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研究生:陳智達
研究生(外文):Tran Tri Dat
論文名稱:學習加強的貝爾曼-福特演算法
論文名稱(外文):A learning-augmented Bellman–Ford algorithm
指導教授:張經略
指導教授(外文):Ching-Lueh Chang
口試委員:周志岳吳晉賢
口試委員(外文):Chih-Yueh ChouChin-Hsien Wu
口試日期:2024-07-27
學位類別:碩士
校院名稱:元智大學
系所名稱:資訊工程學系
學門:工程學門
學類:電資工程學類
論文種類:學術論文
論文出版年:2024
畢業學年度:112
語文別:英文
論文頁數:20
中文關鍵詞:貝爾曼-福特演算法學習增強演算法最短路徑問題人工智慧
外文關鍵詞:Bellman–Ford AlgorithmLearning-Augmented AlgorithmShortest Path ProblemsArtificial Intelligence
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本論文給出一演算法,使得當輸入有重量的有向圖G=(V,E)、點s∈V及一預測(且可能錯誤)的根於s之最短路徑樹T時,該演算法會在O(η|V||E|+|E|)時間內輸出所有點v∈V的最短s-v距離,其中η表示滿足d_G (s,v)≠d_T (s,v)的點v∈V所佔之比例。我們的演算法修改了貝爾曼-福特演算法
This thesis shows an algorithm that, given a weighted directed graph G=(V,E), a vertex s∈V and a predicted (and possibly wrong) shortest-path tree T rooted at s, outputs the shortest s-v distance for all v∈V in O(η|V||E|+|E|) time, where η denotes the fraction of vertices v∈V satisfying d_G (s,v)≠d_T (s,v). Our algorithm modifies the Bellman–Ford algorithm.
1. Introduction
2. Result
3. Conclusions
REFERENCES
[1]R. Bellman, “On a routing problem,” Q. Appl. Math., vol. 16, no. 1, pp. 87–90, 1958.
[2]L. R. Ford, Network Flow Theory. Santa Monica, CA: RAND Corporation, 1956.
[3]A. V. Goldberg and C. Harrelson, “Computing the shortest path: A* search meets graph theory.,” in SODA: Symposium on Discrete Algorithms, 2005, vol. 5, pp. 156–165.
[4]U. Meyer and P. Sanders, “Δ-stepping: a parallelizable shortest path algorithm,” J. Algorithms, vol. 49, no. 1, pp. 114–152, 2003.
[5]Z. Akata et al., “A research agenda for hybrid intelligence: augmenting human intellect with collaborative, adaptive, responsible, and explainable artificial intelligence,” Computer, vol. 53, no. 8, pp. 18–28, 2020.
[6]S. Raisch and S. Krakowski, “Artificial intelligence and management: The automation–augmentation paradox,” Acad. Manage. Rev., vol. 46, no. 1, pp. 192–210, 2021.
[7]T. Dao, A. Gu, A. Ratner, V. Smith, C. De Sa, and C. Ré, “A kernel theory of modern data augmentation,” in ICML: International Conference on Machine Learning, 2019, pp. 1528–1537.
[8]E. Du, F. Wang, and M. Mitzenmacher, “Putting the “Learning,” in ICML: International Conference on Machine Learning, 2021, pp. 2860–2869.
[9]C. L. Hedrick, “Routing information protocol,” RFC Editor, 1988.
[10]J. Kelly and M. Walker, “The Critical Path Method,” Remington Rand DuPont Corp., 1957.
[11]S. Khuller, B. Raghavachari, and N. Young, “Balancing minimum spanning trees and shortest-path trees,” Algorithmica, vol. 14, no. 4, pp. 305–321, 1995.

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