Race logic, an arrival-time-coded logic family, has demonstrated energy and performance improvements for applications ranging from dynamic programming to machine learning. However, the various ad hoc mappings of algor...
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Race logic, an arrival-time-coded logic family, has demonstrated energy and performance improvements for applications ranging from dynamic programming to machine learning. However, the various ad hoc mappings of algorithms into hardware rely on researcher ingenuity and result in custom architectures that are difficult to systematize. We propose to associate race logic with the mathematical field of tropical algebra, enabling a more methodical approach toward building temporal circuits. This association between the mathematical primitives of tropical algebra and generalized race logic computations guides the design of temporally coded tropical circuits. It also serves as a framework for expressing high-level timing-based algorithms. This abstraction, when combined with temporal memory, allows for the systematic exploration of race logic-based temporal architectures by making it possible to partition feed-forward computations into stages and organize them into a state machine. We leverage analog memristor-based temporal memories to design such a state machine that operates purely on time-coded wavefronts. We implement a version of Dijkstra's algorithm to evaluate this temporal state machine. This demonstration shows the promise of expanding the expressibility of temporal computing to enable it to deliver significant energy and throughput advantages.
Rigid point cloud registration has become an essential task in robotics and computer vision. The main challenges are the extraction of key points and the correspondences, especially on the low-overlap point clouds. Th...
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This paper describes a new version of the AlgoView system for 3D visualization and interactive analysis of information graphs of algorithms. The developed system consists of two interacting parts: a functional computa...
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In a graph, the switching operation reverses adjacencies between a subset of vertices and the others. For a hereditary graph class G, we are concerned with the maximum subclass and the minimum superclass of G that are...
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In this short note, we give a novel algorithm for O(1) round triangle counting in bounded arboricity graphs. Counting triangles in O(1) rounds (exactly) is listed as one of the interesting remaining open problems in t...
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In Clique Cover, given a graph G and an integer k, the task is to partition the vertices of G into k cliques. Clique Cover on unit ball graphs has a natural interpretation as a clustering problem, where the objective ...
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Single-Source Shortest Path (SSSP) algorithms are essential in various applications, from optimizing transportation networks to analyzing social networks. This paper focuses on implementing and optimizing a parallel D...
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We study the generic identifiability of causal effects in linear non-Gaussian acyclic models (LiNGAM) with latent variables. We consider the problem in two main settings: When the causal graph is known a priori, and w...
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We study the generic identifiability of causal effects in linear non-Gaussian acyclic models (LiNGAM) with latent variables. We consider the problem in two main settings: When the causal graph is known a priori, and when it is unknown. In both settings, we provide a complete graphical characterization of the identifiable direct or total causal effects among observed variables. Moreover, we propose efficient algorithms to certify the graphical conditions. Finally, we propose an adaptation of the reconstruction independent component analysis (RICA) algorithm that estimates the causal effects from the observational data given the causal graph. Experimental results show the effectiveness of the proposed method in estimating the causal effects. Copyright 2024 by the author(s)
Reliability is a crucial factor influencing electricity network planning and has gained considerable attention in the past decade due to the increasing number of weather-related outage events. This article explores co...
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Reliability is a crucial factor influencing electricity network planning and has gained considerable attention in the past decade due to the increasing number of weather-related outage events. This article explores connections between network topology and reliability, and proposes a graph-based approach to enhance the reliability of distribution systems by installing new tie-lines. The problem is cast here as an edge-connectivity augmentation problem, with 2-edge connectivity being desired to ensure service restoration under the outage of any single line in the network. However, in practice, such a target may not be economical or feasible. Therefore, a systematic optimization framework is presented in this article to model partial augmentations to the system for improving the reliability at a select subset of nodes. This approach allows for selectively strengthening parts of the network based on connectivity requirements. The article also proposes the use of graph-based metrics to characterize the reliability of distribution networks. Applications of the approach to realistic distribution test systems demonstrate its effectiveness in identifying line additions that can favorably impact system reliability. Numerical results also quantify the reliability improvement achievable through partial augmentation.
We introduce an object called a tree growing sequence (TGS) in an effort to generalize bijective correspondences between G-parking functions, spanning trees, and the set of monomials in the Tutte polynomial of a graph...
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We introduce an object called a tree growing sequence (TGS) in an effort to generalize bijective correspondences between G-parking functions, spanning trees, and the set of monomials in the Tutte polynomial of a graph G. A tree growing sequence determines an algorithm which can be applied to a single function, or to the set P-G,P-q of G-parking functions. When the latter is chosen, the algorithm uses splitting operations - inspired by the recursive definition of the Tutte polynomial - to iteratively break P-G,P-q into disjoint subsets. This results in bijective maps tau and rho from P-G,P-q to the spanning trees of G and Tutte monomials, respectively. We compare the TGS algorithm to Dhar's algorithm and the family described by Chebikin and Pylyavskyy in 2005. Finally, we compute a Tutte polynomial of a zonotopal tiling using analogous splitting operations. (c) 2021 Elsevier B.V. All rights reserved.
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