Consistency Maintenance Based on the Mark & Retrace Technique in Groupware Systems

Consistency Maintenance Based on the Mark & Retrace Technique in Groupware Systems Ning Gu, Jiang-Ming Yang and Qi-Wei Zhang Fudan University Jiang-Ming Yang

OUTLINE • Introduction & Motivation • Address Space Transformation • Mark & Retrace Technique • Efficiency Analysis • Undo Supported • Related Works & Conclusions Fudan University, Cooperative Information and Systems Laboratory

INTRODUCTION • What’s Group Editors? • Most commonly used groupware applications. • Multiple users’ participation • User can edit and modify shared data objects, such as word, graphics, and media documents, using a computer network. • Techniques for building group editors have been widely applied and practiced. • A Powerful research vehicles in exploring solution to consistency problems. Fudan University, Cooperative Information and Systems Laboratory

MOTIVATION & CHALLENGE • In the past decade, OT method has been gradually improved. • Control Algorithms • OT Functions • An OT algorithm which can maintains the CCI model and solved TP2 puzzle and false-tie (ERV) puzzle will be very intricate. Fudan University, Cooperative Information and Systems Laboratory

ADDRESS SPACE TRANSFORMATION • Example 1: • Initial document is “abd”. • O4 and O5 are two concurrent operations. • In OT Technique, due to the existence of concurrent operation O4, O5 shall be transformed to Insert [“c”, 2] before execution on site U1. Fudan University, Cooperative Information and Systems Laboratory

ADDRESS SPACE TRANSFORMATION Fudan University, Cooperative Information and Systems Laboratory

THE STRUCTURE OF MARK & RETRACE • A document is a liner structure composed of characters. • Each character may have several operations targeting itself while each operation targets only one character. • Add the effective / ineffective mark information to every node in the liner structure. • The address space can be expressed as the effective character nodes from left to right. Fudan University, Cooperative Information and Systems Laboratory

THE RETRACING PROCEDURE • The goal of the Retracing procedure is to retrace the address space to the state at a given timestamp SV. • Consider the following four situations. • if SVOins ≥ SV , then this node is marked ineffective; • if SVOins ≤ SV and there is no Delete targeting this character node, then this node is marked effective; • if SVOins ≤ SV and SVOdel ≥ SV , then this node is marked effective; • if SVOins ≤ SV but SVOdel ≤ SV , then this node is marked ineffective. Fudan University, Cooperative Information and Systems Laboratory

THE CONTROL ALGORITHM • Control-Algorithm (DocS, O), execute O on DocS. • Retracing(DocS, SVO) • Execute the operation O, and attach the operation with its timestamp to the character node. • SVS[R] ⇐ SVS[R] + 1 • Retracing(DocS, SVS) Fudan University, Cooperative Information and Systems Laboratory

EXAMPLE 1: • Effective node & ineffective node • User U1 intends to execute operation Insert[“c”, 3] with timestamp <1,1,2>. • User’s view is “ad”. Fudan University, Cooperative Information and Systems Laboratory

EXAMPLE 1: • First, retrace the document to the state at the time of timestamp <1,1,2>. • Conceal the effect of operation Delete[“b”, 2]. • Character node “b” become “Effective”. • User’s view is “abd”. Fudan University, Cooperative Information and Systems Laboratory

EXAMPLE 1: • The document’s state at the time of timestamp <1,1,2> is the state at the time of operation’s ( Insert [“c”, 3] ) generation. • Operation Insert [“c”, 3] can be executed directly in this new address space. Fudan University, Cooperative Information and Systems Laboratory

EXAMPLE 1: • The State Vector of the local site has been adjusted to <2,1,2> after the execution is finished. • And then it retraces to the view “acd” of new State Vector by restoring the effect of operation Delete[“b”, 2] and adding the execution effect of the new operation Insert[“c”, 3]. Fudan University, Cooperative Information and Systems Laboratory

OPERATION EXECUTION • The Delete operation’s execution is simple. The process is to find the corresponding character node, attach the operation on the character node and then perform the Retracing procedure to give this node a correct effective/ineffective mark. • The Insert is to search for an Inserting position in the address space, which is corresponding to a range in document between two effective character nodes. There may exist some other ineffective character nodes in this range. • A Range-Scan process to determine the right-and-left relation between the new Insert and these ineffective character nodes and then find an accurate position. Fudan University, Cooperative Information and Systems Laboratory

OPERATION EXECUTION • To realize the comparability between two Insert operations, define a TOrder function: • Given two character nodes CNaand CNb. The attached operations are generated at site a and site b, and are timestamped by SVaand SVb. • TOrder(CNa) < TOrder(CNb), iff sum(SVa) < sum(SVb) a < b, when sum(SVa) = sum(SVb) Where sum(SV) = Fudan University, Cooperative Information and Systems Laboratory

