Constructing Transaction Serialization Order for Incremental. Data Warehouse Refresh. Ming-Ling Lo and Hui-I Hsiao. IBM T. J. Watson Research Center

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1 Construting Transation Serialization Order for Inremental Data Warehouse Refresh Ming-Ling Lo and Hui-I Hsiao IBM T. J. Watson Researh Center July 11, 1997 Abstrat In typial pratie of data warehouse, the warehouse data is kept in a separate site from the operation data. Changes to the operation data to propagated to the warehouse site periodially, usually by shipping the new log entries in the operation site. When the operation site is a parallel a parallel DBMS, it is neessary to arrange the log entries into an oherent order for the warehouse data to maintain onsisteny and integrity. This paper solves the problem by presenting a simple method for onstruting a global transation order out of a set of loal logs of a parallel or distributed system. For serial database systems, transation order an easily be inferred from loal database logs. For parallel or distributed database systems, sine eah loal log les has only partial information of eah transation, this problem beomes diulty. In this paper, we present a simple method that determines the order of transations by examining only the relative position of their vote and ommit entries, and needs not looking into what data items eah transation aesses. Based on this mehanism, we present a method that eiently onstruts a global transation order. Coneptually, our method rst onnets the vote and ommit symbols of loal log les into a network. Then it traverse the network to detet inonsisteny in the ordering of ommit symbols in dierent log. It then resolves the inonsisteny by adjusting the position of ommit symbols in the network. Our method has the following features. First, it examines only the vote and ommit entries of transations, but not the data aessing entries. Seond, for vote or ommit 1

2 entries, only their relative positions and their transation ID (to identify from whih transation an entry omes) requires attention. No other information reorded in the vote or ommit entry needs be examined. Finally, it has low omplexity. For a set of loal logs with l totally, only O(l) ost is required both in terms of time and spae. 1 Introdution Data warehouses [Inm96] has beome an inreasingly important faility for deision support and data mining appliations. In suh appliations, information are gather from operation sites for study and analysis. While it is possible to install the warehouse data on the same site as the operation databases, the typial pratie in data ware housing is to separate the warehouse data from operation databases [CD97]. Change on the operation side are later shipped or propagated to the warehouse at onvenient time to reet new information gathered. One reason for doing this is that operational databases are typially used by mission ritial OLTP appliations and any degradation in OLTP performane ould potentially redue ompany's revenue and inome. A seond reason is that OLTP and deision support appliations have very dierent funtional and performane harateristis, and it is very diult to optimizing a system to satisfy both types of workload. One key issue in an environment where warehouse site and operation site is separated is how to propagate eiently the hanges in the operational database to the warehouse database. Copying the omplete operational database to the warehouse site is apparently ineient. Another solution is to propagate the update from operational database to warehouse database ontinuously to keep the warehouse database losely up-to-date. The ARM mehanism proposed by Bhide et al. [BGHJ92], for example, an be applied in data warehouse environment. In most of the data warehousing environment, however, absolute up-todate information is not required. The most ost eetive approah therefore is to propagate the updates to warehouse database periodially, whih an be ahieved by shipping the (possibly ompressed) log reords of operation site and apply them to warehouse database. When the operational database is on a parallel or distributed database system, as is inreasingly ommon, the problem beomes more omplex. The operation site and ware- 2

3 house site may have dierent number of nodes, and/or dierent data partitioning. Unless the operation site and the warehouse site has exatly the same number of nodes and the same data partitioning, applying the parallel logs in the operational site to the warehouse independently may result in inonsisteny and violate data integrity. For instane, on operation site a reord an be reated, moved to another node, and deleted there. When propagating logs from operation site to the warehouse site, if the operation logs are not applied in orret order, it is possible that the delete will be enountered rst. It is therefore neessary to ombine the logs from the operation site into a oherent log before shipping to the warehouse site. This paper solves this problem by presenting an eient method for onstruting a global transation order out of a set of loal logs [MHLP91, Gra78] in a parallel or distributed database system. In addition to failitating warehouse update, onstruting global transation order has the added benet of providing transation exeution history in a distributed or parallel database systems. Suh information is often the objet of mining itself, and an also be a part of historial data. For serial database systems, transation order an easily be inferred from loal database logs. For parallel or distributed database systems, sine eah loal log les has only partial information, this problem beomes diulty. Some systems reord additional information in the log entries that an be used for global transation order onstrution, suh as virtual timestamps [Hsi94]. However, not all systems have the help of additional information. In this paper, we present a method that onstrut a global transation order from the loal logs of a parallel or distributed database system by examining the patterns in the log along. It does not require modiation to the log entry format or to the logging subsystem. Speially, our method onstruts a global transation order by examining only the relative pattern of the vote symbols and ommit symbols in the loal logs, and enfores an ordering of \transation A before transation B" when there is a relative pattern of C A? V B? C B in some loal log, where C X and V X is the ommit and vote symbols of transation X, respetively. Based on our basi mehanism for ordering two arbitrary transations, we present a method that eiently onstruts a global transation order by sanning eah eah loal 3

