arXiv subjects

Shashwat Chandra

Publications and source records attributed to Shashwat Chandra.

3 recordsLinked to original sources

arXiv2024

Improved All-Pairs Approximate Shortest Paths in Congested Clique

In this paper, we present a new randomized $O(1)$-approximation algorithm for the All-Pairs Shortest Paths (APSP) problem in weighted undirected graphs that runs in just $O(\log \log \log n)$ rounds in the Congested-Clique model. Before our work, the fastest algorithms achieving an $O(1)$-approximation for APSP in weighted undirected graphs required $\operatorname{poly}(\log n)$ rounds, as shown by Censor-Hillel, Dory, Korhonen, and Leitersdorf (PODC 2019 & Distributed Computing 2021). In the unweighted undirected setting, Dory and Parter (PODC 2020 & Journal of the ACM 2022) obtained $O(1)$-approximation in $\operatorname{poly}(\log \log n)$ rounds. By terminating our algorithm early, for any given parameter $t \geq 1$, we obtain an $O(t)$-round algorithm that guarantees an $O\left(\log^{1/2^t} n\right)$ approximation in weighted undirected graphs. This tradeoff between round complexity and approximation factor offers flexibility, allowing the algorithm to adapt to different requirements. In particular, for any constant $\varepsilon > 0$, an $O\left(\log^\varepsilon n\right)$-approximation can be obtained in $O(1)$ rounds. Previously, $O(1)$-round algorithms were only known for $O(\log n)$-approximation, as shown by Chechik and Zhang (PODC 2022). A key ingredient in our algorithm is a lemma that, under certain conditions, allows us to improve an $a$-approximation for APSP to an $O(\sqrt{a})$-approximation in $O(1)$ rounds. To prove this lemma, we develop several new techniques, including an $O(1)$-round algorithm for computing the $k$-nearest nodes, as well as new types of hopsets and skeleton graphs based on the notion of $k$-nearest nodes.

cs.DS↗

arXiv2024

Fast Broadcast in Highly Connected Networks

We revisit the classic broadcast problem, wherein we have $k$ messages, each composed of $O(\log{n})$ bits, distributed arbitrarily across a network. The objective is to broadcast these messages to all nodes in the network. In the distributed CONGEST model, a textbook algorithm solves this problem in $O(D+k)$ rounds, where $D$ is the diameter of the graph. While the $O(D)$ term in the round complexity is unavoidable$\unicode{x2014}$given that $\Omega(D)$ rounds are necessary to solve broadcast in any graph$\unicode{x2014}$it remains unclear whether the $O(k)$ term is needed in all graphs. In cases where the minimum cut size is one, simply transmitting messages from one side of the cut to the other would require $\Omega(k)$ rounds. However, if the size of the minimum cut is larger, it may be possible to develop faster algorithms. This motivates the exploration of the broadcast problem in networks with high edge connectivity. In this work, we present a simple randomized distributed algorithm for performing $k$-message broadcast in $O(((n+k)/\lambda)\log n)$ rounds in any $n$-node simple graph with edge connectivity $\lambda$. When $k = \Omega(n)$, our algorithm is universally optimal, up to an $O(\log n)$ factor, as its complexity nearly matches an information-theoretic $\Omega(k/\lambda)$ lower bound that applies to all graphs, even when the network topology is known to the algorithm. The setting $k = \Omega(n)$ is particularly interesting because several fundamental problems can be reduced to broadcasting $\Omega(n)$ messages. Our broadcast algorithm finds several applications in distributed computing, enabling $O(1)$-approximation for all distances and $(1+\epsilon)$-approximation for all cut sizes in $\tilde{O}(n/\lambda)$ rounds.

cs.DC↗

arXiv2022

MorphMLP: An Efficient MLP-Like Backbone for Spatial-Temporal Representation Learning

Recently, MLP-Like networks have been revived for image recognition. However, whether it is possible to build a generic MLP-Like architecture on video domain has not been explored, due to complex spatial-temporal modeling with large computation burden. To fill this gap, we present an efficient self-attention free backbone, namely MorphMLP, which flexibly leverages the concise Fully-Connected (FC) layer for video representation learning. Specifically, a MorphMLP block consists of two key layers in sequence, i.e., MorphFC_s and MorphFC_t, for spatial and temporal modeling respectively. MorphFC_s can effectively capture core semantics in each frame, by progressive token interaction along both height and width dimensions. Alternatively, MorphFC_t can adaptively learn long-term dependency over frames, by temporal token aggregation on each spatial location. With such multi-dimension and multi-scale factorization, our MorphMLP block can achieve a great accuracy-computation balance. Finally, we evaluate our MorphMLP on a number of popular video benchmarks. Compared with the recent state-of-the-art models, MorphMLP significantly reduces computation but with better accuracy, e.g., MorphMLP-S only uses 50% GFLOPs of VideoSwin-T but achieves 0.9% top-1 improvement on Kinetics400, under ImageNet1K pretraining. MorphMLP-B only uses 43% GFLOPs of MViT-B but achieves 2.4% top-1 improvement on SSV2, even though MorphMLP-B is pretrained on ImageNet1K while MViT-B is pretrained on Kinetics400. Moreover, our method adapted to the image domain outperforms previous SOTA MLP-Like architectures. Code is available at https://github.com/MTLab/MorphMLP.

cs.CV↗