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1. Physics-guided Energy-efficient Path Selection Using On-board Diagnostics Data

   https://doi.org/10.1145/3406596  

   Li, Yan; Kotwal, Pratik; Wang, Pengyue; Xie, Yiqun; Shekhar, Shashi; Northrop, William (October 2020, ACM/IMS Transactions on Data Science)

   null (Ed.)

   Given a spatial graph, an origin and a destination, and on-board diagnostics (OBD) data, the energy-efficient path selection problem aims to find the path with the least expected energy consumption (EEC). Two main objectives of smart cities are sustainability and prosperity, both of which benefit from reducing the energy consumption of transportation. The challenges of the problem include the dependence of EEC on the physical parameters of vehicles, the autocorrelation of the EEC on segments of paths, the high computational cost of EEC estimation, and potential negative EEC. However, the current cost estimation models for the path selection problem do not consider vehicles’ physical parameters. Moreover, the current path selection algorithms follow the “path + edge” pattern when exploring candidate paths, resulting in redundant computation. Our preliminary work introduced a physics-guided energy consumption model and proposed a maximal-frequented-path-graph shortest-path algorithm using the model. In this work, we propose an informed algorithm using an admissible heuristic and propose an algorithm to handle negative EEC. We analyze the proposed algorithms theoretically and evaluate the proposed algorithms via experiments with real-world and synthetic data. We also conduct two case studies using real-world data and a road test to validate the proposed method. 

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2. Eco-PiNN: A Physics-informed Neural Network for Eco-toll Estimation

   https://doi.org/10.1137/1.9781611977653.ch94  

   Li, Yan; Yang, Mingzhou; Eagon, Matthew; Farhadloo, Majid; Xie, Yiqun; Northrop, William; Shekhar, Shashi (January 2023, Proceedings of the SIAM International Conference on Data Mining)

   The eco-toll estimation problem quantifies the expected environmental cost (e.g., energy consumption, exhaust emissions) for a vehicle to travel along a path. This problem is important for societal applications such as eco-routing, which aims to find paths with the lowest exhaust emissions or energy need. The challenges of this problem are threefold: (1) the dependence of a vehicle's eco-toll on its physical parameters; (2) the lack of access to data with eco-toll information; and (3) the influence of contextual information (i.e. the connections of adjacent segments in the path) on the eco-toll of road segments. Prior work on eco-toll estimation has mostly relied on pure data-driven approaches and has high estimation errors given the limited training data. To address these limitations, we propose a novel Eco-toll estimation Physics-informed Neural Network framework (Eco-PiNN) using three novel ideas, namely, (1) a physics-informed decoder that integrates the physical laws governing vehicle dynamics into the network, (2) an attention-based contextual information encoder, and (3) a physics-informed regularization to reduce overfitting. Experiments on real-world heavy-duty truck data show that the proposed method can greatly improve the accuracy of eco-toll estimation compared with state-of-the-art methods. *The full version of the paper can be accessed at https://arxiv.org/abs/2301.05739 

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3. Even 1xn Edge-Matching and Jigsaw Puzzles are Really Hard

   Bosboom, J.; Demaine, E.D.; Demaine, M.L.; Hesterberg, A.; Manurangsi, P.; Yodpinyanee, A. (January 2017, Journal of information processing)

   We prove the computational intractability of rotating and placing n square tiles into a 1 × n array such that adjacent tiles are compatible—either equal edge colors, as in edge-matching puzzles, or matching tab/pocket shapes, as in jigsaw puzzles. Beyond basic NP-hardness, we prove that it is NP-hard even to approximately maximize the number of placed tiles (allowing blanks), while satisfying the compatibility constraint between nonblank tiles, within a factor of 0.9999999702. (On the other hand, there is an easy (1/2)-approximation.) This is the first (correct) proof of inapproximability for edge-matching and jigsaw puzzles. Along the way, we prove NP-hardness of distinguishing, for a directed graph on n nodes, between having a Hamiltonian path (length n − 1) and having at most 0.999999284 (n − 1) edges that form a vertex-disjoint union of paths. We use this gap hardness and gap-preserving reductions to establish similar gap hardness for 1 × n jigsaw and edge-matching puzzles. 

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4. Map-matching using shortest paths

   https://doi.org/10.1145/3191801.3191812  

   Chambers, Erin; Fasy, Brittany Terese; Wang, Yusu; Wenk, Carola (January 2018, IWISC)

   We consider several variants of the map-matching problem, which seeks to find a path Q in graph G that has the smallest distance to a given trajectory P (which is likely not to be exactly on the graph). In a typical application setting, P models a noisy GPS trajectory from a person traveling on a road network, and the desired path Q should ideally correspond to the actual path in G that the person has traveled. Existing map-matching algorithms in the literature consider all possible paths in G as potential candidates for Q. We find solutions to the map-matching problem under different settings. In particular, we restrict the set of paths to shortest paths, or concatenations of shortest paths, in G. As a distance measure, we use the Fréchet distance, which is a suitable distance measure for curves since it takes the continuity of the curves into account. 

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5. Efficient Exact Subgraph Matching via GNN-based Path Dominance Embedding

   Ye, Y; Lian, X; Chen, M (August 2024, Proceedings of the International Conference on Very Large Data Bases)

   The classic problem of exact subgraph matching returns those subgraphs in a large-scale data graph that are isomorphic to a given query graph, which has gained increasing importance in many real-world applications such as social network analysis, knowledge graph discovery in the Semantic Web, bibliographical network mining, and so on. In this paper, we propose a novel and effective graph neural network (GNN)-based path embedding framework (GNN-PE), which allows efficient exact subgraph matching without introducing false dismissals. Unlike traditional GNN-based graph embeddings that only produce approximate subgraph matching results, in this paper, we carefully devise GNN-based embeddings for paths, such that: if two paths (and 1-hop neighbors of vertices on them) have the subgraph relationship, their corresponding GNN-based embedding vectors will strictly follow the dominance relationship. With such a newly designed property of path dominance embeddings, we are able to propose effective pruning strategies based on path label/dominance embeddings and guarantee no false dismissals for subgraph matching. We build multidimensional indexes over path embedding vectors, and develop an efficient subgraph matching algorithm by traversing indexes over graph partitions in parallel and applying our pruning methods. We also propose a cost-model-based query plan that obtains query paths from the query graph with low query cost. Through extensive experiments, we confirm the efficiency and effectiveness of our proposed GNN-PE approach for exact subgraph matching on both real and synthetic graph data. 

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