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Academic literature on the topic 'Shortest paths'

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Published: 4 June 2021
Last updated: 4 April 2023

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Journal articles on the topic "Shortest paths"

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Kamiński, Marcin, Paul Medvedev, and Martin Milanič. "Shortest paths between shortest paths." Theoretical Computer Science 412, no. 39 (September 2011): 5205–10. http://dx.doi.org/10.1016/j.tcs.2011.05.021.

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Torchiani, Carolin, Jan Ohst, David Willems, and Stefan Ruzika. "Shortest Paths with Shortest Detours." Journal of Optimization Theory and Applications 174, no. 3 (July 25, 2017): 858–74. http://dx.doi.org/10.1007/s10957-017-1145-9.

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Lofgren, Christopher B. "Reconstructing shortest paths." Annals of Operations Research 20, no. 1 (December 1989): 179–85. http://dx.doi.org/10.1007/bf02216928.

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Klein, Cerry M. "Fuzzy shortest paths." Fuzzy Sets and Systems 39, no. 1 (January 1991): 27–41. http://dx.doi.org/10.1016/0165-0114(91)90063-v.

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CHEN, JINDONG, and YIJIE HAN. "SHORTEST PATHS ON A POLYHEDRON, Part I: COMPUTING SHORTEST PATHS." International Journal of Computational Geometry & Applications 06, no. 02 (June 1996): 127–44. http://dx.doi.org/10.1142/s0218195996000095.

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We present an algorithm for determining the shortest path between any two points along the surface of a polyhedron which need not be convex. This algorithm also computes for any source point on the surface of a polyhedron the inward layout and the subdivision of the polyhedron which can be used for processing queries of shortest paths between the source point and any destination point. Our algorithm uses a new approach which deviates from the conventional “continuous Dijkstra” technique. Our algorithm has time complexity O(n2) and space complexity Θ(n).
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Matthew Carlyle, W., and R. Kevin Wood. "Near-shortest and K-shortest simple paths." Networks 46, no. 2 (2005): 98–109. http://dx.doi.org/10.1002/net.20077.

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Goldstone, Richard, Rachel Roca, and Robert Suzzi Valli. "Shortest Paths on Cubes." College Mathematics Journal 52, no. 2 (March 15, 2021): 121–32. http://dx.doi.org/10.1080/07468342.2021.1866944.

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Elkin, Michael. "Computing almost shortest paths." ACM Transactions on Algorithms 1, no. 2 (October 2005): 283–323. http://dx.doi.org/10.1145/1103963.1103968.

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Cheng, Siu-Wing, and Jiongxin Jin. "Approximate Shortest Descending Paths." SIAM Journal on Computing 43, no. 2 (January 2014): 410–28. http://dx.doi.org/10.1137/130913808.

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Barma, M. "Shortest paths in percolation." Journal of Physics A: Mathematical and General 18, no. 6 (April 21, 1985): L277—L283. http://dx.doi.org/10.1088/0305-4470/18/6/003.

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Dissertations / Theses on the topic "Shortest paths"

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Nagubadi, RadhaKrishna. "K Shortest Path Implementation." Thesis, Linköpings universitet, Databas och informationsteknik, 2013. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-95451.

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The problem of computing K shortest loopless paths, or ranking of the K shortest loopless paths between a pair of given vertices in a network is a well-studied generalization of shortest path problem. The K shortest paths problem determines not only one shortest path but the K best shortest paths from s to t in an increasing order of weight of the paths. Yen’s algorithm is known to be the efficient and widely used algorithm for determining K shortest loopless paths. Here, we introduce a new algorithm by modifying the Yen’s algorithm in the following way: instead of removing the vertices and the edges from the graph, we store them in two different sets. Then we modified the Dijkstra’s algorithm by taking these two sets into consideration. Thus the algorithm applies glass box methodology by using the modified Dijkstra’s algorithm for our dedicated purpose. Thus the efficiency is improved. The computational results conducted over different datasets, shows the proposed algorithm has better performance results.
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Shinn, Tong-Wook. "Combining Shortest Paths, Bottleneck Paths and Matrix Multiplication." Thesis, University of Canterbury. Computer Science and Software Engineering, 2014. http://hdl.handle.net/10092/9740.

