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Computing Shortest Paths with Uncertainty [chapter]

T. Feder, R. Motwani, L. O'Callaghan, C. Olston, R. Panigrahy
<span title="">2003</span> <i title="Springer Berlin Heidelberg"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
We consider the problem of estimating the length of a shortest path in a DAG whose edge lengths are known only approximately but can be determined exactly at a cost.  ...  In particular, we study the problem of nding the cheapest set of edges such that, if exactly these edges are queried, the length of the shortest path will be known, within an additive 0 that is given as  ...  The length of a path in G can be computed with uncertainty and represented as an interval containing the exact length.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/3-540-36494-3_33">doi:10.1007/3-540-36494-3_33</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/f54dw34arbgdfom5x22apcylkq">fatcat:f54dw34arbgdfom5x22apcylkq</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20041217213320/http://www-2.cs.cmu.edu:80/~olston/publications/sp.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/38/ae/38aecacfa72099c5f8da4cb221826b29a56ca661.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/3-540-36494-3_33"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

Probabilistic Shortest Path Tractography in DTI Using Gaussian Process ODE Solvers [chapter]

Michael Schober, Niklas Kasenburg, Aasa Feragen, Philipp Hennig, Søren Hauberg
<span title="">2014</span> <i title="Springer International Publishing"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
Finally, we provide a quantitative evaluation of different metrics and algorithms showing that the adjoint metric [8] combined with our algorithm produces paths which agree most often with experts.  ...  We use the uncertainty both in visualization of individual tracts as well as in heat maps of tract locations.  ...  This captures the uncertainty inherent in the shortest path computation which can be used when visualizing the results.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-319-10443-0_34">doi:10.1007/978-3-319-10443-0_34</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/w4i665ecjrf47mwcbuapbdmdz4">fatcat:w4i665ecjrf47mwcbuapbdmdz4</a> </span>
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Algorithms and Uncertainty Sets for Data-Driven Robust Shortest Path Problems [article]

André Chassein and Trivikram Dokka and Marc Goerigk
<span title="2018-02-09">2018</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
We consider robust shortest path problems, where the aim is to find a path that optimizes the worst-case performance over an uncertainty set containing all relevant scenarios for arc costs.  ...  We then compare the performance of the resulting robust paths within and outside the sample, which allows us to draw conclusions what the most suited uncertainty set is.  ...  They are complemented with Figure 6 showing the total computation times for the methods over all 200 shortest path calculations.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1802.04149v1">arXiv:1802.04149v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/ncpbdr7sibbzvog25z4h2uairy">fatcat:ncpbdr7sibbzvog25z4h2uairy</a> </span>
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A Greedy Algorithm for Fuzzy Shortest Path Problem using Quasi-Gaussian Fuzzy Weights

Madhushi Verma, K. K. Shukla
<span title="">2013</span> <i title="IGI Global"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/e7ukxbzfqfghpkwsprkpgo6wje" style="color: black;">International Journal of Fuzzy System Applications</a> </i> &nbsp;
To model the uncertainty involved, for the first time we use the Gaussian fuzzy numbers as weights and a method has been presented in this paper to determine the fuzzy shortest path.  ...  The issue of performing fuzzy arithmetic operations to calculate the fuzzy shortest path length and the corresponding fuzzy shortest path in the network has been addressed and to tackle it the concept  ...  This gives rise to the fuzzy shortest path problem (FSPP) where the weights are taken as fuzzy numbers in order to deal with the uncertainty.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.4018/ijfsa.2013040104">doi:10.4018/ijfsa.2013040104</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/odvpeeqpd5afhl7cokpjjplpwa">fatcat:odvpeeqpd5afhl7cokpjjplpwa</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20190226013950/http://pdfs.semanticscholar.org/6ac7/de33a9befbb4150757572efb29387253f40b.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/6a/c7/6ac7de33a9befbb4150757572efb29387253f40b.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.4018/ijfsa.2013040104"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> Publisher / doi.org </button> </a>

An Experimental Comparison of Uncertainty Sets for Robust Shortest Path Problems [article]

Trivikram Dokka, Marc Goerigk
<span title="2017-04-27">2017</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
This lead to the development of robust shortest path problems, where all possible arc travel times are contained in a so-called uncertainty set of possible outcomes.  ...  Research in robust shortest path problems typically assumes this set to be given, and provides complexity results as well as algorithms depending on its shape.  ...  They are complemented with Figure 4 showing the total computation times for the methods over all 200 shortest path calculations.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1704.08470v1">arXiv:1704.08470v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/eky3rdhi2nasdhifalv4pmgkde">fatcat:eky3rdhi2nasdhifalv4pmgkde</a> </span>
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Page 22 of Journal of Research and Practice in Information Technology Vol. 25, Issue 1 [page]

