems. The most popular onurreny ontrol approahes developed for entralised database systems have been suessfully adopted in the distributed environments Transations A transation ould be viewed as a transformation of a database from one onsistent state to another onsistent state[5]. Usually, a transation an be issued interatively by users or be embedded in the appliation program written in a high-level language suh as C, PASCAL or COBOL et. A transation is a partiular exeution of a program that manipulates the database by means of read and write operations. It an be defined as a sequene of database read and write operations, or more formally as a partial order of read and write operations. In addition, the transation ontains a Commit or Abort as its last operation, to indiate whether the exeution it represents terminated suessfully or not. In general, we use r i [x] (or w i [x]) to denote the exeution of a read (or write) issued by transation T i on data item x. In a transation a data item an be read and/or written at most one. Traditionally, transations are expeted to satisfy the following four onditions, known as ACID properties [10], namely, Atomiity, Consisteny, Isolation and Durability. The ACID properties an be trivially ahieved by the serial exeution of transations. However, this is not a pratial solution for the database management sine it seriously impairs system performane. Usually, the database systems are operating in the multi-programming, multi-user environments, and the transations are expeted to be exeuted in the database system onurrently. When several transations exeute onurrently, their operations are exeuted in an interleaved manner. Operations from one transation may be exeuted between operations of other transations. This interleaving an ause an inonsistent database. The database system must monitor and ontrol the onurrent exeutions of transations so

4 that overall orretness and database onsisteny are maintained. A shedule indiates the interleaved order in whih the operations of transations were exeuted. If the operations of various transations are not interleaved (i.e. the exeutions of transations are ordered one after another) in a shedule, the shedule is serial. The serial exeution of a set of transations preserves the onsisteny of the database. As serial exeution does not support onurreny, the equivalent shedules has been developed and applied for omparisons of a shedule with a serial shedule, suh as view equivalene and onflit equivalene of shedules. In general, two shedules are equivalent if they have the same set of operations produing the same effets in the database. Definition 1 Two shedules S 1 ;S 2 are view equivalent if: 1. for any transations T i, the data items read by T i in both shedules are the same; 2. for eah data item x, the latest value of x is written by the same transation in both shedules S 1 and S 2. Definition 2 Two operations are said to be in onflit if: 1. they ome from different transations; 2. they both operate on the same data item; and 3. at least one of them is a write operation. Definition 3 Two shedules S 1 ;S 2 are onflit equivalent if: for any pair of transations T i ;T j in both shedules and any two onfliting operations o ip 2 T i and o jq 2 T j, suh that if the exeution order o ip preedes o jq in a shedule, say, S 1, the same exeution order must exist in S 2. Definition 4 A shedule is onflit serialisable if it is onflit equivalent to a serial shedule. A shedule is view serialisable if it is view equivalent to a serial shedule. A onflit serialisable shedule is also view serialisable but not vie versa, sine definition of view serialisability aepts a shedule whih may not neessarily be onflit serialisable. There is no effiient mehanism to test shedules for view serialisability. It was proven that heking for view serialisability is NP-omplete problem[18]. The onflit serialisability an be verified through a onflit graph. The onflit graph among transations is onstruted as following: for eah transation T i, there is a node in the graph (we also name the node T i ). For any pair of onfliting operations (o i ;o j ), where o i from T i and o j from T j, respetively, and o i omes earlier than o j, then add an ar from T j to T i in the onflit graph. Theorem 1 A shedule is onflit serialisable if and only if its onflit graph is ayli [3]. The serialisation order of a set of transations an be determined by their onfliting operations in a serialisable shedule. In order to produe onflit serialisable shedules, many onurreny ontrol algorithms have been developed suh as Two Phase Loking (2PL), Timestamp Ordering (TO), Optimisti Conurreny (OC) Control, et.. As our work is losely related to Timestamp Ordering algorithm, we will review TO in the next subsetion Timestamp Ordering (TO) The timestamp ordering is a tehnique whereby the serialisation order is determined by the unique timestamp assigned to eah transation before it starts. Eah transation is assigned a timestamp by its transation manager (TM). The TM attahes suh a timestamp to all operations issued by the transation. Furthermore, for eah aessed data item A, there is a read timestamp t r (A) to reord the timestamp of the latest read, and a write timestamp t w (A) to reord the latest write. Any write operation of a timestamp earlier than the item s read timestamp is rejeted. Likewise, any read or write operation earlier than the item s write timestamp is rejeted. Rejeting an operation of a transation leads to transation abort and restart. Restarted transations adopt new and later timestamps. The basi TO algorithm has been proved to be a orret method whih an produe serialisable shedules[2]. The rules of basi TO an be summerised as follows. TO Rules: (Basi Timestamp Ordering Conurreny Control). 1. For eah data item A, there are two timestamps t r and t w,wheret r is the largest timestamp of those transations whih have read A and t w is the largest timestamp of those transations whih have written to A. Eah transation T has also a timestamp t to reord its starting time. 2. Read operation: When a transation T requests to read A, observe the following rules: (a) if t(t ) >t w (A), T reads A, and sets max(t(t ), t r (A)) as the new value of t r (A). (b) if t(t ) <t w (A), T annot read A, and has to be rolled bak. 3. Write operation: When T requests to write A, observe the following three rules: (a) if t(t ) > max(t r (A);t w (A)), the request an be granted and the new value of t(a) is set to t(t ).