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We provide a formal mathematical definition of the Shortest Paths for All Flows (SP-AF) problem and provide many efficient algorithms. The SP-AF problem combines the well known Shortest Paths (SP) and Bottleneck Paths (BP) problems, and can be solved by utilising matrix multiplication. Thus in our research of the SP-AF problem, we also make a series of contributions to the underlying topics of the SP problem, the BP problem, and matrix multiplication. For the topic of matrix multiplication we show that on an n-by-n two dimensional (2D) square mesh array, two n-by-n matrices can be multiplied in exactly 1.5n ‒ 1 communication steps. This halves the number of communication steps required by the well known Cannon’s algorithm that runs on the same sized mesh array. We provide two contributions for the SP problem. Firstly, we enhance the breakthrough algorithm by Alon, Galil and Margalit (AGM), which was the first algorithm to achieve a deeply sub-cubic time bound for solving the All Pairs Shortest Paths (APSP) problem on dense directed graphs. Our enhancement allows the algorithm by AGM to remain sub-cubic for larger upper bounds on integer edge costs. Secondly, we show that for graphs with n vertices, the APSP problem can be solved in exactly 3n ‒ 2 communication steps on an n-by-n 2D square mesh array. This improves on the previous result of 3.5n communication steps achieved by Takaoka and Umehara. For the BP problem, we show that we can compute the bottleneck of the entire graph without solving the All Pairs Bottleneck Paths (APBP) problem, resulting in a much more efficient time bound. Finally we define an algebraic structure called the distance/flow semi-ring to formally introduce the SP-AF problem, and we provide many algorithms for solving the Single Source SP-AF (SSSP-AF) problem and the All Pairs SP-AF (APSP-AF) problem. For the APSP-AF problem, algebraic algorithms are given that utilise faster matrix multiplication over a ring.
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Zhao, Hong Jun. "Towards online shortest paths computation." Thesis, University of Macau, 2011. http://umaclib3.umac.mo/record=b2550689.

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Chénier, Christian. "Shortest paths in weighted polygons." Thesis, University of Ottawa (Canada), 1996. http://hdl.handle.net/10393/10034.

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Consider a polygon P and two points $p,\ q\in P.$ Suppose that to move from p to q, we can travel along the edges of P or through the interior of P. Assume that the speed at which we can travel along the edges of P is one unit per second, and the travel speed through the interior of P is 1/s units per seconds ($s>1$). The problem consists of finding the shortest path between p and q. We solve this problem in O(n) time for convex polygons. For simple polygons, we show two algorithms. The first algorithm runs in O(E log n) time using O(E) space (where E is the size of the visibility of P). The second algorithm has two variations which both require O(n E log n) preprocessing (where E is the number of edges in the visibility graph of P). The first variation takes O(n log n) query time and O($n\sp2$ log n) space. The second variation has a query time of O(n log$\sp2$ n) but uses $O(n\sp2)$ space. For the orthogonal case, we give a O(E) time and space algorithm.
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Gao, Guo-Gang. "Planning shortest paths amongst discs." Thesis, McGill University, 1988. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=64080.

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Moffat, Alistair. "Fast algorithms for shortest paths." Thesis, University of Canterbury. Computer Science, 1985. http://hdl.handle.net/10092/7926.

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The problem of finding all shortest paths in a non-negatively weighted directed graph is addressed, and a number of new algorithms for solving this problem on a graph of n vertices and m edges are given. The first of these requires in the worst case min { 2mn, nᶟ } + O(n²˙⁵ ) addition and binary comparisons on path and edge costs, improving the previous bound (Dantzig, 1960) of n³ + O(n²logn) operations in a computational model where addition and comparison are the only operations permitted on path costs. The second algorithm presented, and the main result of this thesis, has an expected running time of O(n²logn) on graphs with edge weights drawn from an endpoint independent probability distribution, improving asymptotically the previous bound (Bloniarz, 1980) of O(n²lognlog*n), and resolving a major open problem (Bloniarz, 1983) concerning the complexity of the all pairs shortest path problem. Some variations on the new algorithm are analysed, and it is shown that two superficially good heuristics have a bad effect on the running time. A third variation reduces the worst case running time to O(nᶟ), making the method competitive with the O(nᶟ) classical algorithms of Dijkstra (1959) and Floyd (1962). The new algorithm is not just of theoretical interest - experimental results are given that show the algorithm to be fast for operational use, running an order of magnitude faster than the algorithms of Dijkstra and Floyd. The closely linked problem of distance matrix multiplication is also investigated, and a number of fast average time distance matrix multiplication algorithms are given.
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Chase, Melissa. "Shortest Path Problems: Multiple Paths in a Stochastic Graph." Scholarship @ Claremont, 2003. https://scholarship.claremont.edu/hmc_theses/143.

