Venue: NeurIPS 2022 Conference

Reviews:

final_score: rating: 6: Weak Accept: Technically solid, moderate-to-high impact paper, with no major concerns with respect to evaluation, resources, reproducibility, ethical considerations.
review_content: summary: This paper improves the computation speed and memory cost of GTW [Wang, et al, 2016] method, for the multiple time-series joint alignment problem. Two major enhancements are introduced. The first is excess pushing with linear component operations, which treats components (the number is much less than nodes) as the basic unit. The second is a bi-directional pushing (push excess and push deficit), where pairwise DTW initialization is used.
Comprehensive experiments on both synthetic and real world datasets are conducted to evaluate the speed and memory improvement of the proposed method.

strengths_and_weaknesses: Strengths:
1. The joint alignment problem is of great importance and interest to the community. The GTW method converts the alignment problem into a max-flow problem that sheds the light on solving it optimally via techniques in graph theory. This paper further pushes this direction to speed up the process and reduce the memory cost significantly. This makes the GTW approach feasible in real world applications.
2. The paper has illustrative figures to demonstrate the approach.
3. Time and space complexity analysis is provided.
4. Several max-flow algorithms are included in the experiments part. The proposed method performs consistently much better than those baselines.

Weakness:
1. The paper lacks some introduction / background on graph techniques, making it slightly difficult to follow especially when defining ‘drain’, ‘discharge’ and ‘component’. With an illustrative example that demonstrates how these operations are done, would significantly improve the readability of the paper.
2. The most critical problem lies in the definition of GTW. In GTW, the joint alignment problem is converted to a slightly different problem: constraint the similarity of pairwise warping functions / paths. The warping function could vary a lot, but the effect could be very similar. Let me use edit distance to illustrate (slightly different than DTW, but shares similar DP spirits, so I use this as an easy example). Given a reference string, there is one string that needs prepending a letter to match the reference (this is one warping). There is another string that needs appending a letter to match the reference (another warping). These two warping / editing functions are very different, but their integral is the same (both accumulate to only one insertion edit), so their effects are also similar as well. Therefore, some external metric, like the integral of the warping function, their difference should be considered as the penalty, instead of the function itself. GTW makes this definition for ease of computation via max-flow algorithms, but lacks the practical meaning as it is often hard to interpret the warping functions’ difference, and hard to apply to practical tasks like finding the centroids of time series. I think this formulation reduces the interests of GTW based approaches to the community.

questions: See above and I am willing to hear more opinions.

limitations: NA
review_title: null

final_score: rating: 7: Accept: Technically solid paper, with high impact on at least one sub-area, or moderate-to-high impact on more than one areas, with good-to-excellent evaluation, resources, reproducibility, and no unaddressed ethical considerations.
review_content: summary: This paper proposes an algorithm BILCO for solving graphical time warping, an alignment method for multiple time series data. The authors realized a fast and memory-saving algorithm by focusing on the special characteristics of DTW graphs. Experimental results, including results for real data, show that their two proposed methods, ELCO and bidirectional pushing, dramatically reduce computation and memory consumption.
strengths_and_weaknesses: - The authors propose an algorithm for joint alignment that is much faster (10x~) and memory-saving than other methods.
- Experimentally, the proposed method is applied to three real datasets that require multiple alignment, and shows impressive speedup and memory-saving performance.


- The proposed method is not for general multiple time series alignment problem, but is an algorithm for solving a narrower problem, graphical time warping, in which warping paths in given neighbor relationships should be close, as written in Eq.(1). The application of the proposed method to general multiple alignment problem and other problems is not discussed.

questions: - Are there any other applications of the proposed method other than graphical time warping?

typo
- l.170: source side $V_T$
limitations: This paper proposes an algorithm for solving time series data alignment, which does not involve negative social impact.
review_title: null

final_score: rating: 6: Weak Accept: Technically solid, moderate-to-high impact paper, with no major concerns with respect to evaluation, resources, reproducibility, ethical considerations.
review_content: summary: This paper investigates the joint alignment of multiple time series. Compared to the existing max-flow method on GTW, the proposed method makes use of two properties of the joint alignment max-flow problem, i.e., joint alignment is a generalization of pairwise alignment, and a coarse approximate solution to joint alignment can be readily estimated, for significantly reducing computational time and space.
strengths_and_weaknesses: Strengths:
1. The observation of two important properties of the joint alignment max-flow problem.
2. The corresponding designs to the two properties, i.e., Excess pushing with Linear Component Operations (ELCO) that integrates DP and the push-relabel approach, and a bidirectional-pushing strategy to utilize prior knowledge as initialization, are reasonable for improving efficiency.
3. The complexity analysis provides good insights in comparison.
4. The experiments on both synthetic and real datasets indicate the efficiency of the proposed method.

Weakness:
1. The experiments focus on comparing time and space efficiency of different methods. Alignment accuracy could be compared to indicate whether there is a trade-off between effectiveness and efficiency of the proposed method.
questions: 1. Is it reasonable to include the comparison of the alignment performance of the compared methods?
2. Are there any trade-off between the alignment performance and the efficiency of the proposed method?

limitations: The authors addressed the potential negative societal impact of the work well.
review_title: null

Meta-review: metareview: In this paper, the authors propose an algorithm BILCO for solving graphical time warping, an alignment method for multiple time series data. Overall, the proposed approach is interesting, and all reviewers are positive. Thus, I also vote for acceptance. 
confidence: Certain
Decision: Accept