5 (b) if t w (A) > t(t ) > t r (A), the write operation needs not be performed. () if t(t ) <t r (A), T annot write A and it has to be rolled bak. The timestamp ordering is free from deadlok and starvation sine there is no waiting in this algorithm. In fat waiting is meaningless in this approah as the rejetion of an operation only depends on the greatest TO value of the item. When an aess request of a transation is rejeted, the transation is aborted. Other advantage of the basi timestamp ordering method over 2PL is that it provides a great degree of onurreny by produing some more flexibility shedules. 3. Cooperative transation proessing In traditional database appliations suh as banking and airline reservation systems, transations are short and nonooperative, and usually an be finished in minutes or muh shorter. The serialisability is a well aepted orretness riterion for these appliations. The ooperative transation proessing in different appliations may have different requirements and require different system supports to oordinate the work of multiple users and to maintain the onsisteny. So far there is no single ommon aepted orretness riteria and onurreny ontrol approahes. In this setion we will give a definition of advaned or ooperative transations, and develop a general orretness riterion. Regarding to ooperative transations, one an also find other terms in literature suh as non-traditional transation, long transations, advaned transations and interative transations et.. The advaned transation proessing or ooperative transations proessing have been investigated in groupware[9, 22, 23], workflow systems[12, 20] and advaned database transation models[1, 7]. From these areas, one an derive the following ommon properties and requirements: 1. The ooperative work involves multiple onurrent users/transations. 2. Exhanging and sharing of persistent data between different users/transations need to be supported. 3. It needs to ensure the onsistene between individual and group. 4. The users/transations are often distributed. 5. Ativities are often performed interatively by human and usually of long duration. Based on these, we give the following definition: Definition 5 An advaned transation (ooperative transation group) is defined as a set (group) of ooperative transations T 1 ;T 2 ; :::; T n, with the following properties: 1. eah ooperative transation T i is a sequene (or partial order) of read(x) and write(y) operations; 2. for the same data item, there might be more than one read(x), written as read 1 (x); read 2 (x),,inaooperative transation, eah read(x) will get a different value depending on the time and interation with other transations; and 3. similarly, for eah y, there might be more than one write(y), written as write 1 (y); write 2 (y),. The first part shows that an advaned transation is a ooperative transation group. If the size of group is one, it will beome a single transation. Property 1 is the same as that in the traditional transation. Properties 2 and 3 indiate some ooperative features. The first read(x) may read other transation s ommitted or unommitted data depending on the onurreny ontrol employed. After the first read operation on x, the data item might be updated by another traditional transation or another ooperative transation, then it an read the new value in the next read(x). Similarly, after the first write operation on x, due to the ooperative feature, a transation may read some new data from other transations, then issue another write(x) to inorporate this to the urrent proessing. The later write(x) an undo the previous write, or do further update to show the new semantis. Similar to distributed database transations, the advaned transation definition ould be extended to a distributed advaned transation as following: Definition 6 A distributed advaned transation (distributed ooperative transation group) is defined as a set (group) of ooperative transations T 1 ;T 2 ; :::; T n, with the following properties: 1. eah transation T i onsists of a set of subtransations T j i at site j, j2 [1..m], m is the number of sites in a distributed system. Some T j i might be empty if T i has no subtransation at site j; 2. eah subtransation is a sequene (or partial order) of read(x) and write(y) operations; 3. for the same data item x, there might be more than one read(x), written as read 1 (x); read 2 (x),,inaooperative transation, eah read(x) will get a different value depending on the time and interation with other transations; and 4. similarly, for eah y, there might be more than one write(y), written as write 1 (y); write 2 (y),.