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Shortest path problems arise in a variety of applications ranging from transportation planning to network routing among others. One group of these problems involves finding shortest paths in graphs where the edge weights are defined by probability distributions. While some research has addressed the problem of finding a single shortest path, no research has been done on finding multiple paths in such graphs. This thesis addresses the problem of finding paths for multiple robots through a graph in which the edge weights represent the probability that each edge will fail. The objective is to find paths for n robots that maximize the probability that at least k of them will arrive at the destination. If we make certain restrictions on the edge weights and topology of the graph, this problem can be solved in O(n log n)time. If we restrict only the topology, we can find approximate solutions which are still guaranteed to be better than the single most reliable path.
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Wang, I.-Lin. "Shortest paths and multicommodity network flows." Diss., Georgia Institute of Technology, 2003. http://hdl.handle.net/1853/23304.

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Tabatabai, Bijan Oni. "An investigation of shortest paths algorithms." Thesis, Durham University, 1987. http://etheses.dur.ac.uk/6685/.

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In this work, we classify the shortest path problems, review all source algorithms and analyse the different implementations of single source algorithms using various list structures and labelling techniques. Furthermore, we study the Sensitivity Analysis of one-to-all problems and present an algorithm, Senet, for their Post Optimality Analysis. Senet determines all the critical values for the weight of an arc (which could be optimal, non-optimal or non-existant) at which the optimal solution changes. Senet also provides the updated optimal solution for every range formed by two successive critical values.
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Garcia, Renan. "Resource constrained shortest paths and extensions." Diss., Atlanta, Ga. : Georgia Institute of Technology, 2009. http://hdl.handle.net/1853/28268.

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Thesis (M. S.)--Industrial and Systems Engineering, Georgia Institute of Technology, 2009.
Committee Co-Chair: George L. Nemhauser; Committee Co-Chair: Shabbir Ahmed; Committee Member: Martin W. P. Savelsbergh; Committee Member: R. Gary Parker; Committee Member: Zonghao Gu.
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Books on the topic "Shortest paths"

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

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

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

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

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

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

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

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Book chapters on the topic "Shortest paths"

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Neumann, Frank, and Carsten Witt. "Shortest Paths." In Bioinspired Computation in Combinatorial Optimization, 111–31. Berlin, Heidelberg: Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-16544-3_8.

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Sierksma, Gerard, and Diptesh Ghosh. "Shortest Paths." In International Series in Operations Research & Management Science, 17–35. Boston, MA: Springer US, 2009. http://dx.doi.org/10.1007/978-1-4419-5513-5_4.

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Korte, Bernhard, and Jens Vygen. "Shortest Paths." In Algorithms and Combinatorics, 157–71. Berlin, Heidelberg: Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-24488-9_7.

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Hochstättler, Winfried, and Alexander Schliep. "Shortest Paths." In CATBox, 53–67. Berlin, Heidelberg: Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-642-03822-8_5.

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Korte, Bernhard, and Jens Vygen. "Shortest Paths." In Algorithms and Combinatorics, 139–52. Berlin, Heidelberg: Springer Berlin Heidelberg, 2000. http://dx.doi.org/10.1007/978-3-662-21708-5_7.

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Korte, Bernhard, and Jens Vygen. "Shortest Paths." In Algorithms and Combinatorics, 139–52. Berlin, Heidelberg: Springer Berlin Heidelberg, 2002. http://dx.doi.org/10.1007/978-3-662-21711-5_7.

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Shekhar, Shashi, and Hui Xiong. "Shortest Paths." In Encyclopedia of GIS, 1055. Boston, MA: Springer US, 2008. http://dx.doi.org/10.1007/978-0-387-35973-1_1207.

