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1

Crisler, Nancy. Shortest paths. Lexington, Mass: COMAP, 1993.

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2

Li, Fajie, and Reinhard Klette. Euclidean Shortest Paths. London: Springer London, 2011. http://dx.doi.org/10.1007/978-1-4471-2256-2.

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3

Icking, Christian. Shortest paths for line segments. New York: Courant Institute of Mathematical Sciences, New York University, 1992.

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4

Akman, Varol. Unobstructed Shortest Paths in Polyhedral Environments. Berlin, Heidelberg: Springer Berlin Heidelberg, 1987. http://dx.doi.org/10.1007/3-540-17629-2.

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5

Brandimarte, Paolo. From Shortest Paths to Reinforcement Learning. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-61867-4.

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6

Unobstructed shortest paths in polyhedral environments. Berlin: Springer-Verlag, 1987.

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7

Sharir, Micha. On shortest paths amidst convex polyhedra. New York: Courant Institute of Mathematical Sciences, New York University, 1985.

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8

Baltsan, Avikam. On shortest paths between two convex polyhedra. New York: Courant Institute of Mathematical Sciences, New York University, 1985.

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9

Reinhard, Klette, ed. Euclidean shortest paths: Exact or approximate algorithms. London: Springer-Verlag, 2011.

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10

Dynamic Algorithms for Shortest Paths and Matching. [New York, N.Y.?]: [publisher not identified], 2016.

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11

Cuerington, Andrè M. The shortest path problem in the plane with obstacles: Bounds on path lengths and shortest paths within homotopy classes. Monterey, Calif: Naval Postgraduate School, 1991.

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12

Wensheng, Liu. Shortest paths for sub-Riemannian metrics on rank-two distributions. Providence, R.I: American Mathematical Society, 1995.

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13

Crane, Jerry Allen. Searching for shortest and safest paths along obstacle common tangents. Monterey, Calif: Naval Postgraduate School, 1991.

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14

Ruppert, Eric. Parallel algorithms for the k shortest paths and related problems. Toronto: University of Toronto, Dept. of Computer Science, 1996.

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15

Adamatzky, Andrew, ed. Shortest Path Solvers. From Software to Wetware. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-77510-4.

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16

Dunn, Christine E. Notes on shortest path algorithms for GIS. Lancaster: North West Regional Research Laboratory, 1989.

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17

1956-, Ahuja Ravindra K., and Sloan School of Management, eds. Faster algorithms for the shortest path problem. Cambridge, Mass: Sloan School of Management, Massachusetts Institute of Technology, 1988.

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18

Tipici, Z. R. Shortest path and minimum cost low algorithms. Manchester: UMIST, 1993.

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19

Camil, Demetrescu, Goldberg Andrew V, and Johnson David S. 1945-, eds. The shortest path problem: Ninth DIMACS implementation challenge. Providence, R.I: American Mathematical Society, 2009.

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20

Young, Neal E. Faster parametric shortest path and minimum balance algorithms. Cambridge, Mass: Sloan School of Management, Massachusetts Institute of Technology, 1990.

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21

GSA schedules: The shortest path to federal contract dollars. [Bethesda, Md]: Wood River Technologies, 2008.

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22

Kant's shorter writings: Critical paths outside the Critiques. Newcastle-upon-Tyne, UK: Cambridge Scholars Publishing, 2016.

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23

Allan, David. 802.1aq shortest path bridging design and evolution: The architects' perspective. New York, NY: Wiley, 2012.

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24

Anand, Sachin. Graph theory and algorithms:implementation of Dijkstra's shortest path algorithm in Java. Oxford: Oxford Brookes University, 2001.

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25

Guibas, Leonidas J. Linear time algorithms for visibility and shortest path problems inside simple polygons. New York: Courant Institute of Mathematical Sciences, New York University, 1986.

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26

Shing, Man-Tak. Persistence search -- a new search strategy for the dynamic shortest path problem. Monterey, Calif: Naval Postgraduate School, 1991.

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27

Farhat, Idriss. Evaluation of shortest path algorithms for an application of the travelling salesman problem. Oxford: Oxford Brookes University, 2004.

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28

Ahuja, Ravindra K. Improved primal simplex algorithms for shortest path, assignment and minimum cost flow problems. Cambridge, Mass: Alfred P. Sloan School of Management, Massachusetts Institute of Technology, 1988.

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29

Cisco OSPF Command and Configuration Handbook (paperback). Indianapolis: Cisco Press, 2008.

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30

Conceptual data modeling and database design: A fully algorithmic approach : The shortest advisable path. Oakville, ON: Apple Academic Press, 2015.

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31

Johnson, George. A shortcut through time: The path to a quantum computer. New York, NY: Alfred A. Knopf, 2003.