6 Similar to that in traditional transations, we assume that for write operations on x, there must be a read operation before the the first write in a ooperative transation. It is natural to read the data first before the update, ie. one s update may depend on the read value or one may use read operation to opy the data into the loal memory, then update the data and write it bak (when ommits). In advaned transation appliations, ooperative transations ould read and write a data item more than one, whih is different from traditional transations. The reason to read a data item more than one is to know the reent result and therefore make the urrent transation more aurate. However, this will bring the problem on the serialisability among ooperative transations, as a ooperative transation may read a data item before another transation starts and also read the data updated by the same transation. If so, the shedule between these two transations will not be serialisable. However, from the semanti point of view, the most important read or write on the same data item will be the last read or write. If we give high priority on the last read or write onflits in developing the orretness riteria, we ould have an f-onflit (final onflit) graph and therefore propose an f-onflit serialisability theorem. Definition 7 The f-onflit graph among transations is onstruted as following: for eah transation T i,thereisa node in the graph (we also name the node T i ). For any pair of final onfliting operations (o i ;o j ), where o i from T i and o j from T j, respetively, and o i omes earlier than o j, add an ar from T j to T i in the onflit graph. Definition 8 A shedule is f-onflit serialisable if and only if its f-onflit graph is ayli. The f-onflit serialisation order of a set of transations an be determined by their f-onfliting operations in a f- onflit serialisable shedule. From the definition, one an see the relationship between onflit serialisability and f- onflit serialisability: Theorem 2 If a shedule is onflit serialisable, it is also f-onflit serialisable, the vise versa is not true. The onflit serialisability is a speial ase of f-onflit serialisability in traditional transation proessing. Definition 9 A shedule of distributed advaned transations is f-onflit serialisable if and only if the following two properties are satisfied: 1. the shedule of subtransations at eah site is f-onflit serialisable; and 2. the f-onflit serialisation order at all sites are the same. Advaned transation or ooperative transation proessing in different appliations may have different appliation dependent requirements and require different system supports to oordinate the work of multiple users and to maintain the onsisteny. As a result, different synhronisation, oordination and ontrol mehanisms within a ooperative transation group are developed. The f-onflit serialisability in onjuntion with appliation dependent semantis ould be used for designing and testing advaned transations proessing approahes. The appliation dependent requirements an be refleted in the detailed transation strutures. For example, when there are several write operations on the same x, the later writes might be an undo and then a redo of the operation (or perform a different operation). The undo operations might be reverse operations or ompensating operations, and the redo operations ould be a ontingeny operations or new operations whih may need to keep the intention (user intention) of the original write [21, 22], or to inorporate the new semantis. 4. A novel timestamp ordering approah Though the ooperative transation proessing has been addressed in several researh areas, the interativity and long duration of ooperative transations have not been explored thoroughly, espeially their interations with traditional transations when both traditional transations and ooperative transations o-exist. In this ase, both types of transations o-exist, traditional (short) transations should not be bloked due to onflit with ooperative (long) transations, and the ooperative (long) transations should not be aborted due to the onflit with traditional transations. To explore the interative feature, ooperative transations should be able to read the reent data. For example, suppose that, a ooperative transation starts today, and will take a few days or maybe months to finish, and a short onfliting transation will only need a few minutes or muh shorter, but due to late arrival of a write operation or onflit with a long transation, it has been aborted, and started again and sueeded with a later timestamp. In suh a ase, the long transation would not be able to read this updated value when it finishes one month later. Just imaging that a design or a result from a long transation is based on some old database value, whih has been updated several times already. How would one rank the result of this long transation, updated or obsolete? So we argue that the result of suh short transations should be revealed to long ooperative transations. Due to the interativity of ooperative transations, users should be able to inorporate the new result into the transation by issuing some new operations or ompensating some earlier operations. In this setion, we will disuss the relationship between