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Goddijn, Aad, Martin Kindt, and Wolfgang Reuter. "Shortest paths." In Geometry with Applications and Proofs, 129–39. Rotterdam: SensePublishers, 2014. http://dx.doi.org/10.1007/978-94-6209-860-2_9.

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Jungnickel, Dieter. "Shortest Paths." In Graphs, Networks and Algorithms, 63–98. Berlin, Heidelberg: Springer Berlin Heidelberg, 1999. http://dx.doi.org/10.1007/978-3-662-03822-2_3.

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Sanders, Peter, and Johannes Singler. "Shortest Paths." In Algorithms Unplugged, 317–24. Berlin, Heidelberg: Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-15328-0_32.

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Conference papers on the topic "Shortest paths"

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Hershberger, John, Valentin Polishchuk, Bettina Speckmann, and Topi Talvitie. "Geometric kth Shortest Paths." In Annual Symposium. New York, New York, USA: ACM Press, 2014. http://dx.doi.org/10.1145/2582112.2595650.

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Elkin, Michael. "Computing almost shortest paths." In the twentieth annual ACM symposium. New York, New York, USA: ACM Press, 2001. http://dx.doi.org/10.1145/383962.383983.

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Cheng, Siu-Wing, and Jiongxin Jin. "Approximate Shortest Descending Paths." In Proceedings of the Twenty-Fourth Annual ACM-SIAM Symposium on Discrete Algorithms. Philadelphia, PA: Society for Industrial and Applied Mathematics, 2013. http://dx.doi.org/10.1137/1.9781611973105.11.

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Eriksson-Bique, Sylvester, John Hershberger, Valentin Polishchuk, Bettina Speckmann, Subhash Suri, Topi Talvitie, Kevin Verbeek, and Hakan Yıldız. "Geometric k Shortest Paths." In Proceedings of the Twenty-Sixth Annual ACM-SIAM Symposium on Discrete Algorithms. Philadelphia, PA: Society for Industrial and Applied Mathematics, 2014. http://dx.doi.org/10.1137/1.9781611973730.107.

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Harutyunyan, Hovhannes A., and Wei Wang. "Broadcasting Algorithm Via Shortest Paths." In 2010 IEEE 16th International Conference on Parallel and Distributed Systems (ICPADS). IEEE, 2010. http://dx.doi.org/10.1109/icpads.2010.110.

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Awerbuch, B. "Randomized distributed shortest paths algorithms." In the twenty-first annual ACM symposium. New York, New York, USA: ACM Press, 1989. http://dx.doi.org/10.1145/73007.73054.

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Tao, Yufei, Cheng Sheng, and Jian Pei. "On k-skip shortest paths." In the 2011 international conference. New York, New York, USA: ACM Press, 2011. http://dx.doi.org/10.1145/1989323.1989368.

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Chen, Danny Z., and Haitao Wang. "Computing Shortest Paths amid Pseudodisks." In Proceedings of the Twenty-Second Annual ACM-SIAM Symposium on Discrete Algorithms. Philadelphia, PA: Society for Industrial and Applied Mathematics, 2011. http://dx.doi.org/10.1137/1.9781611973082.26.

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Bonifaci, Vincenzo, Kurt Mehlhorn, and Girish Varma. "Physarum Can Compute Shortest Paths." In Proceedings of the Twenty-Third Annual ACM-SIAM Symposium on Discrete Algorithms. Philadelphia, PA: Society for Industrial and Applied Mathematics, 2012. http://dx.doi.org/10.1137/1.9781611973099.21.

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Zamazal, Ondřej. "Online ontology shortest paths searcher." In SEMANTiCS '15: 11th International Conference on Semantic Systems. New York, NY, USA: ACM, 2015. http://dx.doi.org/10.1145/2814864.2814894.

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Reports on the topic "Shortest paths"

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Solomonik, Edgar, Aydin Buluc, and James Demmel. Minimizing Communication in All-Pairs Shortest Paths. Fort Belvoir, VA: Defense Technical Information Center, February 2013. http://dx.doi.org/10.21236/ada580350.

