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Cutpaste string operation for collaborative groupware applications
Technology, Innovation and Education volume 1, Article number: 2 (2015)
Abstract
Operational transformation (OT) is a concurrency control approach in multiuser collaborative groupware system. With OT, local operations do not delay and shared document could be edited by users at any time. Most of OT algorithms cannot be formally proved. Till date only two characterwise primitive operations Insert and Delete are proposed and these operations have time complexity of the order of O(H^{2}) where H is the history buffer of operations. In this paper, a new algorithm for cutpaste string operation is proposed with time complexity and space complexity of the order of O(H). It reduces the time and space consumption in performing composite string operation—CutPaste. The proposed algorithm also handles overlapping and splitting of operations. A modified algorithm GSMRITFDD is also proposed that has removed all faults of existing ITDD algorithm.
Background
Groupware system is a multiple user system in which the operations of each user must quickly be propagated to all other shared users (e.g., multiplayer game, realtime computer conferencing).
Groupware system requires sharing of data, fine granularity, concurrency control and fast response times. Consistency and high local responsiveness are specific requirements for multiuser systems (Ellis and Gibbs 1989; Sun et al. 1998). Concurrency control protocols are used to remove inconsistency in the multiuser transactions systems such as Relational Databases, Distributed Systems and Groupware Systems.
Theorem 1
In a consistent shared environment which has replicated data after execution of all operations all have same data.
Traditional concurrency control methods such as Locking and Reversible Execution may cause the loss of some user interaction results. These methods are not suitable for distributed interactive applications which require fast local response satisfying user intentions, intention consistency and convergence. In past 15 years, OT is an acceptable method for consistency and concurrency maintenance in multiuser group editors such as group editors and Google Wave1 (Davis et al. 2002; Ellis and Gibbs 1989; Sun et al. 1998a, b). When compared to other concurrency control methods, OT achieves convergence, causality and intention preservation without sacrificing local responsiveness and concurrent work (Sun et al. 1998a). OT allows users to edit any part of the data which is shared by other users (Bentley and Dourish 1995).
Review of OT algorithms
In last 25 years of OT algorithms, there are two main challenges in OT: First, most of algorithms require an informal condition known as “Intention Preservation” and their correctness cannot be formally proved. Second: except for (Ressel et al. 1996), all existing OT algorithms only support two characterbased operations called insert and delete.
The proposed work studied major OT algorithms (Table 1) including Distributed Operation Transformation (dOPT) algorithm (Ellis and 1989), the Generic Operational Transformation (GOT) algorithm (Sun et al. 1998), GOT Optimized (GOTO) algorithm (Sun et al. 1998), State Difference Transformation (SDT) algorithm (Li and Li 2007), SCOT2 (Suleiman et al. 1998), SCOT 3/4 algorithm (Vidot et al. 2000), Adopted (adOPTed) algorithm (Ressel et al. 1996), AdmissibilityBased Transformation (ABT) algorithm (Li and Li 2010), ABTUndo (ABTU) Algorithm (Li and Li 2007), admissibilitybased sequence transformation (ABST) (Shao et al. 2010a, b), and AdmissibilityBased Transformation with Strings (ABTS) algorithm (Shao et al. 2009).
The ABT (Li and Li 2007) introduces a correctness criterion called admissibility preservation, in which correctness of admissibilitybased transformation (ABT) functions has formally proved. ABTU arranges the operation history in total effectsrelation order and improves the time complexity to O(IHI). In the available literature, only GOT, GOTO and ABTS algorithms support stringwise operations. The time complexity of GOT and GOTO algorithms are O(H^{2}) but time complexity of ABTS is only O(H). So due to less time complexity, ABTS is better stringbased OT algorithm as compared to GOT and GOTO. The proposed work is focused on stringbased OT algorithm which is based on ABT framework.
OT framework
Most of existing OT algorithms have developed under a wellaccepted framework with a condition that algorithm cannot be formally proved. In addition, they generally support two characterbased primitive operations like insert and delete in a linear data structure. Only three algorithms called as GOT, GOTO and ABTS support primitive string operations. This research paper proposes a new novel OT algorithm for composite string operation CutPaste with existing primitive operations.