7 short transations and ooperative transations and develop a onurreny ontrol approah to support the oordination between them. We onsider two kinds of transations, traditional short transations T and long ooperative transations T. To simplify the disussion we treat a ooperative transation group as one logial transation to avoid the disussions on operation synhronisation within a ooperative transation group. In a ooperative transation, it is reasonable to assume that for eah write operation there must be a read operation earlier. It is natural to read the data first before the update, ie. one s update an depend on the read value or use the read operation to opy the data in the loal memory, then update the data and write it bak (when ommits). Similar to the optimisti onurreny ontrol approah, we use a private work spae for the ooperative transation group where all data items read or updated are stored. All read operations are performed by opying the data items into this work spae. Write operations are performed on the private work spae. These values will be refleted to the database after the transation is ommitted. Due to the interative feature, a ooperative transation an be formed with great flexibility as an user an dynamially issue an operation depending on the most urrent information. If a datum has been updated reently after the first read, the ooperative transation may wish to read the data again due to the ooperative feature. Therefore we assume that in a ooperative transation, it ould read and write the same data item more than one. It an issue another read operation if knowing the datum has been hanged reently. In order to inorporate the reent hanges into its own transation, it an perform additional operations or ompensate the previous operations. That is the flexibility of interative work Transation interations We argue that the ooperative transations and traditional transation would not be aborted when there are onflits between ooperative operations and traditional operations. When traditional transations ommit, the ooperative transation may need to read or re-read the new value from them in order to ontinue the work based on the reent results. In suh a ase, some partial rollbak is required. Aording to the order of the onflit operations with respet to the ommit time, and the order of the timestamps, we onsider the following six ases: Case (a). AsshowninFigure2,t(T ) < t(t ), r (A) onflits with, and r (A) omes after T is ommitted. In this ase we will let T ontinue and hange the timestamp t(t ) to a value + (small value, just to indiate it is bigger than ). Aording to the traditional timestamp ordering method, T would be aborted. Figure 2. Case (a) ontinue Case (b). As shown in Figure 3, t(t ) < t(t ), r (A) onflits with, and omes later. In order to let the ooperative transation know this update, a message needs to be sent to T about the update when t ommits. T may need to read this new value. In suh a ase, some partial rollbak may be needed to inorporate this new result. If so, hange the timestamp t(t ) to a value +. After this, T s virtual timestamp will be bigger than T s timestamp. Aording to the traditional timestamp ordering method, both T and T will ontinue as usual, then T will never know this update no matter how long it is, whih does not reflet the advantage of ooperative and interative feature. Figure 3. Case (b) partial rollbak Case (). As shown in Figure 4, t(t ) > t(t ), r (A) onflits with, and omes later. We let T ontinue, and send a message about the update to T when T ommits. T may need to read this value after T ommits. In suh a ase, some partial rollbak may be needed to inorporate this new result. No hange on timestamp t(t ) in this ase. Here the partial rollbak and redo are not the same as that in the database systems reovery, where rollbak refers to undo all the operation to a point and then redo. Depends on the appliations, we may only need to reread the new value and then perform some additional operations to inorporate the hanges, or undo some affeted operations and issue some new ones. Aording to the traditional timestamp ordering method, T will be aborted and restarted with a later timestamp. When it is suessfully ommitted, there is

8 still a onflit between and r (A). This will beome the ase in Figure 3. Following the same disussion, in order to inorporate the reent hanges in the ooperative transations, one needs to re-read A and perform some additional operations. As this re-read is later than the re-read ase in Figure 4, it is reasonable to say the ost is muh higher in ase b than that in ase a. This arguement an be supported by some models on human s memory, referene and orrelation ability. For two related onepts, when reading with two different intervals t1 and t2, t1 <t2, the human s orrelation degree is higher in the first ase of t1 interval. Therefore, the omprehension time is shorter. In addition, as the interval inreases, one might have done more work whih needs to be modified. Therefore, to let T ontinue rather than abort is a reasonable solution. Figure 4. Case () partial rollbak Case (d). AsshowninFigure5,t(T ) > t(t ), r (A) onflits with, and omes later. T will ontinue, and this read will read the urrent value of A, the same as that in TO. Figure 5. Case (d) ontinue Case (e). AsshowninFigure6,t(T ) < t(t ), r (A) onflits with, and omes before T ommits. This is similar to ase b, but the onflit is found when r (A) arrives. Let the ooperative transation ontinue (read A), reord the onflit information and request the system to send the ommit or abort information when T ommits. After t ommits, hange the timestamp t (T ) to +. If T aborts, T will need partial rollbak to this read, and re-read. Aording to the traditional timestamp ordering method, T will be aborted. if T ommits Figure 