4 log les only one. Coneptually, our method rst onnets the vote and ommit symbols of the loal logs into a network. Then it resolves ommit symbol yles using our ommit symbol sliding mehanism, and merge the network into a serial sequene. Our method has the following features: 1. It onstruts global transation orders by examining the relative position of the vote and ommit symbols alone. There is no need to look into what data items eah transation has aessed. 2. For eah vote or ommit symbol, we only need to examine its transation ID. No other information reorded in the log entries needs be examined. For example, we don't need to hek the reorded timestamps, if any. 3. We requires no speial treatment of the oordinators of transations. This simplies the algorithm. 4. We only need to read eah loal log les one, and an thus onstrut transation order very eiently. To the best of our knowledge, this is the rst paper to oer solution to suh problem. The rest of the paper is organized as follows. Setion 2 outlines the general operating environment and desribed the problem we try to solve. In setion 3, we introdue the basi mehanism used in ordering transations. Setion 4 presents our main algorithm and Setion 5 disusses the omplexity of our algorithm. Finally, Setion 6 onludes this paper. 2 Preliminaries We assume a database system that (1) is a parallel or distributed database system, (2) uses two-phase ommit protool [BHG87], and (3) uses two-phase loking protool [BHG87]. In this system, eah node has a loal log, and reords in the log the operations that are invoked on the node. For eah transation there is a oordinator and a set of subordinates, possibly on dierent nodes, working on the transation's behalf. The oordinator initiates and 4

5 manages the transation. The subordinates aess the database and perform omputation. Note that oordinators of dierent transations may reside on dierent nodes. Many variants of the two-phase ommit protool have been proposed, inluding the presumed abort and presumed ommit [MLO86], and the early prepare [SC90] protools. In general, these protools use the two-phase loking protool as their onurreny ontrol protool. Also, when a variant of the two-phase ommit protool is used, in addition to the operational log entries, the oordinator and partiipants of a transation also reord in their respetive loal logs the following transation management entries: in its loal log [BHG87]: Coordinator: 1. start-2pc, 2. Commit or Abort 3. End/Forget Transation. Partiipants: 1. Vote: yes/no, 2. Commit or Abort. Dierent variants of the protools may reord dierent subsets of the above entries in the log, depending on the aspets of performane they try to optimize. However, for most of the variants, the following statement is true: in the absene of failure, or, if there is a failure, after the failure is reovered, for eah ommitted transation there is a vote entry and a ommit entry reorded in eah partiipant log, and vote entries preedes the ommit entry. Our analysis and method apply to any two-phase ommit protool variant that has the above property. The problem we propose to solve is to obtain a global transation order from a set of loal logs, so that the global order does not onit the transation order implied by the loal nodes. Our design goals are: (1) To inur as little overhead as possible in onstruting the ordering. (2) To support the onstruting of both total and partial global order of transation. (3) The onstruted global order must be able to be used in onstruting a global log. Note that to solve this problem, we need only look at the ommitted transations, and need not examine log entries written on behalf of aborted transations at all. 5

