A Generalization of the Shortest Path Problem to Graphs with Multiple Edge-Cost Estimates

• URL: http://arxiv.org/abs/2208.11489v4
• Date: Tue, 1 Aug 2023 13:42:17 GMT
• Title: A Generalization of the Shortest Path Problem to Graphs with Multiple Edge-Cost Estimates
• Authors: Eyal Weiss, Ariel Felner, Gal A. Kaminka
• Abstract summary: The shortest path problem in graphs is a cornerstone of AI theory and applications. We present a framework for weighted directed graphs, where edge weight can be computed (estimated) multiple times. We then present two complete algorithms for the generalized problem, and empirically demonstrate their efficacy.
• Score: 13.046825574678579
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The shortest path problem in graphs is a cornerstone of AI theory and applications. Existing algorithms generally ignore edge weight computation time. We present a generalized framework for weighted directed graphs, where edge weight can be computed (estimated) multiple times, at increasing accuracy and run-time expense. This raises several generalized variants of the shortest path problem. We introduce the problem of finding a path with the tightest lower-bound on the optimal cost. We then present two complete algorithms for the generalized problem, and empirically demonstrate their efficacy.

Related papers

• Tightest Admissible Shortest Path [4.928034044959278]
  shortest path problem in graphs is fundamental to AI. We introduce the problem of finding the admissible shortest path (TASP), a path with the tightest suboptimality bound on the optimal cost. We present a complete algorithm for solving TASP, with guarantees on solution quality.
  arXiv  Detail & Related papers  (2023-08-15T14:39:05Z)
• GraphWalks: Efficient Shape Agnostic Geodesic Shortest Path Estimation [93.60478281489243]
  We propose a learnable network to approximate geodesic paths on 3D surfaces. The proposed method provides efficient approximations of the shortest paths and geodesic distances estimations.
  arXiv  Detail & Related papers  (2022-05-30T16:22:53Z)
• Learning to Solve Combinatorial Graph Partitioning Problems via Efficient Exploration [72.15369769265398]
  Experimentally, ECORD achieves a new SOTA for RL algorithms on the Maximum Cut problem. Compared to the nearest competitor, ECORD reduces the optimality gap by up to 73%.
  arXiv  Detail & Related papers  (2022-05-27T17:13:10Z)
• Shortest Paths in Graphs with Matrix-Valued Edges: Concepts, Algorithm and Application to 3D Multi-Shape Analysis [69.08838724594584]
  Finding shortest paths in a graph is relevant for numerous problems in computer vision and graphics. We introduce the novel graph-theoretic concept of a shortest path in a graph with matrix-valued edges.
  arXiv  Detail & Related papers  (2021-12-08T08:23:37Z)
• Towards Time-Optimal Any-Angle Path Planning With Dynamic Obstacles [1.370633147306388]
  Path finding is a well-studied problem in AI, which is often framed as graph search. We present two algorithms, grounded in the same idea, that can obtain provably optimal solutions to the considered problem.
  arXiv  Detail & Related papers  (2021-04-14T07:59:53Z)
• Towards Optimally Efficient Tree Search with Deep Learning [76.64632985696237]
  This paper investigates the classical integer least-squares problem which estimates signals integer from linear models. The problem is NP-hard and often arises in diverse applications such as signal processing, bioinformatics, communications and machine learning. We propose a general hyper-accelerated tree search (HATS) algorithm by employing a deep neural network to estimate the optimal estimation for the underlying simplified memory-bounded A* algorithm.
  arXiv  Detail & Related papers  (2021-01-07T08:00:02Z)
• Online Dense Subgraph Discovery via Blurred-Graph Feedback [87.9850024070244]
  We introduce a novel learning problem for dense subgraph discovery. We first propose a edge-time algorithm that obtains a nearly-optimal solution with high probability. We then design a more scalable algorithm with a theoretical guarantee.
  arXiv  Detail & Related papers  (2020-06-24T11:37:33Z)
• Learning to Solve Combinatorial Optimization Problems on Real-World Graphs in Linear Time [12.43303621344215]
  We develop a new framework to solve any optimization problem over graphs without expert knowledge. Our method trains a graph neural network using reinforcement learning on an unlabeled training set of graphs. We demonstrate our approach on both NP-hard problems with optimality gaps close to 1, and show that our method is able to generalize well.
  arXiv  Detail & Related papers  (2020-06-06T01:35:45Z)
• Lagrangian Decomposition for Neural Network Verification [148.0448557991349]
  A fundamental component of neural network verification is the computation of bounds on the values their outputs can take. We propose a novel approach based on Lagrangian Decomposition. We show that we obtain bounds comparable with off-the-shelf solvers in a fraction of their running time.
  arXiv  Detail & Related papers  (2020-02-24T17:55:10Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.