Minimizing Interference-to-Signal Ratios in Multi-Cell Telecommunication Networks

Round 1

Reviewer 1 Report

The paper is well written and the topic is interesting, the applications of such a procedure presented by the authors are important. 

Besides supporting the acceptance of the paper I have some concern regarding some points you may think about. 

1. It seems that the objective function Eq. (2) of the optimization problem of minimizing total inference increases montonically with the number of clusters, at least according to Fig. 1. (c). I.e. it takes its minimum value when the number of clusters is one. Thus, the motivation behind clustering does not directly appear through the objective function of the optimizaton problem solved by a clustering procedure, but one can expect to get better objective function values by properly optimize the number of clusters and the cluster structure. Although when presenting the results the Authors do not highlight that what exactly (and measurably) improved in the user-base station allocation process using clusters compared to e.g. greedy allocation (assigning the user to the closest available station). I accept that we get a better solution for the cell-edge problem using clustering, but better than what, and how exactly?   

2. Eq. (4) should be defined properly. I think the sum of vectors are taken elementwise as usual, but may be worth to clarify.

3. The experimental setup, seems a bit unrealistic, at least to me. In some places we may consider that the users are located uniformly at random. However I would have tried different distributions (like Poisson, some heavy-tailed, etc.) in case of the users.  Can it be assumed that the base stations are located uniformly (and randomly) in any case? Maybe, but a short discussion of the motivation (realities, assumptions) of the experimental setup would be useful. 

Author Response

Response to Reviewer 1 ---------------------- 1. The reviewer is correct. We have discussed the question in the revised version, see the paragraph entitled ``Engineering complexity'' in the introduction (in addition to the subsection of the same title in Section 3). 2. We have clarified this in the text surrounding eq. (4). 3. In the revision, we consider a case where the base-stations are uniformly distributed (Scenario 1), and a second case where the distribution of the base-stations is non-uniform (Scenario 2). These scenarios simulate an urban and a rural environment, respectively. Scenarios 1 and 2 are introduced at the beginning of Section 4.

Reviewer 2 Report

This paper presents a novel clustering algorithm for minimizing the interference-to-signal ratios in multi-cell telecommunication networks. The algorithm is based on a dot-product similarity measure between base-stations and a hierarchical clustering method that divides the problem into three subproblems. The paper claims that its algorithm is faster and more effective than the spectral clustering method, which is a common approach for this problem. The paper provides some theoretical analysis and simulation results to support its claims.

The paper is well-written and organized, and it addresses an important and challenging problem in wireless communication networks. The paper introduces a new similarity measure that captures the dynamic relations between base-stations and users, and it proposes a simple and deterministic algorithm that can handle large-scale networks. The paper also compares its algorithm with the spectral clustering method on synthetic instances, and shows that its algorithm typically provides higher quality solutions with lower complexity.

However, the paper also has some limitations and weaknesses that could be improved. For example:

- The paper does not provide any formal proof or guarantee for the optimality or approximation ratio of its algorithm. It also does not discuss the computational complexity of its algorithm in detail, or compare it with other existing methods.

- The paper does not consider any realistic scenarios or real-world data sets for its simulation experiments. It only uses randomly and uniformly generated placements of base-stations and users, which may not reflect the actual distribution and behavior of these agents in real networks.

- The paper does not address some practical issues or constraints that may affect the performance or applicability of its algorithm, such as the upper bound on the number of base-stations in each cluster, the frequency of updating the clustering solution, or the communication overhead between base-stations and users.

- The paper does not provide any clear motivation or justification for choosing the parameters or settings of its algorithm, such as the path attenuation exponent, the distance thresholds, or the number of clusters.

These limitations and weaknesses suggest that the paper could be further extended and refined to provide more rigorous and comprehensive evaluation of its algorithm, and to explore more realistic and diverse scenarios and applications for its problem.

My suggestions for improving this paper are:

- Provide some formal analysis or proof for the optimality or approximation ratio of the proposed algorithm, or at least some theoretical justification or intuition for why it works well.

- Conduct more extensive and realistic simulation experiments using real-world data sets or scenarios, such as those from existing wireless networks or benchmarks. Compare the proposed algorithm with other state-of-the-art methods on these data sets or scenarios, and report the statistical significance and robustness of the results.

- Discuss some practical issues or constraints that may affect the performance or applicability of the proposed algorithm, such as the upper bound on the number of base-stations in each cluster, the frequency of updating the clustering solution, or the communication overhead between base-stations and users. Explain how these issues or constraints can be addressed or overcome by the proposed algorithm, or what are the trade-offs or limitations involved.