6 2.1 Serialization Order In the ourse of our desription, we also draw upon the following onepts: Serialization Order: Given a set of objets, we an order them into a total order (a sequene) or a partial order. When the set of objets are transations, we all this order a "serialization order" of the set of transations. The order in whih two transations appear in the total or partial order is also alled the "serialization order" of the two transations. Serialization Requirement: In a DBMS, the system may perform its operations in ertain way, so that it is only meaningful to view one transation as preeeding another. In this ase we say that the DBMS requires one transation be serialized before another transation. This is alled the "serialization requirement" of the two transations by the system. In other words, the serialization requirement between two transations is the order in whih two transations should be serialized. For example, in a DBMS using the two-phase loking protool, if two transations aess a ommon data item, the database system will grant the lok to the data item to one transation rst then the other. In this ase there is a serialization requirement between the two transations. Serialization Impliation: A database log reords the operations that are performed on its assoiated node. The sequene and type of operations, together with the semantis of the system in whih they are exeuted, arry information regarding the serialization requirement by the system. This information is alled the "serialization impliation" of the log le. 2.2 Alternatives The most obvious solutions to this problem are either to examine the timestamp information for eah transation, or the data items aessed by eah transations. All suh information is reorded in the loal logs. However, global timestamps are not always available in every DBMS, and examining data items aessed by eah transation requires examining almost all log entries and performing ompliated analysis. 6

7 Another possibility is to examine the order of ommit entries in the loal logs. However, the ommit entries alone does not provide enough information for onstruting a global transation order. In a parallel or distributed database system, a database node logs its ommit entries in the order it proesses them, instead of in the order imposed by the system serialization requirements. Therefore, even if the ommit of transation A is logged before the ommit of transation B in some log, any one of the following situations an still happen: 1. A must be serialized before B. 2. B must be serialized before A. 3. There is no serialization requirement between A and B. The reason is that the ommit entry of one transation may preeed that of another simply beause it is proessed earlier, and the two transations may not have aess any ommon data item at all. Also, the ommit entries of the same two transations may appear in different order in dierent log les, even when there exists a serialization requirement between them. This happens when dierent nodes in the parallel or distributed system experiene dierent ommuniation delays. A third alternative is to order transation by the order of their vote entries. This alternative relies on (1) partiipants gaining no new loks after voting, and (2) partiipants to synhronize themselves with the oordinators before vote. That is, it requires partiipants, after nishing their jobs, to send a \done" message to the oordinator, and the oordinator, upon reeiving suh messages, sends out a \prepare to ommit" message to all partiipants. However, in pratie a oordinator an ombine the last request to a partiipant and and the \prepare to ommit" ommand in one message to optimize on performane. This is partiularly useful for short update-only transations where eah partiipant performs only one write. In general, the order of ommit or vote entries alone does not always provide enough information to onstrut a global serialization order. In the following setion, we present a method that examines a partiular pattern of vote and ommit entries, whih leads to a simple implementation for onstruting global transation order. 7

8 3 Basi Ordering Method Our method uses a mehanism that examining only the pattern of the vote and ommit entries of loal logs to onstrut a global transation order. We assume that the implementation of the two-phase loking protool is suh that a transation annot aquire loks on a node after it asts its vote on that node. This requirement is implied by most two-phase ommit protool variants and is in fat the way most database systems are implemented. It is stated here expliitly for larity. When used with two-phase ommit protools, the two-phase loking protool an in general release loks in two ways. The rst possibility is to release read loks after the vote, and write loks after the ommit point. This is what is desribed or implied by most two-phase ommit protool literature [GR93, MLO86, SC90]. The seond possibility is that both read loks and write loks are released after the ommit point. This is in fat the strit two-phase loking protool [BHG87]. Although this alternative is more restritive in allowing onurreny, many real-life systems, inluding IBM DB2/PE, implemented this lok release strategy. The reason for this hoie is twofold. First, if the ommit operation is very eient, it may not be ost eetive to release read loks before ommit and write lok afterwards [BHG87]. Seond, it is diult to detet the end of the voting phase of ommit, sine one partiipant may invoke another as part of the voting phase. A partiipant may be alled to do additional work after that partiipant has voted to ommit the transation. This situation is alled rejoining the transation [GR93]. In the following disussions, we will rst present our analysis assuming strit two-phase loking, and disuss the impliation of releasing read loks after vote later. We denote the vote and ommit entries for a transation A as V A and C A, and for two entries E 1 and E 2 in the same log, use E 1? E 2 to mean that E 1 preedes E 2. Note that E 1? E 2 only means E 1 omes before E 2 in the sequene. It does not mean E 1 is the symbol immediately before E 2. We say E 1? E 2 is a relative pattern (pattern for short) onerning E 1 and E 2. A seond subsript is used to denote the node (or log) at whih an operation ours. Therefore, C A1 means the ommit operation of transation A at node (or log) 1, and V B2 means the vote operation of transation B at node (or log) 2. 8

