arXiv subjects

Jason Li

Publications and source records attributed to Jason Li.

At least 109 records · Page 6Linked to original sources

arXiv2022

Deterministic Min-cut in Poly-logarithmic Max-flows

We give a deterministic algorithm for finding the minimum (weight) cut of an undirected graph on $n$ vertices and $m$ edges using $\text{polylog}(n)$ calls to any maximum flow subroutine. Using the current best deterministic maximum flow algorithms, this yields an overall running time of $\tilde O(m \cdot \min(\sqrt{m}, n^{2/3}))$ for weighted graphs, and $m^{4/3+o(1)}$ for unweighted (multi)-graphs. This marks the first improvement for this problem since a running time bound of $\tilde O(mn)$ was established by several papers in the early 1990s. Our global minimum cut algorithm is obtained as a corollary of a minimum Steiner cut algorithm, where a minimum Steiner cut is a minimum (weight) set of edges whose removal disconnects at least one pair of vertices among a designated set of terminal vertices. The running time of our deterministic minimum Steiner cut algorithm matches that of the global minimum cut algorithm stated above. Using randomization, the running time improves to $m^{1+o(1)}$ because of a faster maximum flow subroutine; this improves the best known randomized algorithm for the minimum Steiner cut problem as well. Our main technical contribution is a new tool that we call *isolating cuts*. Given a set of vertices $R$, this entails finding cuts of minimum weight that separate (or isolate) each individual vertex $v\in R$ from the rest of the vertices $R\setminus \{v\}$. Naïvely, this can be done using $|R|$ maximum flow calls, but we show that just $O(\log |R|)$ suffice for finding isolating cuts for any set of vertices $R$. We call this the *isolating cut lemma*.

cs.DS↗

arXiv2022

Edge Connectivity Augmentation in Near-Linear Time

We give an $\tilde{O}(m)$-time algorithm for the edge connectivity augmentation problem and the closely related edge splitting-off problem. This is optimal up to lower order terms and closes the long line of work on these problems.

cs.DS↗

arXiv2022

Adapting TTS models For New Speakers using Transfer Learning

Training neural text-to-speech (TTS) models for a new speaker typically requires several hours of high quality speech data. Prior works on voice cloning attempt to address this challenge by adapting pre-trained multi-speaker TTS models for a new voice, using a few minutes of speech data of the new speaker. However, publicly available large multi-speaker datasets are often noisy, thereby resulting in TTS models that are not suitable for use in products. We address this challenge by proposing transfer-learning guidelines for adapting high quality single-speaker TTS models for a new speaker, using only a few minutes of speech data. We conduct an extensive study using different amounts of data for a new speaker and evaluate the synthesized speech in terms of naturalness and voice/style similarity to the target speaker. We find that fine-tuning a single-speaker TTS model on just 30 minutes of data, can yield comparable performance to a model trained from scratch on more than 27 hours of data for both male and female target speakers.

cs.SD↗

arXiv2021

Breaking the $n^k$ Barrier for Minimum $k$-cut on Simple Graphs

In the minimum $k$-cut problem, we want to find the minimum number of edges whose deletion breaks the input graph into at least $k$ connected components. The classic algorithm of Karger and Stein runs in $\tilde O(n^{2k-2})$ time, and recent, exciting developments have improved the running time to $O(n^k)$. For general, weighted graphs, this is tight assuming popular hardness conjectures. In this work, we show that perhaps surprisingly, $O(n^k)$ is not the right answer for simple, unweighted graphs. We design an algorithm that runs in time $O(n^{(1-ε)k})$ where $ε>0$ is an absolute constant, breaking the natural $n^k$ barrier. This establishes a separation of the two problems in the unweighted and weighted cases.

cs.DS↗

arXiv2021

Minimum Cuts in Directed Graphs via Partial Sparsification

We give an algorithm to find a minimum cut in an edge-weighted directed graph with $n$ vertices and $m$ edges in $\tilde O(n\cdot \max(m^{2/3}, n))$ time. This improves on the 30 year old bound of $\tilde O(nm)$ obtained by Hao and Orlin for this problem. Our main technique is to reduce the directed mincut problem to $\tilde O(\min(n/m^{1/3}, \sqrt{n}))$ calls of {\em any} maxflow subroutine. Using state-of-the-art maxflow algorithms, this yields the above running time. Our techniques also yield fast {\em approximation} algorithms for finding minimum cuts in directed graphs. For both edge and vertex weighted graphs, we give $(1+ε)$-approximation algorithms that run in $\tilde O(n^2 / ε^2)$ time.