<span title="">1993</span> <i title="Australian Computer Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_journal-of-research-practice-information-technology" style="color: black;">Journal of Research and Practice in Information Technology </a> </i> &nbsp;
of the shortest path.  ...  Specifically, we present “performance guarantees” for the impeded robot; that is, we measure the ratio of the length of the path computed by the heuristics to the length of the shortest path.  ... 
<span class="external-identifiers"> </span>
<a target="_blank" rel="noopener" href="https://archive.org/details/sim_journal-of-research-practice-information-technology_1993-02_25_1/page/22" title="read fulltext microfilm" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Archive [Microfilm] <div class="menu fulltext-thumbnail"> <img src="https://archive.org/serve/sim_journal-of-research-practice-information-technology_1993-02_25_1/__ia_thumb.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a>

An Experimental Comparison of Uncertainty Sets for Robust Shortest Path Problems

Trivikram Dokka, Marc Goerigk, Marc Herbstritt
<span title="2017-09-01">2017</span> <i > <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/cwlyu7p66nbrzna5rkunsyazti" style="color: black;">Algorithmic Approaches for Transportation Modeling, Optimization, and Systems</a> </i> &nbsp;
This led to the development of robust shortest path problems, where all possible arc travel times are contained in a so-called uncertainty set of possible outcomes.  ...  Research in robust shortest path problems typically assumes this set to be given, and provides complexity results as well as algorithms depending on its shape.  ...  They are complemented with Figure 4 showing the total computation times for the methods over all 200 shortest path calculations.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.4230/oasics.atmos.2017.16">doi:10.4230/oasics.atmos.2017.16</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/atmos/DokkaG17.html">dblp:conf/atmos/DokkaG17</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/ywm5nt34qfff7fe2u7i5xoudz4">fatcat:ywm5nt34qfff7fe2u7i5xoudz4</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20220307212159/https://drops.dagstuhl.de/opus/volltexte/2017/7903/pdf/OASIcs-ATMOS-2017-16.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/66/aa/66aaec13852558c214df6ff37a6333e7ff6e72a2.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.4230/oasics.atmos.2017.16"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> Publisher / doi.org </button> </a>

Shortest path problem with uncertain arc lengths

Yuan Gao
<span title="">2011</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/nkrwe4pmozafvnd72yxufztpku" style="color: black;">Computers and Mathematics with Applications</a> </i> &nbsp;
Uncertainty theory provides a new tool to deal with the shortest path problem with nondeterministic arc lengths.  ...  With help from the operational law of uncertainty theory, this paper gives the uncertainty distribution of the shortest path length.  ...  In this paper, we have investigated the uncertainty distribution of the shortest path length, the α-shortest path, and the most shortest path in networks with uncertain arc lengths.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.camwa.2011.07.058">doi:10.1016/j.camwa.2011.07.058</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/5i3kgnrbnfhxjkvaiz7cpymjti">fatcat:5i3kgnrbnfhxjkvaiz7cpymjti</a> </span>
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An efficient solution algorithm for solving multi-class reliability-based traffic assignment problem

Bi Yu Chen, William H.K. Lam, Agachai Sumalee, Hu Shao
<span title="">2011</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/q5bfnofiffaoldjsebw7gavjjm" style="color: black;">Mathematical and computer modelling</a> </i> &nbsp;
Traffic assignment problem Multi-user classes Reliability-based user equilibrium Reliable shortest path problem Travel time uncertainty a b s t r a c t The multi-class reliability-based user equilibrium  ...  (RUE) problem has been intensively studied in recent years, as it can capture the route choice behaviors of users with heterogeneous risk-aversion under demand and supply uncertainties.  ...  The proposed shortest path algorithm is then, further incorporated into a path-based traffic assignment algorithm using a column generation technique.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.mcm.2011.04.015">doi:10.1016/j.mcm.2011.04.015</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/uk4m2bkuzjcwfeywy6nnq6n2mi">fatcat:uk4m2bkuzjcwfeywy6nnq6n2mi</a> </span>
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Methods to Determine Node Centrality and Clustering in Graphs with Uncertain Structure [article]

Joseph J. Pfeiffer III, Jennifer Neville
<span title="2011-04-02">2011</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
In order to represent and reason with these types of uncertainty, we move beyond the discrete graph framework and develop social network measures based on a probabilistic graph representation.  ...  More specifically, we develop measures of path length, betweenness centrality, and clustering coefficient---one set based on sampling and one based on probabilistic paths.  ...  Now, when there is uncertainty about the edges in G, we can compute the expected average shortest path length by considering the distribution of graphs G.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1104.0319v1">arXiv:1104.0319v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/mi3zz6k4jneulkzzqwmp2rxtne">fatcat:mi3zz6k4jneulkzzqwmp2rxtne</a> </span>
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An Inverse Shortest Path Problem on an Uncertain Graph