9 Our basi mehanism to onstrut a global transation order is as follows: For any two transations A and B, if there is a relative pattern C A? V B? C B, we order A before B in our global transation order. No other pattern ditates our global transation order. 3.1 Ordering under Strit Two-Phase Loking First we assume strik two-phase loking. This mehanism works orretly beause of the following theorems. Theorem 1: If there is a serialization requirement of A before B by the system, then there is a relative pattern of C A? V B? C B in at least one loal log. Proof: Under two-phase loking protool, a serialization requirement of transation A before B means transation A and B aess a ommon data item D in some node, and A aquire the lok on the data item before B does. Sine transation B annot aess any more data item after the vote V B is asted, it must aquire the lok on and aess D before its vote. Beause the system uses strik two-phase loking, A releases the lok to D only after its ommit. Thus the vote of B must follow the ommit of A. That is, C A? V B. 2 Theorem 2: For any two transations A and B, if the relative pattern C A? V B? C B appears in some loal log, the pattern C B? V A? C A annot appear in any other loal logs. Proof: We use E 1! E 2 to denote that the event E 1 is written to log ours before the event E 2 is written to log. Note the denition does not require E 1 and E 2 to belong to the same log le. When E 1 and E 2 do belong to the same the log, E 1! E 2 and E 1? E 2 are equivalent. The two-phase ommit protool guarantees that for any given transation, the votes at all nodes are written to log before the ommit at any node is written to log. This is beause 9

10 the oordinator must ollet all votes before it sends out its deision to any node. Thus, V T X! C T Y for any transation T and any pair of nodes X and Y. Suppose there is a pattern C AL? V BL in some log L. For an arbitrary log X, we have V AX! C AL! V BL! C BX. This in turn means V AX! C BX and V AX? C BX. Thus the vote symbol of A must preeed the ommit symbol of B in any log. 2 Note that two transations A and B may not aess any ommon data item and still have the pattern C A? V B? C B on a log by hane. However, from the theorems above, we see that the mehanism has the following properties: No miss: If there is a serialization requirement of A before B by the system, there is a pattern of C A? V B? C B in at least one loal log, thus our mehanism will identify it. No fault: If there is a relative pattern C A? V B? C B in some loal logs, then either the serialization requirement between transations A and B is A before B, or there is no serialization requirement at all. Either way, it is safe to order A before B. No hange: If we see C A? V B? C B in one loal log, we will never see C B? V A? C A in any other loal log. Thus, we never need to hange the global order one it is determined. 3.2 Ordering under Early Read Lok Release When read loks are release after vote, vote and ommit pattern annot orret identify all serialization requirements. To see this, onsider two transation A and B. Transation A, among other things, aess data item D. After A votes and releases the read lok to D, transation B aquires write lok to D, writes to D, ommits and releases the write lok to D. At this point A reahes its ommit point. The pattern for A and B will be V A? V B? C B? C A. Though there is a serialization requirement A? B, our method does not identify it. That is, under early release of read loks, examining vote and ommit pattern annot identify read-write onits. However, it an still identify write-read and write-write onits. 10

11 Theorem 3: In a system where the write loks of a transation are released after its ommit point, if there is a serialization requirement of A before B by the system due to write-read or write-write onit, then there is a relative pattern of C A? V B? C B in at least one loal log. Proof: The proof is similar to that of Theorem 3.1, exept that now A release its write lok after C A, and B must aquire the oniting share lok or write lok before its vote. 2 Although our method does not produe an ordering that does not reet all serialization impliation in the logs, for the purpose of warehouse database updates, the transation ordering produed will still result in orret warehouse databases. There are two reasons. First, our method arranges all updates to a partiular data item in the same order as they ourred during their original exeution. Most importantly, in our ordering the nal write to every data item is the same as in the original exeution. Seond, when apply write operations to the warehouse database opy, the arguments of write operations are taken from what is reorded in the log, instead of determined by previous reads as in ordinary exeution. Thus the ontents to be written to the warehouse database the write operations are always the same as that written to the operation database. Missing read-write onits is therefore immaterial in the data warehouse updates. 4 Transation Ordering Algorithm Based on the above theorem, algorithms an be designed to onstrut global transation orders by examining only the vote and ommit symbols of transation partiipants. At a rst look, one an devise a simple algorithm as follows: Consider eah transation as a node in a graph, then examine the loal log les. For eah pattern of C A? V B? C B deteted, add an direted edge from T A to T B. When all logs are sanned and edges added, sort the (ayli) graph into a sequene. On loser examinations, however, suh an straightforward algorithm involves extremely 11