cs.DS↗

arXiv2021

A Nearly Optimal All-Pairs Min-Cuts Algorithm in Simple Graphs

We give an $n^{2+o(1)}$-time algorithm for finding $s$-$t$ min-cuts for all pairs of vertices $s$ and $t$ in a simple, undirected graph on $n$ vertices. We do so by constructing a Gomory-Hu tree (or cut equivalent tree) in the same running time, thereby improving on the recent bound of $\tilde{O}(n^{2.5})$ by Abboud et al. (STOC 2021). Our running time is nearly optimal as a function of $n$.

cs.DS↗

arXiv2021

Approximate Gomory-Hu Tree Is Faster Than $n-1$ Max-Flows

The Gomory-Hu tree or cut tree (Gomory and Hu, 1961) is a classic data structure for reporting $(s,t)$ mincuts (and by duality, the values of $(s,t)$ maxflows) for all pairs of vertices $s$ and $t$ in an undirected graph. Gomory and Hu showed that it can be computed using $n-1$ exact maxflow computations. Surprisingly, this remains the best algorithm for Gomory-Hu trees more than 50 years later, *even for approximate mincuts*. In this paper, we break this longstanding barrier and give an algorithm for computing a $(1+ε)$-approximate Gomory-Hu tree using $\text{polylog}(n)$ maxflow computations. Specifically, we obtain the runtime bounds we describe below. We obtain a randomized (Monte Carlo) algorithm for undirected, weighted graphs that runs in $\tilde O(m + n^{3/2})$ time and returns a $(1+ε)$-approximate Gomory-Hu tree algorithm w.h.p. Previously, the best running time known was $\tilde O(n^{5/2})$, which is obtained by running Gomory and Hu's original algorithm on a cut sparsifier of the graph. Next, we obtain a randomized (Monte Carlo) algorithm for undirected, unweighted graphs that runs in $m^{4/3+o(1)}$ time and returns a $(1+ε)$-approximate Gomory-Hu tree algorithm w.h.p. This improves on our first result for sparse graphs, namely $m = o(n^{9/8})$. Previously, the best running time known for unweighted graphs was $\tilde O(mn)$ for an exact Gomory-Hu tree (Bhalgat et al., STOC 2007); no better result was known if approximations are allowed. As a consequence of our Gomory-Hu tree algorithms, we also solve the $(1+ε)$-approximate all pairs mincut and single source mincut problems in the same time bounds. (These problems are simpler in that the goal is to only return the $(s,t)$ mincut values, and not the mincuts.) This improves on the recent algorithm for these problems in $\tilde O(n^2)$ time due to Abboud et al. (FOCS 2020).

cs.DS↗

arXiv2021

Augmenting Edge Connectivity via Isolating Cuts

We give an algorithm for augmenting the edge connectivity of an undirected graph by using the isolating cuts framework (Li and Panigrahi, FOCS '20). Our algorithm uses poly-logarithmic calls to any max-flow algorithm, which yields a running time of $\tilde O(m + n^{3/2})$ and improves on the previous best time of $\tilde O(n^2)$ (Benczúr and Karger, SODA '98) for this problem. We also obtain an identical improvement in the running time of the closely related edge splitting off problem in undirected graphs.

cs.DS↗

arXiv2021

Optimal Bounds for the $k$-cut Problem

In the $k$-cut problem, we want to find the lowest-weight set of edges whose deletion breaks a given (multi)graph into $k$ connected components. Algorithms of Karger \& Stein can solve this in roughly $O(n^{2k})$ time. On the other hand, lower bounds from conjectures about the $k$-clique problem imply that $Ω(n^{(1-o(1))k})$ time is likely needed. Recent results of Gupta, Lee \& Li have given new algorithms for general $k$-cut in $n^{1.98k + O(1)}$ time, as well as specialized algorithms with better performance for certain classes of graphs (e.g., for small integer edge weights). In this work, we resolve the problem for general graphs. We show that the Contraction Algorithm of Karger outputs any fixed $k$-cut of weight $αλ_k$ with probability $Ω_k(n^{-αk})$, where $λ_k$ denotes the minimum $k$-cut weight. This also gives an extremal bound of $O_k(n^k)$ on the number of minimum $k$-cuts and an algorithm to compute $λ_k$ with roughly $n^k \mathrm{polylog}(n)$ runtime. Both are tight up to lower-order factors, with the algorithmic lower bound assuming hardness of max-weight $k$-clique. The first main ingredient in our result is an extremal bound on the number of cuts of weight less than $2 λ_k/k$, using the Sunflower lemma. The second ingredient is a fine-grained analysis of how the graph shrinks -- and how the average degree evolves -- in the Karger process.