Jian Zhou, Fan Yang, Ke Wang
<span title="2014-09-07">2014</span> <i title="Academy Publisher"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/drz46fz5hfbfnerxeguotm7kmy" style="color: black;">Journal of Networks</a> </i> &nbsp;
In this paper, the inverse shortest path problem is considered on a graph with uncertain edge weights.  ...  The inverse shortest path problem is to minimize the modification on the edge weights such that a predetermined path becomes the shortest one from the origin to the destination with respect to the new  ...  [12] studied the computational complexity of the inverse shortest path problem with upper bounds on the sum of weights of the shortest path from the origin to the destination under l 2 norm, and proved  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.4304/jnw.9.9.2353-2359">doi:10.4304/jnw.9.9.2353-2359</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/amoujf3verelznsbfucxtwgitq">fatcat:amoujf3verelznsbfucxtwgitq</a> </span>
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Planning Reliable Paths With Pose SLAM

Rafael Valencia, Marti Morta, Juan Andrade-Cetto, Josep M. Porta
<span title="">2013</span> <i title="Institute of Electrical and Electronics Engineers (IEEE)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/dg2bd7saqzaj3e4myjqwziwpa4" style="color: black;">IEEE Transactions on robotics</a> </i> &nbsp;
The maps built by standard feature-based SLAM methods cannot be directly used to compute paths for navigation, unless enriched with obstacle or traversability information with the consequent increase in  ...  Here, we propose a method that directly uses the Pose SLAM graph of constraints to determine the path between two robot configurations with lowest accumulated pose uncertainty, i.e., the most reliable  ...  Fig. 11 . 11 Real path execution of the shortest and most reliable paths to the goal with our mobile robot. The green line shows the planned paths computed with our method.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/tro.2013.2257577">doi:10.1109/tro.2013.2257577</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/66ftwgtadnadtka5nsk6plchgi">fatcat:66ftwgtadnadtka5nsk6plchgi</a> </span>
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Search using multiple UAVs with flight time constraints

P.B. Sujit, D. Ghose
<span title="">2004</span> <i title="Institute of Electrical and Electronics Engineers (IEEE)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/a4fagdf2dnbrlghfkdsaomn6vm" style="color: black;">IEEE Transactions on Aerospace and Electronic Systems</a> </i> &nbsp;
The search algorithm is based on the k-shortest path algorithm that maximizes the effectiveness of the search in terms of searching through the maximum uncertainty region, given a constraint on the endurance  ...  We compare the performance of this algorithm with a random search and a greedy strategy search. We also implement the algorithm for the case of multiple UAVs searching an unknown region.  ...  Marzal on the use of their k-shortest path algorithm.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/taes.2004.1310000">doi:10.1109/taes.2004.1310000</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/l7o3leq3jrgkxdpw6x5bcsiiba">fatcat:l7o3leq3jrgkxdpw6x5bcsiiba</a> </span>
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Global Uncertainty-based Selection of Relative Poses for Multi Camera Calibration

F. Bajramovic, J. Denzler
<span title="">2008</span> <i title="British Machine Vision Association"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/6bfo5625nvdfvbgyf7ldi5wmfe" style="color: black;">Procedings of the British Machine Vision Conference 2008</a> </i> &nbsp;
We show that our criterion is equivalent to computing a shortest subgraph consisting of shortest triangle connected paths and provide an efficient algorithm.  ...  We present theoretically sound local and global uncertainty measures on relative poses and a selection criterion based on these measures.  ...  Hence, we use shortest paths from a common relative pose to all cameras. We choose the reference edge e ∈ E with mimimum total uncertainty ω(U).  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.5244/c.22.74">doi:10.5244/c.22.74</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/bmvc/BajramovicD08.html">dblp:conf/bmvc/BajramovicD08</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/npu2cnxub5cu7iu52frphfv67e">fatcat:npu2cnxub5cu7iu52frphfv67e</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170809114913/http://hera.inf-cv.uni-jena.de:6680/pdf/Bajramovic08:GUS.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/35/d3/35d3895cffeccc76d447f6db1f406ff450d7573b.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.5244/c.22.74"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> Publisher / doi.org </button> </a>

Inverse Shortest Path in a Graph with Rough Edge Weights

Sagarika Biswal, S. P.
<span title="2016-08-16">2016</span> <i title="Foundation of Computer Science"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/b637noqf3vhmhjevdfk3h5pdsu" style="color: black;">International Journal of Computer Applications</a> </i> &nbsp;
The inverse shortest path problem occurs mostly in reconstruction type of problems where, minimum modifications of the edge weights of a network are made to make a predetermined path to be shortest.  ...  In order to deal with the belief degree rationally, the uncertainty theory was developed by Liu [5] in 2007 and subsequently applied the theory to model the shortest path problem.  ...  P 0 is the predetermined path from origin to destination which is required to be the shortest path with respect to the new weights. The inverse shortest path problem can be formulated as follows.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.5120/ijca2016911143">doi:10.5120/ijca2016911143</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/acpms3gi5zae5etl3s7oovqvsu">fatcat:acpms3gi5zae5etl3s7oovqvsu</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20180602220912/https://www.ijcaonline.org/archives/volume148/number6/biswal-2016-ijca-911143.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/4c/22/4c221eef2a381b84cb9d30080e0291744a7696c2.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.5120/ijca2016911143"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> Publisher / doi.org </button> </a>
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