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Page 3310 of Mathematical Reviews Vol. , Issue 2004d [page]

2004 Mathematical Reviews  
Linear time algorithms are pre- sented to solve the w-path partition problem for any path or tree with nonnegative edge-weights.  ...  The best previous time bound for recognizing these classes of graphs is O(m). Welsh-Powell opposition graphs are recognized in O(n?) time, improving the previous bound of O(n*).  ... 

Characterizing LR-visibility polygons and related problems☆☆The extended abstract of this paper was presented at the Tenth Canadian Conference on Computational Geometry, 1998

Binay K. Bhattacharya, Subir Kumar Ghosh
2001 Computational geometry  
Our algorithm for this problem checks LR-visibility by traversing shortest path trees rooted at s and t in DFS manner and it runs in linear time.  ...  Using our characterization of LR-visibility polygons, we show that the shortest path tree rooted at a vertex or a boundary point can be computed in linear time for a class of polygons which contains LR-visibility  ...  The shortest path trees rooted at s and t can be computed in linear time by the algorithm of Guibas et al. [11] .  ... 
doi:10.1016/s0925-7721(00)00024-9 fatcat:a5ktlbhvcnfildru3vbdk2jwgi

Computing Minimum Cycle Bases in Weighted Partial 2-Trees in Linear Time [article]

Carola Doerr, G. Ramakrishna, Jens M. Schmidt
2014 arXiv   pre-print
We present a linear time algorithm for computing an implicit linear space representation of a minimum cycle basis (MCB) in weighted partial 2-trees, i.e., graphs of treewidth two.  ...  an implicit O(n n) space representation of an MCB in O(n ^5 n) time---by a polylog factor for the special case of partial 2-trees.  ...  Partial 2-trees can be recognized in linear time [4] . Our main result is a linear time algorithm for computing an implicit O(n)-space representation of a minimum cycle basis in partial 2-trees.  ... 
arXiv:1303.0728v2 fatcat:lg4znhrg3rao7acfxlyilj2g74

On orientations and shortest paths

Rafael Hassin, Nimrod Megiddo
1989 Linear Algebra and its Applications  
An orientation is called ideal with respect to a given set of pairs of vertices if it does not increase the shortest-path distances between the members of any of the pairs.  ...  A polynomial-time algorithm is given for constructing an ideal orientation with respect to two given pairs and any positive edge-lengths, or else recognizing that no such orientation exists.  ...  We first direct the tree Tj towards c. This is a preprocessing step rather than the actual orientation, and it takes linear time in the size of Tj.  ... 
doi:10.1016/0024-3795(89)90481-3 fatcat:w5f54xcluret5e3tekxskfmv4i

A note on the subgraphs of the (2×∞)-grid

Josep Díaz, Marcin Kamiński, Dimitrios M. Thilikos
2010 Discrete Mathematics  
We give a linear-time algorithm checking whether a graph is a subgraph of the (2 × k)-grid for some value of k. Our algorithm is based on a detailed characterization of the structure of such graphs.  ...  be performed in time O(|T |) and procedure recognize-tree also runs in time O(|T |).  ...  can be easily solved in linear time.  ... 
doi:10.1016/j.disc.2009.03.046 fatcat:enx3pmjm4nefxggq4jpvnqegmm

Page 5551 of Mathematical Reviews Vol. , Issue 95i [page]

1995 Mathematical Reviews  
Recognizing shortest-path trees in linear time. (English summary) Inform. Process. Lett. 52 (1994), no!2, 77-85.  ...  A shortest- path tree of graph G is a rooted spanning tree of G such that, from the root to any vertex, the path going along only tree edges is a shortest path.  ... 

Time-dependent shortest paths in bounded treewidth graphs [article]

Glencora Borradaile, Morgan Shirley
2017 arXiv   pre-print
We present a proof that the number of breakpoints in the arrival function between two terminals in graphs of treewidth w is n^O(^2 w) when the edge arrival functions are piecewise linear.  ...  For instance, the treewidth of any tree graph is 1. Time-dependent shortest paths Consider a graph G = (V, E).  ...  Polynomial bounds on arrival functions We consider time-dependent shortest paths in graphs with continuous piecewise-linear edge arrival functions.  ... 
arXiv:1706.01508v1 fatcat:mthvbgby3ffk7mvys6wnox4wcy

