Allocating resources to process tasks during runtime (online) is hard. A solution method for such allocation is required to be computationally efficient while being subjected to uncertainties such as resources suddenl...
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This paper investigates the numerical implementation of solving initial value problems (IVPs) using the Precise Integration Method (PIM). For the solution of IVPs, PIM employs a recursive calculation based on matrix e...
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InfiniBand interconnect network is widely used in parallel computing. Network adapter (HCA) is one of the necessary hardware components for architecture deployment. With the expansion of nodes in parallel computing sy...
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Single Instruction Multiple Thread (SIMT) based processor and parallel model are effective ways to solve computation problems exist in big data era. Commonly, work load is organized into mass parallel computing thread...
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We study four NP-hard optimal seat arrangement problems, which each have as input a set of n agents, where each agent has cardinal preferences over other agents, and an n-vertex undirected graph (called seat graph). T...
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ISBN:
(纸本)9781956792034
We study four NP-hard optimal seat arrangement problems, which each have as input a set of n agents, where each agent has cardinal preferences over other agents, and an n-vertex undirected graph (called seat graph). The task is to assign each agent to a distinct vertex in the seat graph such that either the sum of utilities or the minimum utility is maximized, or it is envy-free or exchange-stable. Aiming at identifying hard and easy cases, we extensively study the algorithmic complexity of the four problems by looking into natural graph classes for the seat graph (e.g., paths, cycles, stars, or matchings), problem-specific parameters (e.g., the number of non-isolated vertices in the seat graph or the maximum number of agents towards whom an agent has non-zero preferences), and preference structures (e.g., non-negative or symmetric preferences). For strict preferences and seat graphs with disjoint edges and isolated vertices, we correct an error in the literature and show that finding an envy-free arrangement remains NP-hard in this case.
Optimal transport (OT) is a popular and powerful tool for comparing probability measures. However, OT suffers a few drawbacks: (i) input measures required to have the same mass, (ii) a high computational complexity, a...
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Optimal transport (OT) is a popular and powerful tool for comparing probability measures. However, OT suffers a few drawbacks: (i) input measures required to have the same mass, (ii) a high computational complexity, and (iii) indefiniteness which limits its applications on kernel-dependent algorithmic approaches. To tackle issues (ii)(iii), Le et al. (2022) recently proposed Sobolev transport for measures on a graph having the same total mass by leveraging the graph structure over supports. In this work, we consider measures that may have different total mass and are supported on a graph metric space. To alleviate the disadvantages (i)-(iii) of OT, we propose a novel and scalable approach to extend Sobolev transport for this unbalanced setting where measures may have different total mass. We show that the proposed unbalanced Sobolev transport (UST) admits a closed-form formula for fast computation, and it is also negative definite. Additionally, we derive geometric structures for the UST and establish relations between our UST and other transport distances. We further exploit the negative definiteness to design positive definite kernels and evaluate them on various simulations to illustrate their fast computation and comparable performances against other transport baselines for unbalanced measures on a graph.
Computing a similarity measure (or a distance) between two complex objects is a fundamental building block for a huge number of applications in a wide variety of domains. Since many tasks involve computing such simila...
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ISBN:
(纸本)9783031469930;9783031469947
Computing a similarity measure (or a distance) between two complex objects is a fundamental building block for a huge number of applications in a wide variety of domains. Since many tasks involve computing such similarities among many pairs of objects, many algorithmic techniques and data structures have been devised in the past to reduce the number of similarity computations and to reduce the complexity of computing the similarity (e.g., dimension-reduction techniques). In this paper, we focus on computing the similarity of two sets and show that computing the similarity of two random samples drawn from the respective sets leads to an (asymptotically) unbiased estimator of the true similarity, with relative standard error going to zero as the size of the involved sets grows, and of course at a much lower computational cost as we compute the similarity of the significantly smaller samples. While this result has been known for a long time since Broder's seminal paper (Broder, 1997) for the Jaccard similarity index, we show here that the result also holds for many other similarity measures, such as the well-known cosine similarity, Sorensen-Dice, the first and second Kulczynski coefficients, etc.
To address challenges in handling missing values in multivariate time series data, such as low efficiency, insufficient utilization of temporal features, and inadequate reasoning capability under high missing rates, t...
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In the present context, the rise of artificial intelligence (AI) has brought to light the importance of expediting processes due to the advancement in AI. This issue holds significance across various domains of machin...
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With the complexity and variability of cyber attacks increasing, current approaches for constructing attack scenarios often overlook the continuity of attack behaviors. These approaches lead to challenges in dynamical...
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