12 high spae and time omplexity, and is thus impratial to implement. Assuming there are n transations, sine the number of serialization requirements between transations is O(n 2 ), to maintain the edges expliitly we need O(n 2 ) spae, and at least O(n 2 ) time. With large number of transations, the quadrati spae and time omplex will be prohibitive expensive. To overome this problem, instead of maintaining ordering information expliitly, we adopt the following general strategy in designing our algorithm: 1. We use the ommit symbols as the marker of transation order. That is, transation A is onsideration to be ordered before transation B if its ommit entry appears before that of B in some log. 2. In ases where ommit symbols of a set of transations have inonsistent order in dierent logs, we adjust the positions of ommit symbols in some logs to make all log having the same order for the set of transations. Eventually this will results in all logs having onsistent orders of ommit symbols. 3. The loal logs an then be merged easily to produe a global order. Suh an approah has the following advantages advantages. First, There is no need for maintaining large expliit data strutures. Seond, although the order of ommit symbols does not guarantee serialization requirements, in pratie, for the majority for the transations, espeially when the system is not heavily loaded, the order of ommit symbols does reet their serialization requirements. We thus only need to proess those ases when the ommit symbol positions ontradit the serialization requirements. Details of the algorithm is desribed in the following setions. 4.1 Adjusting Symbol Positions The key steps of this approah are the identiation of inonsisteny in ommit symbol ordering, and adjusting the positions of ommit symbols to ahieve ordering onsisteny. 12

13 L1 Ci Vj Cj L2 Cj Ci vote or ommit symbol Figure 1: Example of a ommit symbol yles involve log les L 1 and L 2. Inonsisteny in ommit symbol ordering in dierent logs reets in ommit symbol yles. That is, inonsisteny ours when there are ommit symbol yles in the logs and vie versa. The ation of adjusting ommit symbol positions to make the order of ommit symbols onsistent on all loal logs amounts to resolving ommit symbol yles. Formally, ommit symbol yles are dened as follows: Denition: Given a set of loal logs, if there exist some ommits symbols C 1 ; C 2 ; :::; C n?1 ; C n, suh that relative patterns C 1? C 2 ; C 2? C 3 ; :::; C n?1? C n ; C n? C 1 exist in some loal logs, we say that there is ommit symbol yle or simply a yle onsisting of C 1 ; C 2 ; :::; C n. Eah of C k? C k+1, for 1 <= k <= n? 1, and C n? C? 1 is alled a segment of the yle. Figure 1 shows an example of a two-segment ommit symbol yle. There are two logs involved in this yles. On log L 1, C i? C j forms a segment of the yle. On log L 2, C j? C i is the other segment. Denition: Let C i? C j in some loal log be a segment of some yle. If relative pattern C i? V j? C j exist in the log, we say the segment is diretly supported by serialization impliation of the log. In the example in Figure 1, sine there is a pattern of C i?v j?c j on log L 1, the segment C i? C j is a supported segment. When a ommit symbol yle is identied, we must adjust the positions of the ommit 13

14 L1 Ci Vj Cj L2 Ci Cj vote or ommit symbol Figure 2: Example of a ommit symbol yles resolved. symbols on some unsupported segment to resolve the yle and make the transation order onsistent in all logs. Sine the relative patterns of vote and ommit symbols imply serialization impliations, adjusting positions of ommit symbols may hange the relative patterns and reate or destroy the serialization impliations of a loal log. The ation of adjusting ommit symbols must therefore be done in a disiplined and well-ontrolled fashion. We adhere to the following priniples when adjusting symbol positions: 1. The serialization impliation of any loal log should be hanged as little as possible. 2. If a piee of serialization impliation is deleted, it must still exist in some other logs. The total serialization impliation in the set of loal logs is never redued. 3. If a piee of serialization impliation is reated, no other log an have oniting serialization impliation The Slide Operation We use the bakward slide (or slide) operation to ahieve a disiplined way of adjusting ommit symbols. The slide operation only moves, or slides, ommit symbols. Further, it slides a ommit symbol only in in the bakward diretion along the same log, and never slides a ommit symbol past its orresponding vote symbol. Figure 2 shows the ommit symbol yle resolved by slide C i on L2 to the position immediate before C j. 1 This priniple is neessary sine we try to onstrut a total order out of a set of loal logs whih implies only a partial order, and thus inevitably need to reate serialization impliation beyond the system's serialization requirements. 14

