Title: value: An efficient implementation for solving the all pairs minimax path problem in an undirected dense graph
Authors: value: Gangli Liu
Venue: ICLR 2025
Keywords: value: Minimax path problem
Longest-leg path distance
Min-Max-Jump distance
Widest path problem
Maximum capacity path problem
Bottleneck edge query problem
All points path distance
Floyd-Warshall algorithm
Minimum spanning tree

Abstract: value: We provide an efficient $ O(n^2) $ implementation for solving the all pairs minimax path problem or  widest path problem in an undirected dense graph. It is a code implementation of the Algorithm 4 (MMJ distance by Calculation and Copy) in a previous paper. The distance matrix is also called the all points path distance (APPD). We conducted experiments to test the implementation and algorithm, compared it with several other algorithms for solving the APPD matrix.  Result shows Algorithm 4 works good for solving the widest path or minimax path APPD matrix.  It can drastically improve the efficiency for computing the APPD matrix.  There are several theoretical outcomes which claim the APPD matrix can be solved accurately in $ O(n^2) $ . However, they are impractical because there is no code implementation of these algorithms. It seems Algorithm 4 is the first algorithm that has an actual code implementation for solving the APPD matrix of minimax path or widest path problem in $ O(n^2) $, in an undirected dense graph.


Review discussion:
Judging from the manuscript, this is the first implementation for $O(n^2)$ time algorithm for the all pairs minimax path problem. Because this algorithm works for any graph including dense graph (where $m=\Theta(n^2)$), this is actually an optimal algorithm.
The most prominent weakness of this work is that it only provides an implementation of the existing method of the previous paper of Liu (arXiv 2023). I think the implementation itself can be considered as a significant contribution when the original algorithm has some difficulties in implementing and they are tackled by some novel or dedicated techniques.
However, the implemented algorithm (Figure 1(a)) is much simpler that seems to be easily implemented, and actually it is implemented by short Python codes (Figure 1(b)). We do not find any implementation techniques in Section 3; Section 3 consists of just an explanation for the existing method of Liu. This means that obtaining simple algorithm that is easy for implement has already been done in the previous work.
Thus, I think this is not a significant contribution.
Another weakness of this work is that it is never compared empirically with the existing (and traditional) O(n^2) algorithm. In the conclusion, the authors claim that the SLINK algorithm of Sibson (1973) is difficult to implement by quoting the conversation with other people.
However, we easily find some SLINK implementations such as https://github.com/battuzz/slink and https://github.com/jackyust/SLINK_CLINK .
Moreover, the paper of Sibson also has a FORTRAN implementation of his algorithm.
Thus, it is questionable that the SLINK algorithm is hard to implement.
At least, the authors should try to implement SLINK and compare it with the proposed implementation.
Minor comments:
- The citations should be enclosed with brackets. Maybe you use \citet{...} instead of \citep{...}, don't you?
- Tables 1 and 2 are significantly wider than the paper width; please fit these tables into the paper width.
Since the APPD matrix contains O(n^2) elements, explicitly computing APPD matrix in O(n^2) time is an optimal algorithm.
Thus, I want to consider a variant of this problem: given a graph $G$ with $n$ vertices and $m$ edges, we preprocess $G$ to build a data structure $D$ that can answer the minimax path distance of any vertex pair in reasonable time. For relatively dense graphs, where $m=o(n^2)$ and $m=\omega(n)$, we can expect to lower the preprocessing time or space requirement below $n^2$ at the cost of query time of $D$. Do you know any existing works for this problem?
No ethics review needed.
Question:
"Another weakness of this work is that it is never compared empirically with the existing (and traditional) O(n^2) algorithm."
Response:
Although Dr. Murphy indicated the SLINK algorithm can be revised to solve the APPD matrix in $O(n^2)$ time. I do NOT agree with him about this opinion. I do agree with him that there is no code implementation to solve the APPD matrix in $O(n^2)$ time before this paper. If you agree with Dr. Murphy that the SLINK algorithm can be revised to solve the APPD matrix in $O(n^2)$ time. Please provide your code so that we can test it.
In simple words, there is no other existing (and traditional) O(n^2) code implementation to be compared with, the implementation introduced in this paper is the first and the only one by far.
the problem is well motivated in general.
while the problem is well motivated, finding an implementation for the algorithm is not very well motivated. It seems that no implementation existed before because the algorithms were not very efficient, and the algorithm of Liu is quite simple and efficient. The mere fact of coding that algorithm up is a simple classroom exercise it seems. If there are techniques used for going from the pseucode to the implementation, the authors have not described them, and it seems from the code that there are no such techniques.
Besides the above fundamental point, the write up could be polished, there are several grammatical mistakes.
abstract: "it is a code implementation of..." -> " this paper is a code implementation of the minimax path algorithm in Liu".
line 18:: works good -> works well.
line 106:: the sense -> the sign
in the related work it is good to note if there are any other papers like your paper where they implement an algorithm from a previous paper.
