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1. Joinable Parallel Balanced Binary Trees

   https://doi.org/10.1145/3512769  

   Blelloch, Guy ; Ferizovic, Daniel ; Sun, Yihan ( June 2022 , ACM Transactions on Parallel Computing)

   In this article, we show how a single function,join, can be used to implement parallelbalanced binary search trees(BSTs) simply and efficiently. Based onjoin, our approach applies to multiple balanced tree data structures, and a variety of functions for ordered sets and maps. We describe our technique as an algorithmic framework calledjoin-based algorithms. We show that thejoinfunction fully captures what is needed for rebalancing trees for a variety of tree algorithms, as long as the balancing scheme satisfies certain properties, which we refer to asjoinabletrees. We discuss four balancing schemes that are joinable: AVL trees, red-black trees, weight-balanced trees, and treaps. We present a variety of tree algorithms that apply to joinable trees, includinginsert,delete,union,intersection,difference,split,range,filter, and so on, most of them also parallel. These algorithms are generic across balancing schemes. Many algorithms are optimal in the comparison model, and we provide a general proof to show the efficiency in work for joinable trees. The algorithms are highly parallel, all with polylogarithmic span (parallel dependence). Specifically, the set-set operationsunion,intersection, anddifferencehave work\( O(m\log (\frac{n}{m}+1)) \)and polylogarithmic span for input set sizes\( n \)and\( m\le n \).

   We implemented and tested our algorithms on the four balancing schemes. In general, all four schemes have quite similar performance, but the weight-balanced tree slightly outperforms the others. They have the same speedup characteristics, getting around 73\( \times \)speedup on 72 cores (144 hyperthreads). Experimental results also show that our implementation outperforms existing parallel implementations, and our sequential version achieves close or much better performance than the sequential merging algorithm in C++ Standard Template Library (STL) on various input sizes.

    

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2. Advancing Hyperdimensional Computing Based on Trainable Encoding and Adaptive Training for Efficient and Accurate Learning

   https://doi.org/10.1145/3665891  

   Kim, Jiseung ; Lee, Hyunsei ; Imani, Mohsen ; Kim, Yeseong ( June 2024 , ACM Transactions on Design Automation of Electronic Systems)

   Hyperdimensional computing (HDC) is a computing paradigm inspired by the mechanisms of human memory, characterizing data through high-dimensional vector representations, known as hypervectors. Recent advancements in HDC have explored its potential as a learning model, leveraging its straightforward arithmetic and high efficiency. The traditional HDC frameworks are hampered by two primary static elements: randomly generated encoders and fixed learning rates. These static components significantly limit model adaptability and accuracy. The static, randomly generated encoders, while ensuring high-dimensional representation, fail to adapt to evolving data relationships, thereby constraining the model’s ability to accurately capture and learn from complex patterns. Similarly, the fixed nature of the learning rate does not account for the varying needs of the training process over time, hindering efficient convergence and optimal performance. This paper introduces\(\mathsf {TrainableHD} \), a novel HDC framework that enables dynamic training of the randomly generated encoder depending on the feedback of the learning data, thereby addressing the static nature of conventional HDC encoders.\(\mathsf {TrainableHD} \)also enhances the training performance by incorporating adaptive optimizer algorithms in learning the hypervectors. We further refine\(\mathsf {TrainableHD} \)with effective quantization to enhance efficiency, allowing the execution of the inference phase in low-precision accelerators. Our evaluations demonstrate that\(\mathsf {TrainableHD} \)significantly improves HDC accuracy by up to 27.99% (averaging 7.02%) without additional computational costs during inference, achieving a performance level comparable to state-of-the-art deep learning models. Furthermore,\(\mathsf {TrainableHD} \)is optimized for execution speed and energy efficiency. Compared to deep learning on a low-power GPU platform like NVIDIA Jetson Xavier,\(\mathsf {TrainableHD} \)is 56.4 times faster and 73 times more energy efficient. This efficiency is further augmented through the use of Encoder Interval Training (EIT) and adaptive optimizer algorithms, enhancing the training process without compromising the model’s accuracy.