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32

A shortcut through time: The path to a quantum computer. New York: Alfred A. Knopf, 2003.

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33

Logan, Joseph. 7 simple steps to landing your first job: The shortest path from here to hired. Boulder, Co: Maytown Press, 2010.

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34

Moser, Tijmen Jan. The shortest path method for seismic ray tracing in complicated media =: De kortste-routemethode voor seismische raytracing in gecompliceerde media. [Utrecht: Faculteit Aardwetenschappen der Rijksuniversiteit te Utrecht], 1992.

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35

Jenkins, Kevin Dean. The shortest path problem in the plane with obstacles: A graph modeling approach to producing finite search lists of homotopy classes. Monterey, Calif: Naval Postgraduate School, 1991.

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36

Routing first-step. Indianapolis, IN: Cisco Press, 2005.

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37

1975-, Panov Taras E., ed. Toric topology. Providence, Rhode Island: American Mathematical Society, 2015.

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38

Schorr, Amir, and Micha Sharir. On Shortest Paths in Polyhedral Spaces. Creative Media Partners, LLC, 2018.

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39

Akman, Varol. Unobstructed Shortest Paths in Polyhedral Environments. Springer, 2007.

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40

Klette, Reinhard, and Li Fajie. Euclidean Shortest Paths: Exact or Approximate Algorithms. Springer, 2011.

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41

Baltsan, Avikam, and M. Sharir. On Shortest Paths Between Two Convex Polyhedra. Creative Media Partners, LLC, 2018.

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42

Klette, Reinhard, and Fajie Li. Euclidean Shortest Paths: Exact or Approximate Algorithms. Springer London, Limited, 2014.

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43

Ziegelmann, Dr Mark. Constrained Shortest Paths and Related Problems: Constrained Network Optimization. VDM Verlag Dr. Müller, 2010.

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44

Newman, Mark. Computer algorithms. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198805090.003.0008.

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This chapter introduces some of the fundamental concepts of numerical network calculations. The chapter starts with a discussion of basic concepts of computational complexity and data structures for storing network data, then progresses to the description and analysis of algorithms for a range of network calculations: breadth-first search and its use for calculating shortest paths, shortest distances, components, closeness, and betweenness; Dijkstra's algorithm for shortest paths and distances on weighted networks; and the augmenting path algorithm for calculating maximum flows, minimum cut sets, and independent paths in networks.
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45

Brandimarte, Paolo. From Shortest Paths to Reinforcement Learning: A MATLAB-Based Tutorial on Dynamic Programming. Springer International Publishing AG, 2022.

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46

Brandimarte, Paolo. From Shortest Paths to Reinforcement Learning: A MATLAB-Based Tutorial on Dynamic Programming. Springer International Publishing AG, 2021.

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47

Shiffrar, Maggie, and Christina Joseph. Paths of Apparent Human Motion Follow Motor Constraints. Oxford University Press, 2017. http://dx.doi.org/10.1093/acprof:oso/9780199794607.003.0077.

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The phenomenon of apparent motion, or the illusory perception of movement from rapidly displayed static images, provides an excellent platform for the study of how perceptual systems analyze input over time and space. Studies of the human body in apparent motion further suggest that the visual system is also influenced by an observer’s motor experience with his or her own body. As a result, the human visual system sometimes processes human movement differently from object movement. For example, under apparent motion conditions in which inanimate objects appear to traverse the shortest possible paths of motion, human motion instead appears to follow longer, biomechanically plausible paths of motion. Psychophysical and brain imaging studies converge in supporting the hypothesis that the visual analysis of human movement differs from the visual analysis of nonhuman movements whenever visual motion cues are consistent with an observer’s motor repertoire of possible human actions.
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48

Ortega-Arranz, Hector, Diego R. Llanos, and Arturo Gonzalez-Escribano. Shortest Path Problem. Morgan & Claypool Publishers, 2014.

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49

The shortest path. FAO, 2021. http://dx.doi.org/10.4060/cb7278en.

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50

Mann, Peter. Differential Equations. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198822370.003.0035.

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This chapter presents the general formulation of the calculus of variations as applied to mechanics, relativity and field theories. The calculus of variations is a common mathematical technique used throughout classical mechanics. First developed by Euler to determine the shortest paths between fixed points along a surface, it was applied by Lagrange to mechanical problems in analytical mechanics. The variational problems in the chapter have been simplified for ease of understanding upon first introduction, in order to give a general mathematical framework. This chapter takes a relaxed approach to explain how the Euler–Lagrange equation is derived using this method. It also discusses first integrals. The chapter closes by defining the functional derivative, which is used in classical field theory.
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