15 The slide operation has an important property: it only reates serialization impliations, but never destroys them. During the slide operation, the ommit symbol being moved an slide past some other ommit symbols, or the vote symbols of some other transations. From the theorems we proved above, it is easy to see that swithing the order of any two adjaent ommits does not hange any serialization impliation. Lemma 1: For any log, swithing the order of any two adjaent ommits (or two adjaent votes) does not hange the serialization impliation of the log. Proof: We have shown that serialization impliation between two transation A and B is arried only by the pattern C AX? V BX? C BX or C BX? V AX? C AX. That is, if there is a serialization impliation between A and B, their ommit symbols annot be adjaent. Thus swithing two adjaent ommit annot destroy a serialization impliation. Sine the ation of swithing does not introdue a vote symbol between two ommits, it annot reate a serialization impliation either. 2 On the other hand, swithing the order of two adjaent vote and ommit symbols will either reate or destroy a serialization impliation in a log. However, if the swith is moving a ommit symbol that was originally positioned after a vote symbol to the position in front, then no serialization impliation an be destroyed. Lemma 2: The ation of sliding a ommit symbol bakward does not delete any serialization impliation. Proof: Sine a serialization impliation between transation A and B is reeted by the relative pattern C A? V B? C B, it an be delete only if we move C A to positions before V B, whih the slide operation never does. 2 In the following setions, we will disuss how to detet ommit symbol yles, and how to resolve them using the slide operation. 15

16 L1 v v L2 v v L3 v v merge point Figure 3: Example of a set of loal logs onneted into a network. 4.3 Deteting Commit Symbol Cyles To detet ommit symbol yles, rst we onnet all loal logs into a network at ommit symbols. The vote and ommit symbols of transations are onsidered nodes in the network: 1. For every log, eah symbol within the log is onsidered onneted to the symbols immediately before and after the symbol. 2. Eah transation is represented by a merge point, whih has a wait list and an auxiliary support list assoiated with it. The wait list is essential for yles detetion. The support list makes yles resolution more eient. 3. If a transation T has vote and ommit symbols in multiple logs L 1 ; L 2 ; :::; L k, we onnet all these ommit symbols to the merge point of T, and enter L 1 ; L 2 ; :::; L k into the wait list of T. The vote symbols of the orresponding are also onnet to the merge point, and is reorded in the support list. The vote symbols are not onsidered part of the merge point, are is reorded for eieny in yle resolution. Figure 3 show an example of a network onneted from three loal logs. To detet ommit symbol yles, we need to tranverse all logs, from beginning to end. Eah log is onsidered to have a urrent traversal point to keep trak of its urrent position in traversal. The traversal of eah log is in either the stalled or the ative state. The basi idea for merge point is that one the traversal of a log reahes a merge point, it must stall 16

17 L1 v v L2 v m1 v m2 L3 v m3 v merge point urrent traversal point target point Figure 4: A snapshot of log traversal. and wait for all other logs onneted to the merge point to also reah the point. The details of yle detetion are as follows: 1. Pik an arbitrary log L in ative state and advane its urrent traverse point till a merge point is enountered. 2. Delete votes from the support list of their orresponding merge points as they are enounter. This step is not related to yle identiation, but is useful in yle resolution later. 3. When the traversal point reahes a merge point C m : (a) Delete L from the wait list of C m. (b) If the wait list is non-empty, put L into the stalled state. If the wait list is empty, return all logs onneted to C m to the ative state. 4. If all logs are ompletely traversed, end proessing. Otherwise, if there is at least one log that is not stalled, go to step If all logs are in stalled state, at least one ommit symbol yle is enountered. Identify and resolve the yle. 6. Go to step 2. 17