- Provide some clear motivation or justification for choosing the parameters or settings of the proposed algorithm, such as the path attenuation exponent, the distance thresholds, or the number of clusters. Explain how these parameters or settings affect the quality and complexity of the solution, and how they can be tuned or optimized for different scenarios or applications.

The language quality of this paper is generally good and clear, but it could be improved by some minor editing and proofreading. For example:

- There are some typos and grammatical errors in the paper, such as "the two approaches are essentially equivalent with each other" (should be "to each other").

- There are some inconsistent or unclear notations and terminologies in the paper, such as using both "base-station" and "BS", or using both "cluster" and "cell" to refer to the same concept. It would be better to use one consistent term or notation throughout the paper, and define it clearly at the beginning.

- There are some sentences or paragraphs that are too long or complex, which may affect the readability and flow of the paper. It would be better to break them into shorter or simpler sentences or paragraphs, and use transitions or connectors to link them smoothly. 

Author Response

Problems discussed in the review -------------------------------- 1. "The paper does not provide any formal proof or guarantee for the optimality or approximation ratio of its algorithm." The reviwer is correct, we cannot provide any control on the quality of the solution of this NP-hard problem (see page 2). However, it should be instructive to the reviewer that there is no available algorithm with a known approximation ratio. 2. "It also does not discuss the computational complexity of its algorithm in detail, or compare it with other existing methods." This is discussed to some extent already in the submitted version. The theoretical bound for Algorithm 1 are discussed at the end of Section 3.2. In the revision, we have highlighted the theoretical bounds by introducing Lemma 1 in Section 3.2 and Lemma 2 in Section 3.3. See also the sub-section entitled "Analysis of the running times" (present already in the submitted version). 3. "The paper does not consider any realistic scenarios or real-world data sets for its simulation experiments. It only uses randomly and uniformly generated placements of base-stations and users, which may not reflect the actual distribution and behavior of these agents in real networks." We simulate two different scenarios in the revised version, the two main real-life examples discussed in [1] (urban and rural environments). 4. "The paper does not address some practical issues or constraints that may affect the performance or applicability of its algorithm, such as the upper bound on the number of base-stations in each cluster, the frequency of updating the clustering solution, or the communication overhead between base-stations and users." We agree with the reviewer that these are important questions. We partially touch on them at the end of section "Analysis of the running times" and in the third paragraph of Section 5. Naturally, these problems deserve further investigation. For example, we can imagine an additional balancing process on the number of towers between the clusters. All of these question fall beyond our scope for the current paper and we plan to revisit them in our upcoming work. 5. "The paper does not provide any clear motivation or justification for choosing the parameters or settings of its algorithm, such as the path attenuation exponent, the distance thresholds, or the number of clusters." See our response to problem 3. Suggestions proposed by the reviewer ------------------------------------ 1. "Provide some formal analysis or proof for the optimality or approximation ratio of the proposed algorithm, or at least some theoretical justification or intuition for why it works well." Discussed in our response to problem 1. 2. "Conduct more extensive and realistic simulation experiments using real-world data sets or scenarios, such as those from existing wireless networks or benchmarks. Compare the proposed algorithm with other state-of-the-art methods on these data sets or scenarios, and report the statistical significance and robustness of the results." Discussed in our response to problem 3. 3. "Discuss some practical issues or constraints that may affect the performance or applicability of the proposed algorithm, such as the upper bound on the number of base-stations in each cluster, the frequency of updating the clustering solution, or the communication overhead between base-stations and users. Explain how these issues or constraints can be addressed or overcome by the proposed algorithm, or what are the trade-offs or limitations involved." Discussed in our response to problem 4. 4. "Provide some clear motivation or justification for choosing the parameters or settings of the proposed algorithm, such as the path attenuation exponent, the distance thresholds, or the number of clusters. Explain how these parameters or settings affect the quality and complexity of the solution, and how they can be tuned or optimized for different scenarios or applications." Discussed in our response to problem 3. Language suggestions -------------------- 1. "There are some inconsistent or unclear notations and terminologies in the paper, such as using both "base-station" and "BS", or using both "cluster" and "cell" to refer to the same concept. It would be better to use one consistent term or notation throughout the paper, and define it clearly at the beginning." BS is simply an abbrevation for base-station (this is highlighted in the Abbrevations section at the end of the paper). "Cell" is a term used in the field of wireless networks, while "cluster" is the corresponding mathematical term in the graph theory problem.

Round 2

Reviewer 2 Report

The article has been improved in this round of revision. I think it can be accepted after minor language editing.

Minor editing of English language required.