6. Case (e) partial rollbak a Case (f). As shown in Figure 7, t(t ) > t(t ), r (A) onflits with, and r (A) omes later, Similar to ase (e), let the ooperative transation ontinue (read A), reord the onflit information, and request the system to send the ommit or abort information when T ommits. After t ommits, hange the timestamp t (T ) to +. If T aborts, T will need partial rollbak to this read, and re-read, and request the system to send the new result to T after T ommits. Figure 7. Case (f) partial rollbak a The above six ases overed all possible onflits between traditional transations and ooperative transations. Based on these we develop a novel timestamp ordering approah for dealing with their interations The new TO algorithm For eah data item A, we will use four timestamps t r, t r and t w, t w,wheret r is the largest timestamp of those transations whih have read A, t r is a virtual timestamp of the ooperative transations whih have read A, initialised as the starting time of the ooperative transation group, t w is the largest timestamp of those transations whih have written to A, andt w is the virtual timestamp of the ooperative transations whih have written to A. For the onflits between the traditional transations, we will use the basi TO. For the onflits between traditional and ooperative transations, we will give some new rules based on the disussion on the above six ases. New TO Rules: (New Timestamp Ordering Conurreny Control). 1. Read operation: When a transation T requests to read A, observe the following rules: (a) if t(t ) >t w (A), T reads A, and sets max(t(t ), t r (A)) as the new value of t r (A).

9 (b) if t(t ) <t w (A), T annot read A, and has to be rolled bak. 2. Write operation: When T requests to write A, observe the following three rules: (a) if t(t ) > max(t r (A);t w (A)), the request an be granted and the new value of t(a) is set to t(t ). i. If t(t ) <t(t ), r (A) onflits with, and omes later, reord the message about the onflit and the write (need to send to T when T ommits). ii. If t(t ) >t(t ), r (A) onflits with, and omes later. reord the message about the onflit and the write. (b) if t w (A) > t(t ) > t r (A), the write operation needs not be performed. () if t(t ) <t r (A), T annot write A and it has to be rolled bak. 3. T s Read operation: (a) If t(t ) <t(t ), r (A) onflits with, and r (A) omes after T is ommitted. T ontinues and hanges the timestamp t(t )toavalue max(t(t, + ). (b) If t(t ) <t(t ), r (A) onflits with, and r (A) omes later, but before T ommits, reord the onflit information, ask the system to send the ommit or abort message when T ommits or aborts. Then T ontinues (may need rollbak to re-read). () If t(t ) >t(t ), r (A) onflits with, and omes after t ommits, T will ontinue. (d) If t(t ) >t(t ), r (A) onflits with, and r (A) omes later, but before t ommits, reord the onflit information, ask the system to send the ommit or abort message when T ommits or aborts. Then T ontinue (may be rollbak late to re-read). 4. T s Write operation: When requests a write, granted, ontinues the operation. 5. Commit or abort operation: this information and/or onflit messages will be sent to T. 6. Messages from the write transation: When T reeives messages, hek (a) if T is ommitted, i. If t(t ) <t(t ), r (A) onflits with, and omes later. T may need to read the value again, then some partial rollbak to inorporate this new result. If so, hange the timestamp t(t )tovalue+. ii. If t(t ) >t(t ), r (A) onflits with, and omes late, some partial rollbak may be needed to inorporate this new result. No hange on timestamp t(t ). iii. r (A) onflits with, and omes earlier. If so, hange the timestamp t(t )to max(t, + ). (b) if T is aborted, r (A) onflits with, and omes earlier, T needs some partial rollbak to read the old value. No hange on the timestamp t(t ). As we assume that in ooperative transations for eah write operation there must be a read operation before hand, we do not need to onsider the onflits between the traditional write operations and ooperative write operations, sine the earlier onflit treatment between ooperative read operations and traditional write operations will over the treatment on their write - write onflits. Based on the interative features of some ooperative work, the rollbak tehniques will be different from the rollbak in the traditional database reovery. In traditional database, rollbak is used to reover transations from failure[16]. In database reovery, a write-ahead log is used to keep the reords of reent updates. When reovery from failure, a transation may need rollbak to a point or to the beginning of the transation, that means undoing all the operations from a transation to that point. Consequently these operations will be redone. In database, these undo and redo an be done automatially in the system, as all the transation semantis are fixed before submission. In ooperative work environments, many transations are on-line and dynami. When roll bak to a point, one may need to undo only some affeted operations to that point, then perform some new operations. 5. Consisteny and serialisability In the proposed new TO algorithm, both traditional (short) transations and long ooperative transations oexist. In addition, it has the following properties: Theorem 3 Short transations an be proessed in the traditional way as that in the basi TO algorithm, as if there were no ooperative transations, therefore they will not be bloked by ooperative transations. The serialisability among these transations is preserved.