18 Figure 4 show a snapshot during traversing the network presented in gure 3. Note that merge point m 1 and m 2 are bloking eah other, and yles resolution is required before traversal an ontinue. When it happens that all logs stall at some merge points, we know that eah log L must have stopped at some merge point C m (its urrent traversal point) with a non-empty wait list. Further, for eah log L w in the wait list of C m, we know that C m must lie beyond the urrent traversal point of L w (otherwise L w would have been deleted from the wait list of C m ). We would need to wait till L w reahes C m, before traversal of L an proeed again. We all C m a target point of L w (see Figure 4). Whenever a log has a target point, it means that some other logs are waiting for the log to ome up to its target point before the other logs proeed further. At the time when all logs are stalled, the urrent traversal point of eah log must onnet to some merge point whih in turn onnets to the target points of some other logs (see Figure 4). However, not every log has a target point when all logs are stalled. Also, the urrent traversal point and the target point of a log annot be the same, beause that would mean a transation is ommitted twie on a single database node. 4.4 Cyle Resolution When all logs stall, we know that ommit symbol yles are enountered. We need not, however, atually identify the segments of the yles before we an resolve the yles. The basi idea is to nd a merge point C m so that: if C m is involved in ommit symbol yles with some other merge point C x, then all segments C x?c m are unsupported segments. We will then resolve all these yles, by sliding C m to the position immediately in front of C x. Using our urrent framework, this an be easily done by nding a merge point suh that for every target point C ml on log L that is onneted to this merge point, V ml does not lie between the urrent traverse point of of L and C ml. We all this an unsupported merge point. Finding an unsupported merge point is easy: we simple nd a merge point 18

19 with empty support list. Next we prove there will be at least one suh merge point. Theorem 4: When all log traversal stops, there is at least one merge point C m suh that for every target points C ml on log L that is onneted to this merge point, V ml does not lie between the urrent traverse point of of L and C ml. Proof: If a merge point C m does not satisfy the desribed ondition, that means there is a pattern C X?V ml?c ml on some log L, where C X is another merge point. This in turn means that transation orresponding to C m, T m is serialized after T X orresponding to C x. If all merge points do not satisfy the aforementioned ondition, that means the orresponding transation of every merge point is serialized after the transation orresponding to some other merge point, whih is impossible given the original exeution is serializable. 2 One an unsupported merge point is identied. We slide every target point C ml on log L that is onneted to this merge point to the position before the urrent traversal point of L, and make it the urrent traversal point of L. After this operation, there is at least a merge point all of whose ommit symbols are un-bloked, and traversal an be ontinue on logs with these ommit symbols. As stated earlier, when slide operation is performed, we may slide a ommit symbol past a vote symbol (of some other transation), whih may reate a serialization impliation. However, it an be shown that, given our way of traversing the logs, the serialization impliation reated will never ontradit serialization impliations already exist. Theorem 5: Slide a target point C ml of log L to the position immediately before the merge point C x of L will never reate serialization impliations ontraditing existing ones. Proof: Suppose before the slide, there is a vote symbol V yl of a this transation between C xl and C ml, i.e., a relative pattern C xl? V yl? C ml. After we will reate a new serialization impliation of T m? T y, by reating the pattern C ml? C xl? V yl? C yl. For this to be 19

20 ontradition, there must be a relative pattern C yk? V mk? C mk on some other log K. There are two possibilities: (1) C mk is a urrent traversal point, or (2) C mk is a target point, and V mk lies before the urrent traversal point C zk of log K. If C mk is a urrent traversal point, then C yk would have being traversed before we reah C mk. But on log L, V yl and hene C yl lie after the urrent traversal point C xl. This means that traverse on log K would have been bloked at C yk, and C mk annot possibly be the urrent traversal point of log K. If C mk is a target point, and V mk lies before the urrent traversal point C zk of log K, then will be a pattern C yk? V mk? C zk. Again, this is impossibly sine we would have being bloked at C yk, and C zk annot be the urrent traversal point Global Order Constrution Algorithm With the mehanism for yles resolution in plae, the algorithm for onstruting a global transation order an be outlined as follows: 1. Connet all logs into a network. 2. Traverse the logs, detet, and resolve ommit symbol yles in the network. 3. Merge the network into a serial sequene. The rst step onnet loal logs into a network. The seond step detets, and resolve ommit symbol yles. The merging proessing is straightforward. Starting from the beginning of the logs, we traverse logs and output ommit symbols in arbitrary fashion, logs as long as their relative orders in the original logs are not violated. One a merge point is enountered, we annot traverse and output beyond this point before all other log onneted to the merge point has always reahed the merge point. A merge point is output only one. Steps two and three an be merged into one pass of the network in atual implementation, but are stated as separate proess here for larity. 20