OPERATION EXECUTION • INSERT RULES: • 1) The new character node should be inserted in the range. • 2) If there is a existed character node CN, the insert operation of CN is causally before CNnew, CNnew should be inserted on the left of CN. • 3) If there is a existed character node CN1, TOrder(CNnew)<TOrder(CN1) and CN1 do not meets the rule 4, CNnew should be insert on the left of CN1. • 4) Otherwise, if there is two existed character node CN1 and CN2, CN2 is on the right of CN1, CNnew should be inserted on the right of CN2 when : TOrder(CNnew)<TOrder(CN1) TOrder(CNnew)>TOrder(CN2) CN2 is causally before CN1 Fudan University, Cooperative Information and Systems Laboratory

OPERATION EXECUTION • INSERT EXECUTION: • Scan the range from left to right. • If there is a existed character node meets the rule 2, return this position immediately. • If there is a existed character node meets the rule 3, record this position into a variable P. • If the record meets the rule 4, clean the record. Fudan University, Cooperative Information and Systems Laboratory

CAUSALITY PRESERVATION • To achieve causality preservation, we only need to ensure that every remote operation is causally-ready before its execution, which we call execution condition. • It should be noted that even if causality is preserved, the execution order of the operations would still be different because of their different orders of arrival at different sites. Fudan University, Cooperative Information and Systems Laboratory

CONVERGENCE • The Proof： • 2 operations • Same Scan-Ranges • Different Scan-Ranges • n operations Fudan University, Cooperative Information and Systems Laboratory

INTENTION PRESERVATION • Since a Insert operation can find the correct scan-range and a Delete operation can find its corresponding character node at any sites and they do not interfere with other operations, those satisfy operations’ definition. • However, there are still some arguments about the proof of achieving intention preservation, we plan to present more about intention’s formal definition and the complete proof in the next future. Fudan University, Cooperative Information and Systems Laboratory

OPERATION EXECUTION EFFICIENCY • Reorganize the character nodes to a Red-Black Tree and ensure the result of pre-order traversal of the Black-Red tree is the original linear order. • Every node of the tree saves two additional data —the two numbers of the effective character nodes of left sub-tree and right sub-tree. • The amortized costs of Insert and Delete are both O(logn). Fudan University, Cooperative Information and Systems Laboratory

EFFICIENCY OPTIMIZATION OF RETRACING • Use the “Garbage Collection” method to handle a operation list containing the operations which haven’t been executed at some sites. • Suppose the length of operation list is h which means we need to check and change at most h character nodes’ effective/ineffective mark during Retracting process. • In the second Retracing process, we restore the changed nodes instead of the Retracing process. After then, we only need to deal with the targeting character node of the new operation. Fudan University, Cooperative Information and Systems Laboratory

UNDO SUPPORTED • Given an Undo operation O2, Undo[O1], in which O1’s target position is P1 and timestamped by SVO1. The execution process can be performed as follow. • Retrace the address space to the state at the time SVO1; • count to the P1th effective character node and attach O2 on it. • Then the second Retracing process takes this new Undo into consideration and gives this node the correct effective / ineffective mark. • Append a Delete counter to every character node to realize the Multi-version / Single-display strategy. Fudan University, Cooperative Information and Systems Laboratory

RELATED WORKS • The initial concept of Mark & Retrace was proposed early in Document Mark Technique but was not able to solve the dOPT puzzle. • dOPT, adOPTed and GOTO cannot fully satisfy TP2. • NICE and SOCT3/4 is not able to resolve the false-tie (ERV) puzzle. • GOT fail in the case of complicated false-tie (ERV) scenarios. • Imine et al. tried to support TP2 by expanding IT function but fails in solving dOPT puzzle. • A solution of false-tie (ERV) has been realized in Co-Word system, it is still not published. • Li et al. also reported a solution and gave the proof. Fudan University, Cooperative Information and Systems Laboratory

CONCLUSIONS • In this paper we propose a strategy which can maintain CCI model and is different from OT. It does not ensure the operation’s execution correctness by modifying the operation’s address but by transforming the address space of the document. • Since the Mark & Retrace processes do not affect the relative position (left or right) between characters, it is easier to maintain operations’ order. It can not only achieve all the consistency criteria, but can support any Undo as well. Fudan University, Cooperative Information and Systems Laboratory

Thanks! Fudan University, Cooperative Information and Systems Laboratory

Consistency Maintenance Based on the Mark & Retrace Technique in Groupware Systems