10 Proof: This an be shown from Rules 1 and 2, the proess of read and write operations from traditional transations is the same as they are in basi TO. The only extra booking work is to reord the onfliting messages with ooperative transations as shown in Rule 2(a) i and ii, and to send messages to T when ommit as shown in Rule 4. So they will not be bloked by ooperative transations. As basi TO guarantees the serialisability of the transations, the new TO will also preserve the serialisability among traditional transations. Theorem 4 In new TO, ooperative transations will not be aborted when there is a onflit with short transations, rather, it will inorporate the reent updates into its own proessing; Proof: Again this an be shown diretly from Rules 3, 4 and 6. For ooperative work, the orretness riteria will depend on the appliation and ooperative transation proessing models employed. In the REDUCE projet[22], the orretness riteria are formalised through a CCI onsisteny model and these riteria are ahieved through a set of synhronisation and transformation algorithms. As shown in [24], the shedule produed from REDUCE system is f-onflit serialisable. Furthermore, the following general orretness of the novel TO algorithm an be shown. Theorem 5 In the new TO algorithm, a shedule of a ooperative transation T (group) and other short transations ommitted earlier than T ommits, produed from new TO, is f-onflit serialisable. Proof: To prove this theorem, we need to onsider the f- onflit graph of the shedule, and then show that the f- onflit graph is ayli, sine that a shedule is f-onflit serialisable if and only if its f-onflit graph is ayli. We now onstrut the onflit graph in two steps: Step 1. The onflit graph among traditional transations is onstruted as following: for eah transation T i,there is a node in the graph (we also name the node T i ). For any pair of onfliting operations (o i ;o j ), where o i from T i and o j from T j, respetively, and o i omes earlier than o j, add an ar from T j to T i in the onflit graph. As the shedule among the traditional transations is serialisable, there will be no yle among them, and we ould assume their serialisation order as T 1 ;T 2 ; :::; T i ; :::; T n (whih an be done by rearrange transations subsripts). Step 2. Now add a node T for ooperative transation group. Let us see how to add and maintain the ars between T and other transations. We only need to onsider onfliting ases a, b, and d shown in Figures 2-5, as T in ases 6 and 7 are aborted and the ars from and to T will be deleted. For the onflits in ases a and d, there will be only ars from T to T,andt(T ) is hanged to a value bigger than t(t ), it indiates that T an be be serialised after T. For the onflits in ases b and, there might be some ars from T to T initially as some operations from T ome later than the onfliting operations from T. But when T ommits, the onfliting messages will be sent to T. Aording to Rule 6, T will re-read the value written by T, and redo the neessary operations to inorporate this update. After this T is different from the initial T, as the new T has read the value from T, it is now serialisable after T, that s the reason to hange T s timestamp. In the final onflit graph, the ars from T to T now need to be reversed. Hene, there will be new ars from T to any T. Therefore, there will be no yle, and T is serialisable after all the short transations whih are ommitted earlier than T. 2 The f-onflit serialisability is a more generalised form of the traditional onflit serialisability. The theorem an be used for advaned transations suh as long transations, ooperative transations and interative transations when there are more than one read and write on the same data in the transation. 6. Conlusions and future work In traditional database systems, a transation an be aborted due to the onflit operations. Aborting a long transation often means the inreased ost. In order to support both traditional short transation and long ooperative transations, we have proposed a novel timestamp ordering approah in this paper. With our new timestamp ordering (TO) method, short transations an be proessed in the traditional way, as if there are no ooperative transations, therefore not be bloked by long transations; ooperative transations will not be aborted when there is a onflit with short transations, rather, it will inorporate the reent updates into its own proessing; and the serialisabilities, among short transations, and between a ooperative transation (group) and other short transations, are all preserved.

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