Fast recognition algorithms for classes of partial cubes

Boštjan Brešar, Wilfried Imrich, Sandi Klavžar
2003 Discrete Applied Mathematics  
This paper exhibits classes of partial cubes that are not median graphs but can be recognized in O(m log n) steps.  ...  In general, one can recognize whether a graph on n vertices and m edges is a partial cube in O(mn) steps, faster recognition algorithms are only known for median graphs.  ...  Acknowledgements We wish to thank the referees for helpful remarks and for the question about the linearity of Algorithm (A) in n.  ... 
doi:10.1016/s0166-218x(02)00416-x fatcat:z5tshewwrzhm3gxxnrs6u6yduy

Micro crack detection with Dijkstra's shortest path algorithm

Christina Gunkel, Alexander Stepper, Arne C. Müller, Christine H. Müller
2011 Machine Vision and Applications  
It uses a shortest path algorithm for detecting micro cracks in situations where the cracks are surrounded by plastic deformations and where a discrimination between cracks and plastic deformations is  ...  Then the crack paths are determined by * Research supported by the SFB/TR TRR 30 Project D6 Dijkstra's algorithm as longest shortest paths through the darkest parts of the crack clusters.  ...  We are also grateful that Janine Keppler did all the manual labor for calculating the confidence intervals for UTHSCSA Image Tool and that she supported us in finding good threshold values.  ... 
doi:10.1007/s00138-011-0324-1 fatcat:una36g44k5bs7il4b2qldwweme

Page 2812 of Mathematical Reviews Vol. , Issue 92e [page]

1992 Mathematical Reviews  
While Paterson and Wegman’s linear unification algorithm has the lowest time complexity in the worst case, it requires an impor- tant overhead to be implemented.  ...  Summary: “Efficient implementations of Dijkstra’s shortest path algorithm are investigated. A new data structure, called the radix heap, is proposed for use in this algorithm.  ... 

Page 7904 of Mathematical Reviews Vol. , Issue 99k [page]

1999 Mathematical Reviews  
Introduction: “The single source shortest path (SSSP) problem is that of computing a shortest path from a specified vertex to every other vertex on a network.  ...  “In this paper, we present a linear time algorithm to solve the SSSP problem for ladder networks.  ... 

Page 1594 of Mathematical Reviews Vol. , Issue 93c [page]

1993 Mathematical Reviews  
The subgraph and the auxiliary structure are used to construct the tree representation of the original graph in linear time.  ...  Fabrizio Luccio (Pisa) 93c:68078 68R10 05C40 05C85 68Q25 Jamison, Beverly; Olariu, Stephan (1-ODM-C) Recognizing P,-sparse graphs in linear time. SIAM J. Comput. 21 (1992), no. 2, 381-406.  ... 

Fast recognition of classes of almost-median graphs

Wilfried Imrich, Alenka Lipovec, Iztok Peterin, Petra Žigert
2007 Discrete Mathematics  
Moreover, planar almost-median graphs can be recognized in linear time.  ...  In this paper it is shown that a class of almost-median graphs that includes all planar almost-median graphs can be recognized in O(m log n) time, where n denotes the number of vertices and m the number  ...  A bipartite outerplanar graph can be embedded into the hypercube in linear time. Proof. Let G be a bipartite outerplanar graph. By Proposition 6 all faces of G can be recognized in linear time.  ... 
doi:10.1016/j.disc.2006.07.011 fatcat:q777faqnf5hjfcrnvziltgflhq

Page 2422 of Mathematical Reviews Vol. , Issue 96d [page]

1996 Mathematical Reviews  
sorting in linear time.  ...  Summary: “In this paper we continue the study of the path length of trees with known fringe as initiated by R. Klein and D. Wood [J. Assoc. Comput.  ... 

Holiest Minimum-Cost Paths and Flows in Surface Graphs [article]

Jeff Erickson and Kyle Fox and Luvsandondov Lkhamsuren
2018 arXiv   pre-print
Finally, we open the black box in order to generalize a recent linear-time algorithm for multiple-source shortest paths in unweighted undirected planar graphs to work in arbitrary orientable surfaces.  ...  We describe a simple deterministic lexicographic perturbation scheme that guarantees uniqueness of minimum-cost flows and shortest paths in G. The perturbations take O(gn) time to compute.  ...  Applications of Linear-time Algorithm We now turn to applications of the linear-time multiple-source shortest paths algorithm described in the previous section.  ... 
arXiv:1804.01045v1 fatcat:k5uolrcigzdurjfyvo2buj7h4a
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