The insert(p, s) and delete(p, s), insert and delete a string ‘s’ at position ‘p’ in the shared data, respectively. The proposed work has introduced a new composite string operation CutPaste (p1, s, p2) which cut from position ‘p1’ and paste it at position ‘p2’ in shared data with less time complexity.
In OT, shared data are like a linear string ‘s’ of atomic characters in which objects are referred by their positions ‘p’ starting from zero in the string and consider two only primitive string operations, called, insert(p, s) and delete(p, s). At site, there exists a common definition state ‘s’ for all operations. The standard notations are summarized in Table 2 (Shao et al. 2009).
Methods
The proposed algorithm for cutpaste string composite operation ITCutPaste (Inclusive Transformation of CutPaste) is based on inclusive transformation of operational transformation. The algorithm ABTS (Shao et al. 2009), already contains ITII (Inclusive Transformation of Insert–Insert)/ITID (Inclusive Transformation of Insert–Delete)/ITDD (Inclusive Transformation of Delete–Delete)/ITDI (Inclusive Transformation of Delete–Insert) algorithms for transformation of insert and delete string operations. So to perform cutpaste operation, first the substring ‘s’ get deleted from p by operation delete(s, p) and then ‘s’ get inserted at position q by operation insert(s, q). Here, delete(s, p) and insert(s, q) are independent operations. At all sharing sites, transformation functions corresponding to both delete(p, s) and insert(q, s) get called which results in increase in the time complexity.
This research work proposes a single transformation algorithm for composite string operation cutpaste. So all sites require only single transformation function for cutpaste operation. The time complexity of transformation function ITCutPaste for cutpaste operation is same as transformation function for insert or delete ITDI/ITID. It is based on inclusive transformation and ABT Framework so it can be formally proved.
Type of operations
ITCutPaste consists of operations o1, o2 as input and o1′ as output. Operations o1, o2 and o1′ may be string or character operations which operate on shared data in multiuser groupware collaborative applications like group editors.
Definition 1
o1 and o2 are contextually equivalent o1o2, o1Uo2 and if input is o1 and output then output should be o2→o1′.
Design and analysis of algorithms
ITCutPaste consists many subalgorithms ITDCp (Inclusive Transformation of Deletion with CutPaste), ITICp (Inclusive Transformation of Insertion with CutPaste), ITCpI (Inclusive Transformation of CutPaste with Insertion), and ITCpD (Inclusive Transformation of CutPaste with Deletion). The proposed algorithm satisfies causality and admissibility preservation.
Definition 2
If we have exec(o_{i}), then all exec(o_{i−1}) must be completed then only oi satisfies causality.
Definition 3
If o1Uo2 then IT(o1,o2) satisfies admissibility. It does not have inconsistent order at shared environment.
Theorem 2
Let H is admissible history of operation which satisfies causality. Also, sq is a sequence of operations and sq^{~} _{~}H. Then, if o is executed in state s, we have exec(s, H). There should be sq′^{~}~ (sq.o) and sq′ must be consistent.
The ITCutPaste(o1, o2) transforms o1 with another operation o2 with output of this function is o1′. The precondition of ITCutPaste(o1, o2) is o1Uo2 and the postcondition is o2→o1′. The following “Type of operations” presented the algorithm ITDCp and “Design and analysis of algorithms” presented the algorithm ITICp. In algorithm ITCutPaste if o1 operation type is insert and o2 operation type is CutPaste then ITICp is called and if o1 operation type is delete and o2 operation type is CutPaste then ITDCp is called. If o1 operation type is CutPaste and o2 operation type is insert, then ITCpI is called and if o1 operation type is CutPaste and o2 operation type is delete then ITCpD is called.
Algorithm ITDCp
Algorithm ITDCp takes as parameters o1 and o2 and return o1′. Here, o1 is deletion operation and o2 is CutPaste operation. Here, precondition is o1Uo2 and postcondition is o2→o1′. GSMRITFDD(o1, o2) used in Algorithm ITDCp is transformation algorithm to transform o1 (delete) and o2 (delete) operations.
Algorithm ITICp
Algorithm ITICp takes as parameters o1 and o2 and return o1′. Here, o1 is insertion operation and o2 is CutPaste operation. Here, precondition is o1Uo2 and postcondition is o2→o1′.
Algorithm GSMRITFDD
The new algorithm GSMRITFDD is proposed that removed all faults of existing ITDD (Shao et al. 2009) for inclusive transformation of two deletions and work well in all possible cases. It needs to consider the following cases regarding the relations between the two target regions, R1 = s [o1.pos :(o1.str + o1.pos)] and R2 = s[o2.pos:(o2.pos + o2.str)]
Consider the following cases regarding the relations between the two target regions, R2 = s [o2.pos: (o2.pos + lo2.strl)] and R1 = s [o1.pos: (lo1.strl + o1.pos)].

