We thank the reviewers for their input and suggestions. We are pleased all reviewers clearly followed the main motivation and contribution of our paper. Overall the reviewers seemed to view this contribution favorably and even remarked "this is a non-trivial contribution for an important problem." (Review 4)$ Of the three reviewers, two recommended acceptance, and the one reviewer who recommended weak reject did so due to an easy-to-address concern regarding our algorithm's performance. The reviews chiefly addressed minor technical issues (Review 1) and possible improvements in presentation (Review 3, Review 4). As we explain below, these small issues can all be addressed by minor adjustments to the material already present in the manuscript. We begin with the most critical reviewer (Review 1). Reviewer #1 raised concerns about the weaker performance of our algorithm SimpleLocal in comparison with Orecchia and Zhou's (OZ) algorithm LocalImprove. Our basic response is that the OZ algorithm is an important theoretical advance, while our algorithm solves the same problem and is much simpler. We do not know if anyone has ever implemented LocalImprove, but implementing our algorithm is straightforward. In more detail, both algorithms solve the same objective (line 468), and so any result satisfied by the output of the OZ algorithm is matched by our own. Reviewer #1 specifically asked if, given a set C of low-conductance, our algorithm finds a nearby set C' such that the conductance of C and C' differ by only a multiplicative constant. Indeed, this is exactly the result we show in Theorem 4. Moreover, because SimpleLocal solves the same objective, LocalImprove outperforms our algorithm only in terms of its worst-case theoretical runtime. However, implementing the OZ algorithm would be a complicated task, and to the best our knowledge no one has done so in practice. In contrast to this, we provide implementation details for our simple algorithm and display its ability to quickly identify low conductance sets in a massive real-world dataset. As indicated by Reviewer #3, the experimental results we provide confirm that flow-based methods are a viable and practical approach to cut improvement, clearly indicating an improvement over the theoretically-interesting OZ algorithm. We are happy to hear this reviewer feels our paper is a "clear accept," and that it "will provide a new set of techniques for cut analysis." In a similar vein, Reviewer #4 notes that the value of our results is in bringing the "theoretical advance" of OZ "closer to practice." One should not view our result as worse than OZ, but instead as extending that work to be useful for machine learning. Reviewer #3 provides several good points in summarizing our paper that would help non-experts understand the significance of our work. We will be able to incorporate these in the introduction and motivation sections should the manuscript be accepted. The reviewer also suggests de-emphasizing the connection to one-norm regularization. We note though that despite being closely related, the optimization problem and penalty term we deal with here are not the same as the objective for the localized version of PageRank that Gleich and Mahoney address. We feel that our result serves to strengthen the arguments made by Gleich-Mahoney by illustrating a broader trend in strongly-local algorithms resulting from 1-norm penalty terms. For this reason we hope this connection can serve as an important--if only secondary--role in our paper. Another suggested area of de-emphasis is our claim that SimpleLocal "removes the dependence" that Orecchia and Zhou's algorithm has for certain subroutines (Reviewer #4). We acknowledge that these authors' intent was to provide a strongly-local flow-based method with the best theoretical runtime possible, and for this reason black-box subroutines are not the best choice. In our final version we will endeavor to sharpen our statements to appropriately highlight the difference in the aims of these two algorithms. Several small improvements for some of our technical sections were also offered. We are grateful to Reviewer #1 for carefully checking our work in the supplementary material. The issues raised can be easily remedied with an extra line of explanation (lines 85, 93-95), or by fixing a mathematical typo (lines 49, 102). Reviewer #2 additionally pointed out that some of our technical proofs are rather terse despite being simple to derive. When space permits we will endeavor to improve these sections with extra steps and clarification.