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Mount, David M. On Finding Shortest Paths on Convex Polyhedra. Fort Belvoir, VA: Defense Technical Information Center, May 1985. http://dx.doi.org/10.21236/ada166246.

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Zhang, R., and N. Bitar. A Backward-Recursive PCE-Based Computation (BRPC) Procedure to Compute Shortest Constrained Inter-Domain Traffic Engineering Label Switched Paths. RFC Editor, April 2009. http://dx.doi.org/10.17487/rfc5441.

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Zhao, Q., D. Dhody, D. King, Z. Ali, and R. Casellas. PCE-Based Computation Procedure to Compute Shortest Constrained Point-to-Multipoint (P2MP) Inter-Domain Traffic Engineering Label Switched Paths. RFC Editor, August 2014. http://dx.doi.org/10.17487/rfc7334.

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Gao :Q., J., W. Ren, A. Swami, R. Ramanathan, and A. Bar-Noy. Dynamic Shortest Path Algorithms for Hypergraphs. Fort Belvoir, VA: Defense Technical Information Center, January 2012. http://dx.doi.org/10.21236/ada558936.

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Awerbuch, B., and R. G. Gallager. Communication Complexity of Distributed Shortest Path Algorithms. Fort Belvoir, VA: Defense Technical Information Center, June 1985. http://dx.doi.org/10.21236/ada156049.

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Djidjev, Hristo N. Efficient Shortest Path Computations on Multi-GPU Platforms. Office of Scientific and Technical Information (OSTI), August 2013. http://dx.doi.org/10.2172/1091313.

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Carlyle, W. M., Johannes O. Royset, and R. K. Wood. Routing Military Aircraft with a Constrained Shortest-Path Algorithm. Fort Belvoir, VA: Defense Technical Information Center, April 2007. http://dx.doi.org/10.21236/ada486703.

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Allan, D., A. Bragg, and P. Unbehagen. IS-IS Extensions Supporting IEEE 802.1aq Shortest Path Bridging. Edited by D. Fedyk and P. Ashwood-Smith. RFC Editor, April 2012. http://dx.doi.org/10.17487/rfc6329.

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Gantzer, Clark J., Shmuel Assouline, and Stephen H. Anderson. Synchrotron CMT-measured soil physical properties influenced by soil compaction. United States Department of Agriculture, February 2006. http://dx.doi.org/10.32747/2006.7587242.bard.

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Methods to quantify soil conditions of pore connectivity, tortuosity, and pore size as altered by compaction were done. Air-dry soil cores were scanned at the GeoSoilEnviroCARS sector at the Advanced Photon Source for x-ray computed microtomography of the Argonne facility. Data was collected on the APS bending magnet Sector 13. Soil sample cores 5- by 5-mm were studied. Skeletonization algorithms in the 3DMA-Rock software of Lindquist et al. were used to extract pore structure. We have numerically investigated the spatial distribution for 6 geometrical characteristics of the pore structure of repacked Hamra soil from three-dimensional synchrotron computed microtomography (CMT) computed tomographic images. We analyzed images representing cores volumes 58.3 mm³ having average porosities of 0.44, 0.35, and 0.33. Cores were packed with < 2mm and < 0.5mm sieved soil. The core samples were imaged at 9.61-mm resolution. Spatial distributions for pore path length and coordination number, pore throat size and nodal pore volume obtained. The spatial distributions were computed using a three-dimensional medial axis analysis of the void space in the image. We used a newly developed aggressive throat computation to find throat and pore partitioning for needed for higher porosity media such as soil. Results show that the coordination number distribution measured from the medial axis were reasonably fit by an exponential relation P(C)=10⁻C/C0. Data for the characteristic area, were also reasonably well fit by the relation P(A)=10⁻ᴬ/ᴬ0. Results indicates that compression preferentially affects the largest pores, reducing them in size. When compaction reduced porosity from 44% to 33%, the average pore volume reduced by 30%, and the average pore-throat area reduced by 26%. Compaction increased the shortest paths interface tortuosity by about 2%. Soil structure alterations induced by compaction using quantitative morphology show that the resolution is sufficient to discriminate soil cores. This study shows that analysis of CMT can provide information to assist in assessment of soil management to ameliorate soil compaction.
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