    

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3. An Investigation on Hardware-Aware Vision Transformer Scaling

   https://doi.org/10.1145/3611387  

   Li, Chaojian ; Kim, Kyungmin ; Wu, Bichen ; Zhang, Peizhao ; Zhang, Hang ; Dai, Xiaoliang ; Vajda, Peter ; Lin, Yingyan ( August 2023 , ACM Transactions on Embedded Computing Systems)

   Vision Transformer (ViT) has demonstrated promising performance in various computer vision tasks, and recently attracted a lot of research attention. Many recent works have focused on proposing new architectures to improve ViT and deploying it into real-world applications. However, little effort has been made to analyze and understand ViT’s architecture design space and its implication of hardware-cost on different devices. In this work, by simply scaling ViT’s depth, width, input size, and other basic configurations, we show that a scaled vanilla ViT model without bells and whistles can achieve comparable or superior accuracy-efficiency trade-off than most of the latest ViT variants. Specifically, compared to DeiT-Tiny, our scaled model achieves a\(\uparrow 1.9\% \)higher ImageNet top-1 accuracy under the same FLOPs and a\(\uparrow 3.7\% \)better ImageNet top-1 accuracy under the same latency on an NVIDIA Edge GPU TX2. Motivated by this, we further investigate the extracted scaling strategies from the following two aspects: (1) “can these scaling strategies be transferred across different real hardware devices?”; and (2) “can these scaling strategies be transferred to different ViT variants and tasks?”. For (1), our exploration, based on various devices with different resource budgets, indicates that the transferability effectiveness depends on the underlying device together with its corresponding deployment tool; for (2), we validate the effective transferability of the aforementioned scaling strategies obtained from a vanilla ViT model on top of an image classification task to the PiT model, a strong ViT variant targeting efficiency, as well as object detection and video classification tasks. In particular, when transferred to PiT, our scaling strategies lead to a boosted ImageNet top-1 accuracy of from\(74.6\% \)to\(76.7\% \)(\(\uparrow 2.1\% \)) under the same 0.7G FLOPs; and when transferred to the COCO object detection task, the average precision is boosted by\(\uparrow 0.7\% \)under a similar throughput on a V100 GPU.

    

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4. Minimum Cut and Minimum k -Cut in Hypergraphs via Branching Contractions

   https://doi.org/10.1145/3570162  

   Fox, Kyle ; Panigrahi, Debmalya ; Zhang, Fred ( April 2023 , ACM Transactions on Algorithms)

   On hypergraphs withmhyperedges andnvertices, wherepdenotes the total size of the hyperedges, we provide the following results:

   We give an algorithm that runs in\(\widetilde{O}(mn^{2k-2})\)time for finding a minimumk-cut in hypergraphs of arbitrary rank. This algorithm betters the previous best running time for the minimumk-cut problem, fork> 2.

   We give an algorithm that runs in\(\widetilde{O}(n^{\max \lbrace r,2k-2\rbrace })\)time for finding a minimumk-cut in hypergraphs of constant rankr. This algorithm betters the previous best running times for both the minimum cut and minimumk-cut problems for dense hypergraphs.

   Both of our algorithms are Monte Carlo, i.e., they return a minimumk-cut (or minimum cut) with high probability. These algorithms are obtained as instantiations of a genericbranching randomized contractiontechnique on hypergraphs, which extends the celebrated work of Karger and Stein on recursive contractions in graphs. Our techniques and results also extend to the problems of minimum hedge-cut and minimum hedge-k-cut on hedgegraphs, which generalize hypergraphs.

    

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5. Approximating Nash Social Welfare under Submodular Valuations through (Un)Matchings

   https://doi.org/10.1145/3613452  

   Garg, Jugal ; Kulkarni, Pooja ; Kulkarni, Rucha ( October 2023 , ACM Transactions on Algorithms)

   We study the problem of approximating maximum Nash social welfare (NSW) when allocatingmindivisible items amongnasymmetric agents with submodular valuations. TheNSWis a well-established notion of fairness and efficiency, defined as the weighted geometric mean of agents’ valuations. For special cases of the problem with symmetric agents and additive(-like) valuation functions, approximation algorithms have been designed using approaches customized for these specific settings, and they fail to extend to more general settings. Hence, no approximation algorithm with a factor independent ofmwas known either for asymmetric agents with additive valuations or for symmetric agents beyond additive(-like) valuations before this work.

   In this article, we extend our understanding of theNSWproblem to far more general settings. Our main contribution is two approximation algorithms for asymmetric agents with additive and submodular valuations. Both algorithms are simple to understand and involve non-trivial modifications of a greedy repeated matchings approach. Allocations of high-valued items are done separately by un-matching certain items and re-matching them by different processes in both algorithms. We show that these approaches achieve approximation factors ofO(n) andO(nlogn) for additive and submodular cases, independent of the number of items. For additive valuations, our algorithm outputs an allocation that also achieves the fairness property of envy-free up to one item (EF1).

   Furthermore, we show that theNSWproblem under submodular valuations is strictly harder than all currently known settings with an\(\frac{\mathrm{e}}{\mathrm{e}-1}\)factor of the hardness of approximation, even for constantly many agents. For this case, we provide a different approximation algorithm that achieves a factor of\(\frac{\mathrm{e}}{\mathrm{e}-1}\), hence resolving it completely.

    

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