I fundamentally don't see the point in this paper, it seems that all the heavy work and clever ideas were due to the Liu paper. Your correspondence in the conclusion section talks about a paper that was written before Liu, and I believe that implementing that would be hard, but it doesn't mean that implementing Liu's algorithm is hard. Implementing Liu's algorithm seems like a homework exercise, and please clarify any obstacles in doing this.
No ethics review needed.
The paper has two main contributions:
1. It provides the first code implementation for solving the all pairs minimax path problem or widest path problem in an undirected dense graph, in $O(n^2)$ time.
2. It provides the fastest code implementation for solving the all pairs minimax path problem or widest path problem in an undirected dense graph.
Could a homework exercise make these two contributions? Please indicate the specific homework exercise which has made achievements like listed above.
Liu's paper only proposed some ideas, it was unimplemented and untested. The implementation is not straightforward. You can test to use ChatGPT to implement the algorithm proposed in Liu's paper. It is not easy to implement it correctly.
With the contribution of this paper, we have a usable tool to use it in practice.
It is the State-Of-The-Art tool for solving the APPD matrix.
The problem of finding all pairs of minimax path is interesting and has applications within ML
* A straight-forward implementation of an existing algorithm cannot be considered publishable research
* Writing quality and presentation is extremely poor
* Theoretical claims about complexity is not formally established.
NA
No ethics review needed.
The paper does not contain any significant contribution.
- the paper is in area of exparimental algorithmis with no siginificant contribution to machine learning,
- there is no siginificant contribution to algorithms, i.e., the paper just implents in a straight-forward way the algorithms and tests it, there is not technincal challange in this implementation, nor the tests introduce any nowel methodology,
- the paper makes false statement that previous quadratic time algorithms have not been impmemented - this is not true as even the orginal paper by Sibson from 1973 contains the Fortran implementation of the algorithm.
No questions.
No ethics review needed.
Question:
"the paper is in area of exparimental algorithmis with no siginificant contribution to machine learning"
Response:
This comment suggests reviewer ThN1 has very limited knowledge in the machine learning field.
And the awkward spelling suggests reviewer ThN1 has very limited knowledge in the English language too.
We will not thank the reviewers because none of the reviews is constructive or insightful.
The paper has two main contributions:
1. It provides the first code implementation for solving the all pairs minimax path problem or widest path problem in an undirected dense graph, in $O(n^2)$ time.
2. It provides the fastest code implementation for solving the all pairs minimax path problem or widest path problem in an undirected dense graph.
If the reviewers do NOT agree with these two claims, please provides the Python code to prove their opinions. If you do not have Python code, other code like java, Fortran, or MATLAB is OK, we have many experts in this community to translate it into Python, and compare it with the code implementation introduced in this paper.
Always remember Linus Torvalds' old saying: "Talk is cheap. Show me the code."
I don’t know what  Linus Torvalds would think if he saw the way the authors quoted him.
I praise the author's sense of humor of commanding reviewers to provide code or they would be considered cheap. This made my day!
It will be crazy if a reviewer really provide a snippet.
I think the authors are underestimating their contributions and wish to propose another.
There’s been numerous literatures [1, 2] on writing good **respectable** rebuttals that help authors to write rebuttals while respecting the reviewers.
However, there is a clear gap on how to _not_ write a rebuttal. I feel the authors do a commendable job of that--an important contribution of their research.
I feel the third contribution makes this work stronger. There is an old saying, "Three is better than two."
1. https://deviparikh.medium.com/how-we-write-rebuttals-dc84742fece1
2. https://maartensap.com/notes/rebuttals.html
We are not commanding reviewers to provide code.
When a person has some opinion, she/he needs to provide some evidence to prove her/his point. Reproducible experiments are the best way to prove something in science and technology. In CS, reproducible experiments can be conducted with source code.
So, code is the evidence. People can choose not to provide the evidence, it is not mandatory. Note the "please" word in the comment, it is not "must."
Before this paper, there are zero code implementation for solving the all pairs minimax path problem or widest path problem in an undirected dense graph, in $O(n^2)$  time.
After this paper, we have one such code implementation for solving the problem.

Meta-review:
role: PC
data: comment: value: The program committee has reviewed the discussion on this forum. We remind all participants to review and follow the code of conduct for the conference and professional standard. Further exchange breaching the norm of the professionalism will cause participants to be removed from the conference.
role: AC
data: metareview: value: The paper studies an algorithm for computing minimax path distances in graphs that was proposed in prior work. The main contribution of the work is an implementation and experimental evaluation of the algorithm. There was strong consensus among the reviewers that this work does not meet the bar for acceptance. The paper provides a straightforward implementation of an existing algorithm and there is little relevance of this work to the ICLR community.
additional_comments_on_reviewer_discussion: value: The reviewers raised significant concerns about the significance and relevance of this work to ICLR. After the discussion with the authors, it remained clear that this paper cannot be accepted.
role: PC

Decision: Reject