cs.DS↗

arXiv2021

Offensive Language and Hate Speech Detection with Deep Learning and Transfer Learning

Toxic online speech has become a crucial problem nowadays due to an exponential increase in the use of internet by people from different cultures and educational backgrounds. Differentiating if a text message belongs to hate speech and offensive language is a key challenge in automatic detection of toxic text content. In this paper, we propose an approach to automatically classify tweets into three classes: Hate, offensive and Neither. Using public tweet data set, we first perform experiments to build BI-LSTM models from empty embedding and then we also try the same neural network architecture with pre-trained Glove embedding. Next, we introduce a transfer learning approach for hate speech detection using an existing pre-trained language model BERT (Bidirectional Encoder Representations from Transformers), DistilBert (Distilled version of BERT) and GPT-2 (Generative Pre-Training). We perform hyper parameters tuning analysis of our best model (BI-LSTM) considering different neural network architectures, learn-ratings and normalization methods etc. After tuning the model and with the best combination of parameters, we achieve over 92 percent accuracy upon evaluating it on test data. We also create a class module which contains main functionality including text classification, sentiment checking and text data augmentation. This model could serve as an intermediate module between user and Twitter.

cs.CL↗

arXiv2021

Near-linear-time, Optimal Vertex Cut Sparsifiers in Directed Acyclic Graphs

Let $G$ be a graph and $S, T \subseteq V(G)$ be (possibly overlapping) sets of terminals, $|S|=|T|=k$. We are interested in computing a vertex sparsifier for terminal cuts in $G$, i.e., a graph $H$ on a smallest possible number of vertices, where $S \cup T \subseteq V(H)$ and such that for every $A \subseteq S$ and $B \subseteq T$ the size of a minimum $(A,B)$-vertex cut is the same in $G$ as in $H$. We assume that our graphs are unweighted and that terminals may be part of the min-cut. In previous work, Kratsch and Wahlström (FOCS 2012/JACM 2020) used connections to matroid theory to show that a vertex sparsifier $H$ with $O(k^3)$ vertices can be computed in randomized polynomial time, even for arbitrary digraphs $G$. However, since then, no improvements on the size $O(k^3)$ have been shown. In this paper, we draw inspiration from the renowned Bollobás's Two-Families Theorem in extremal combinatorics and introduce the use of total orderings into Kratsch and Wahlström's methods. This new perspective allows us to construct a sparsifier $H$ of $Θ(k^2)$ vertices for the case that $G$ is a DAG. We also show how to compute $H$ in time near-linear in the size of $G$, improving on the previous $O(n^{ω+1})$. Furthermore, $H$ recovers the closest min-cut in $G$ for every partition $(A,B)$, which was not previously known. Finally, we show that a sparsifier of size $Ω(k^2)$ is required, both for DAGs and for undirected edge cuts.

cs.DS↗

arXiv2021

Deterministic Weighted Expander Decomposition in Almost-linear Time

In this note, we study the expander decomposition problem in a more general setting where the input graph has positively weighted edges and nonnegative demands on its vertices. We show how to extend the techniques of Chuzhoy et al. (FOCS 2020) to this wider setting, obtaining a deterministic algorithm for the problem in almost-linear time.

cs.DS↗

arXiv2021

A Quasipolynomial $(2+\varepsilon)$-Approximation for Planar Sparsest Cut

The (non-uniform) sparsest cut problem is the following graph-partitioning problem: given a "supply" graph, and demands on pairs of vertices, delete some subset of supply edges to minimize the ratio of the supply edges cut to the total demand of the pairs separated by this deletion. Despite much effort, there are only a handful of nontrivial classes of supply graphs for which constant-factor approximations are known. We consider the problem for planar graphs, and give a $(2+\varepsilon)$-approximation algorithm that runs in quasipolynomial time. Our approach defines a new structural decomposition of an optimal solution using a "patching" primitive. We combine this decomposition with a Sherali-Adams-style linear programming relaxation of the problem, which we then round. This should be compared with the polynomial-time approximation algorithm of Rao (1999), which uses the metric linear programming relaxation and $\ell_1$-embeddings, and achieves an $O(\sqrt{\log n})$-approximation in polynomial time.