1.
(By line9) When R2 is completely on the right of R1. In this case, Deletion of R2 does not affect o1 and hence o1 is returned asis.

2.
(By line7) If R1 is on the right of R2. In this case, after R2 is deleted, we shift o1′.pos by 1o2.strl characters to the left to get transformed string operation o1′.

3.
(By line16) R1 is included in R2. In this case, after o2 is executed, R1 is already deleted. So there is no longer need to execute o1. That is why it returns an empty operation ¢.

4.
(By line13) When R2 partially overlaps with R1 around the left border of R1. After o2 is executed, the left part of R1 is already deleted. Hence, in this case, we need to reset o1.pos so that it will start from (o2.pos). So o1.str only needs to include the right part that is not deleted by o2, starting from (o2.pos + lo2.strl)—o1.pos in the original o1.str.

5.
(By line11) When R2 partially overlaps with R1 around the right border of R1. In this case, this is similar to case (4). After o2 is executed, o1 only needs to delete the left part that is not deleted by o2.

6.
(By line18) R2 is included in R1. The deletion of R2 within R1 divides R1 into three parts, among which the middle overlapping part is already deleted by o2. Hence, o1 must be split into two suboperations that delete the two remaining substrings left and right, respectively.
Result and discussion
We have implemented ABTS and ITCutPaste in lab using Qualnet and ASP.Net software in multiuser environment. The Benchmark Dataset of online Group Editor is used to verify it. We have implemented existing IT algorithm ABTS and our proposed algorithm ITCutPaste to perform string composite operation cutpaste. We experimentally conclude that ABTS consumed more time by a factor in multiple of H as compared to ITCutPaste. ITCutPaste satisfies causality preservation and admissibility preservation.
Correctness proof
If we use ABTS to transform cutpaste string operation and if o1 = “insert” and o2 = “CutPaste”, then we need ITID and ITII both for it. ITID applies for all o2.pos ≤ (o1.pos + o1.str) and ITII for all o2.pos ≤ o1.pos. Now, ITICp apply only for (o1.pos > o2.pos && o1.pos < p). Time complexity of ITII, ITID and ITICp is of same order. Since ITICp is for less number of operations in less range, so it consumes less or equal time as compared to ITID/ITII. ITICp could not consume more time as compared to ABTS(ITID + ITII) to operate same cutpaste string operation.
If we use ABTS to transform cutpaste string operation and if o1 = “delete” and o2 = “CutPaste”, then we need ITDI and ITDD both for it. ITDI applies for all o2.pos < (o1.pos + o1.str) and ITDD for all o1.pos >= (o2.pos + o2.str). Now, ITDCp apply only for (o1.pos > o2.pos && o1.pos < p). Time complexity of ITDD, ITDI and ITDCp is of same order. Since ITDCp is for less number of operations in less range, so it consumes less or equal time as compared to ITDI/ITDD. ITDCp could not consume more time as compared to ABTS (ITDI +ITDD) to operate same cutpaste string operation.
Similarly, time complexity of ITCpD is of same order of ITDD/ITID. But to transform o2 = “delete” and o1 = “CutPaste” in case of ABTS, both ITDD and ITID need to get called for greater range of operations but for ITCutPaste only ITCpD is sufficient for same or less range of operations as compared to either ITDD or ITID of ABTS. Also, time complexity of ITCpI is of same order of ITDI/ITII. But to transform o2 = “insert” and o1 = “CutPaste” in case of ABTS, both ITDI and ITII need to get called but for ITCutPaste only ITCpI is sufficient for same or less range of operations as compared to either ITDI or ITII of ABTS. So ITCutPaste is more efficient.
ABTS time consumption for string operation cutpaste is if 2 O(H) then ITCutPaste consumes only O(H) time and space complexity.
A graphical representation of ABTS and ITCutPaste time complexity for various cases is shown below.
Conclusion
OT is the best method for concurrency and consistency control in multiuser groupware systems. Most of OT algorithms support character operations and very few support string primitive operations like insert and delete. The proposed algorithm ITCutPaste for string composite operation cutpaste works well in all conditions and handles overlapping of operations. It is based on ABT framework and can be formally proved. It has time complexity and space complexity O(H) (where H is history buffer) similar to ABTS. The proposed algorithm GSMRITFDD has removed all faults of existing ITDD for inclusive transformation of two deletions and works well in all possible cases.
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Authors’ contributions
SK made substantial contributions to conception and design, acquisition of data, and analysis and interpretation of data; has been involved in drafting the manuscript or revising it critically for important intellectual content; has given final approval of the version to be published, and agrees to be accountable for all aspects of the work in ensuring that questions related to the accuracy or integrity of any part of the work are appropriately investigated and resolved. AK provided full guidance and support in all of the above works. Both authors read and approved the final manuscript.
Competing interests
The authors declare that they have no competing interests.
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Keywords
 Operational Transformation Algorithms
 Concurrency control
 Distributed systems
 Collaborative system
 Groupware system