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The authors positively addressed all the (minor) comments from the previous round of review. The paper is now ready for publication.
[# PeerJ Staff Note - this decision was reviewed and approved by Massimiliano Fasi, a PeerJ Section Editor covering this Section #]
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This revision fulfills all the requirements of the comments suggested in the previous review. Accordingly, I recommend accepting this paper for publication.
The reviewers appreciated the work and all agree on the novelty and soundness of the proposed approach. The reviewers highlighted only some minor issues, mainly related to the paper presentation. I will then recommend a light revision of the paper before publication. In particular, the following points should be addressed:
- Fix typos and unclear parts as suggested by the reviewers.
- Better describe the theoretical results (proofs and algorithms), with examples if possible.
- Highlight the practical implications of the proposed solution (e.g., in the context of networks and data centers).
- Better compare with the related work.
**PeerJ Staff Note:** Please ensure that all review, editorial, and staff comments are addressed in a response letter and that any edits or clarifications mentioned in the letter are also inserted into the revised manuscript where appropriate.
The authors studied a node-disjoint path construction algorithm in the folded divide-and-swap cube. The topic is interesting. The algorithms and experiments are thoroughly done.
The authors have conducted sufficient experiments.
The findings are obtained by sufficient proof and algorithms.
There are some language errors as follows.
1. On page 2, line -11, ", If the rightmost" should be ", if the rightmost".
2. On page 3, Table 1: The table title should be put upon the table. Other tables need similar modifications.
3. On page 6, line 10, "The detail algorithm" should be "The detailed algorithm".
In distributed computing systems, node-disjoint paths are essential for fault-tolerant communication between different nodes. By using multiple disjoint paths, supercomputers can continue to function properly even when some nodes become unavailable due to hardware failures or network issues. This manuscript investigates the problem of constructing node-disjoint paths in the folded divide-and-swap cube (FDSCₙ), a hypercube variant proposed for data center networks. The authors present two key algorithms:
1. QP Algorithm: Constructs a path between any two distinct nodes in FDSCₙ by leveraging structural properties.
2. O2OMain Algorithm: Builds d+2 node-disjoint paths between any two nodes, with a theoretical maximum path length of n+9.
Overall, the article is well organized, and its presentation is good. However, some minor issues still need to be improved:
1. Line 14 Page 3
"which has many superior properties than the hypercube."-> "which has many superior properties to the hypercube."
2. Line 65 Page 4
"For any integers"-> "For any integers"
3. Line 354 Page 12
"Hence, there exists 4 disjoint paths between µ and ν."->"Hence, there exist 4 disjoint paths between µ and ν."
4. Line 363 Page 12
"Hence, there exists 4 disjoint paths between µ and ν."->"Hence, there exist 4 disjoint paths between µ and ν."
The paper is acceptable pending these improvements.
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I have carefully reviewed the manuscript. Overall, the paper presents an interesting exploration of the disjoint path problem in the newly proposed hypercube variant, FDSCn. The topic is relevant to the field of interconnection networks, and the authors' efforts to develop algorithms for constructing disjoint paths are commendable. Disjoint paths play critical roles in interconnection networks. They ensure communication remains viable when some network links/nodes fail. If one path is disrupted, others (disjoint in structure) bypass faults, maintaining data transmission.
The core work, including the proposal of algorithms like QP and O2OMain, as well as theoretical and experimental efforts, is valuable. However, several minor issues need to be addressed to enhance the paper's quality. See the detailed comments below.
Line 21, Page 3: “Super computers”-> ”Supercomputers”
Line 23, 24, Page 3: “super computer”-> ”supercomputer”
Line 38, Page 3: “super computers”->” supercomputers”
Line 32, Page 3: ”Let S⊆V(G). Then N(S)={v∈V(G)∣μ∈S,(v,μ)∈E(G) and μ"∉" V(S)}”->
”Let S⊆V(G). Then N(S)={v∈V(G)∣μ∈S,(v, μ)∈E(G) and v"∉S" }”
Line 110, Page 5: “Any two distinct mudules in D”-> ”Any two distinct modules in D”
Line 124, Page 6:”B_i=x_(2^(k-1)+1) x_(2^(k-1)+2)...x_(2^k ) is module address of D_(B_i )”->”B_i=x_(2^(k-1)+1) x_(2^(k-1)+2)...x_(2^k ) is the module address of D_(B_i )”
Table 2, Page 6: ”where µ lies in”-> ”where µ lies”
Line 143, Page 7: ”We give a algorithm to get the”-> ”We give an algorithm to get the”
Line 158, Page 7: ”then algorithm MinCommonDimension return 3.”-> ”then algorithm MinCommonDimension returns 3.”
Line 171, Page 8: ”The detail algorithm is shown as below”-> ”The detailed algorithm is shown as below”
Line 330, Page 11:” then algorithm 5 only need to construct 3”-> ”, then algorithm 5 only needs to construct 3”
Line 430, Page 14: ”then algorithm 7 need to construct 4 disjoint paths in FDSC4”-> ”then algorithm 7 needs to construct 4 disjoint paths in FDSC4”
Line 496, Page 18: ”We give the detail algorithm as follows.”-> ”We give the detailed algorithm as follows.”
Line 655, Page 22: ”As a newly proposed hypercube variants,”-> ”As a newly proposed hypercube variant,”
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Summary: This paper introduces new algorithms to build multiple independent communication paths in a special type of computer network structure called the folded divide-and-swap cube (FD-SCn). Such paths, called node-disjoint paths, are important because they allow information to flow even if some parts of the network fail. The authors design methods to guarantee that between any two computers (nodes) in the network, there will always be d + 2 separate paths, and each path is not too long (at most n + 9 steps). This makes the FDSCn a strong candidate for use in large data centers and supercomputers, where reliability and efficiency are crucial.
The paper is technically solid, but it is currently very dense and theoretical. With improved clarity, illustrative examples, and a stronger discussion of applications, it would be a valuable contribution.
Comments:
• In the abstract: “has many superior properties than the hypercube” → “has many superior properties compared to the hypercube”.
• Some proofs and algorithm descriptions are very dense; additional explanations or illustrative examples would help readers follow more easily.
• Explain why FDSCn is particularly interesting and highlight practical implications for interconnection networks and data centers.
• Although the related work cites many topologies (hypercubes, BCube, dcell, dragonfly, etc.), the comparison is brief. Expanding on how your work differs from and improves on these prior studies would strengthen the contribution.
• The results are purely theoretical. Including simulations, empirical validation, or at least a discussion of computational experiments for small n would strengthen the article.
• Add experiments or simulations to show practical performance (e.g., average path length, computational overhead).
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