cs.DS↗

arXiv2021

Minimum Cuts in Directed Graphs via $\sqrt{n}$ Max-Flows

We give an algorithm to find a mincut in an $n$-vertex, $m$-edge weighted directed graph using $\tilde O(\sqrt{n})$ calls to any maxflow subroutine. Using state of the art maxflow algorithms, this yields a directed mincut algorithm that runs in $\tilde O(m\sqrt{n} + n^2)$ time. This improves on the 30 year old bound of $\tilde O(mn)$ obtained by Hao and Orlin for this problem.

cs.DS↗

arXiv2021

Vertex Connectivity in Poly-logarithmic Max-flows

The vertex connectivity of an $m$-edge $n$-vertex undirected graph is the smallest number of vertices whose removal disconnects the graph, or leaves only a singleton vertex. In this paper, we give a reduction from the vertex connectivity problem to a set of maxflow instances. Using this reduction, we can solve vertex connectivity in $\tilde O(m^α)$ time for any $α\ge 1$, if there is a $m^α$-time maxflow algorithm. Using the current best maxflow algorithm that runs in $m^{4/3+o(1)}$ time (Kathuria, Liu and Sidford, FOCS 2020), this yields a $m^{4/3+o(1)}$-time vertex connectivity algorithm. This is the first improvement in the running time of the vertex connectivity problem in over 20 years, the previous best being an $\tilde O(mn)$-time algorithm due to Henzinger, Rao, and Gabow (FOCS 1996). Indeed, no algorithm with an $o(mn)$ running time was known before our work, even if we assume an $\tilde O(m)$-time maxflow algorithm. Our new technique is robust enough to also improve the best $\tilde O(mn)$-time bound for directed vertex connectivity to $mn^{1-1/12+o(1)}$ time

cs.DS↗

arXiv2021

$O(1)$ Steiner Point Removal in Series-Parallel Graphs

We study how to vertex-sparsify a graph while preserving both the graph's metric and structure. Specifically, we study the Steiner point removal (SPR) problem where we are given a weighted graph $G=(V,E,w)$ and terminal set $V' \subseteq V$ and must compute a weighted minor $G'=(V',E', w')$ of $G$ which approximates $G$'s metric on $V'$. A major open question in the area of metric embeddings is the existence of $O(1)$ multiplicative distortion SPR solutions for every (non-trivial) minor-closed family of graphs. To this end prior work has studied SPR on trees, cactus and outerplanar graphs and showed that in these graphs such a minor exists with $O(1)$ distortion. We give $O(1)$ distortion SPR solutions for series-parallel graphs, extending the frontier of this line of work. The main engine of our approach is a new metric decomposition for series-parallel graphs which we call a hammock decomposition. Roughly, a hammock decomposition is a forest-like structure that preserves certain critical parts of the metric induced by a series-parallel graph.

cs.DS↗

arXiv2020

SpeakerNet: 1D Depth-wise Separable Convolutional Network for Text-Independent Speaker Recognition and Verification

We propose SpeakerNet - a new neural architecture for speaker recognition and speaker verification tasks. It is composed of residual blocks with 1D depth-wise separable convolutions, batch-normalization, and ReLU layers. This architecture uses x-vector based statistics pooling layer to map variable-length utterances to a fixed-length embedding (q-vector). SpeakerNet-M is a simple lightweight model with just 5M parameters. It doesn't use voice activity detection (VAD) and achieves close to state-of-the-art performance scoring an Equal Error Rate (EER) of 2.10% on the VoxCeleb1 cleaned and 2.29% on the VoxCeleb1 trial files.

eess.AS↗

arXiv2020

UniVL: A Unified Video and Language Pre-Training Model for Multimodal Understanding and Generation

With the recent success of the pre-training technique for NLP and image-linguistic tasks, some video-linguistic pre-training works are gradually developed to improve video-text related downstream tasks. However, most of the existing multimodal models are pre-trained for understanding tasks, leading to a pretrain-finetune discrepancy for generation tasks. This paper proposes UniVL: a Unified Video and Language pre-training model for both multimodal understanding and generation. It comprises four components, including two single-modal encoders, a cross encoder, and a decoder with the Transformer backbone. Five objectives, including video-text joint, conditioned masked language model (CMLM), conditioned masked frame model (CMFM), video-text alignment, and language reconstruction, are designed to train each of the components. We further develop two pre-training strategies, stage by stage pre-training (StagedP) and enhanced video representation (EnhancedV), to make the training process of the UniVL more effective. The pre-train is carried out on a sizeable instructional video dataset HowTo100M. Experimental results demonstrate that the UniVL can learn strong video-text representation and achieves state-of-the-art results on five downstream tasks.

cs.CV↗