21 5 Disussions Assume there are n transations and p nodes, whih means p loal logs, and that the total number of log entries in all nodes are l. Assuming the average number of nodes a transation aesses is f, we know that n f = l. The omplexity of our algorithm is analyzed as follows: 1. To onnet logs into a network at ommit symbol, we need to traverse all logs, and maintain the logs that onnet to a merge point. This require O(l) time and O(l) spae. 2. For yle detetion, we need to traverse all log entries, this is O(l) time. At eah merge point (one per transation), we need to proess all logs that onnet to the merge point. This takes O(n f) = O(l) time. 3. To an identify unsupported merge point, we need to examine at worst all merge points present at the time of the traversal stall. There are at most p merge points present. Eah time this is done we have one less transation to onsider, so the total omplexity of this step is O(n p), whih is (l p ). f 4. One the yle is identied, the slide operation an be implement by a delete and an insert of the network. This is take onstant time for eah yle. Sine resolving eah yle results at least one symbol being un-reahable (the symbol that is moved by the slide operation), there an at least be O(l) yle resolution. 5. Merging the network into a sequene take O(l) time. The total time omplexity is thus O(l p ), or O(n p), where p is the number of nodes in f the database system. 21

22 6 Conlusions In typial pratie of data warehouse, the warehouse data is kept in a separate site from the operation data. Changes to the operation data to propagated to the warehouse site periodially, usually by shipping the new log entries in the operation site. When the operation site is a parallel DBMS, it is neessary to arrange the log entries into an oherent order for the warehouse data to maintain onsisteny and integrity. This paper solves the problem by presenting a simple method for onstruting a global transation order out of a set of loal logs of a parallel or distributed system. In this paper, we present a simple mehanism that determines the order of transations by examining only the relative position of their vote and ommit entries. We show that if there is a serialization requirement of transation A before transation B, then the relative pattern C A?V B?C B must exist in some loal log. Furthermore, when suh a pattern exist, it is always safe to order A before B. Based on this mehanism, we present a method that eiently onstruts a global transation order. Our method uses the position of ommit symbols to denote impliitly the transation order. It rst onnets the vote and ommit symbols of loal log les into a network. Dierent logs are onneted at the merge points. The logs are then traversed to detet inonsisteny in the ordering of ommit symbols in dierent log. The traversal of logs must synhronize at merge point, and ordering inonsisteny an thereby be deteted. Inonsisteny in transation ordering is resolution using a very simple slide operation, whih always moves a ommit symbol bakward in its log, to the position immediately before a oniting ommit symbol. Our method has the following features. First, it examines only the vote and ommit entries of transations, but not the data aessing entries. Seond, for vote or ommit entries, only their relative positions and their transation ID (to identify from whih transation an entry omes) requires attention. Other information reorded in the vote or ommit entry need not be examined. Finally, our method has low omplexity. For a set of loal logs with l totally, only O(l) ost is required both in terms of time and spae. In summary, the 22

23 method we presented is oneptually simple, only requires aessing minimal information, and an leads to eient implementations. Referenes [BGHJ92] A. Bhide, A. Goyal, H. Hsiao, and A. Jhingran. An eient sheme for providing high availability. In Proeedings of 1992 ACM SIGMOD Conferene, San Diego, [BHG87] P. A. Bernstein, V. Hadzilaos, and N. Goodman. Conurreny Control and Reovery in Database Systems. Addison-Wesley, [CD97] S. Chaudhuri and U. Dayal. An overview of data warehousing and olap tehnology. ACM SIGMOD Reord, 26(1):65{74, [GR93] J. Gray and Andreas Reuter. Transation Proessing: Conepts and Tehniques. Morgan Kaufmann, [Gra78] J. Gray. Notes on database operating systems. Operating Systems: An Advanes Course, [Hsi94] H. Hsiao. Virtual timestamp for poin-in-time reovery in db2 pe. IBM DB2 Parallel Edition design doument, [Inm96] W. Inmon. The data warehous and data mining. Communiations of the ACM, Nov [MHLP91] C. Mohen, D. Haderle, B. Linsay, and H. Pirahesh. Aries: a transation reovery method supporting ne-granularity loking and partial rollbaks using writeahead logging. ACM, TODS, 17, [MLO86] C. Mohan, B. Lindsay, and R. Obermark. Transation management in the R distributed database management system. ACM Transation on Database Systems, 11(4):378{96, Deember

24 [SC90] J. Stamos and F. Cristian. A low-ost atomi ommit protool. In Proeedings of Ninth Symposium on Reliable Distributed Systems, pages 66{75. IEEE, Otober