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Reconstruction of the Path Graph [article]

Chaya Keller, Yael Stein
2017 arXiv   pre-print
The path graph G(P) of P is an abstract graph whose vertices are non-crossing spanning paths of P, such that two paths are adjacent if one can be obtained from the other by deleting an edge and adding  ...  graph, and then identifies (uniquely) all edges of each path represented by a vertex of G(P).  ...  Acknowledgments The authors are grateful to Gila Morgenstern for her contribution in the first steps of this research.  ... 
arXiv:1801.00328v1 fatcat:q6inqckxsvcsrhidayifwmov4q

SOME RESULTS ON RECONSTRUCTIBILITY OF COLORED GRAPHS

M. Dowd
2014 International Journal of Pure and Applied Mathematics  
In an earlier paper the author has shown that a graph is reconstructible, except possibly if it has a single-block trunk. Here this result is shown for colored graphs.  ...  Some other results on colored graphs are given. In particular it is shown that reconstructibility is false for edge colored graphs.  ...  Let l(p) denote the length of a path. If G is an inseparable V-graph and p is an induced path with l(p) ≥ 4 then G is reconstructible.  ... 
doi:10.12732/ijpam.v95i2.14 fatcat:2dvlx67zgbhhjgudgkjorff7h4

Graph Reconstruction from Path Correlation Data [article]

Gregory Berkolaiko, Nick Duffield, Mahmood Ettehad, Kyriakos Manousakis
2018 arXiv   pre-print
Network tomography aims to infer these edge weights from their pathwise versions measured on a set of intersecting paths between a subset of boundary vertices, and even the underlying graph when this is  ...  We establish necessary and sufficient conditions for a graph to be reconstructible from this information, and describe an algorithm to perform the reconstruction.  ...  graph from reconstructed paths R.  ... 
arXiv:1804.04574v1 fatcat:fhwv6277cba3ffuzc5z2f2xhbq

Maximum Likelihood de novo reconstruction of viral populations using paired end sequencing data [article]

Raunaq Malhotra, Manjari Mukhopadhyay Steven Wu, Allen Rodrigo, Mary Poss, Raj Acharya
2016 arXiv   pre-print
Using the pairing information of reads in our proposed Viral Path Reconstruction Algorithm (ViPRA), we generate a small subset of paths from a De Bruijn graph of reads that serve as candidate paths for  ...  Our proposed method MLEHaplo then generates a maximum likelihood estimate of the viral population using the paths reconstructed by ViPRA.  ...  ACKNOWLEDGMENTS This work was supported by the National Science Foundation (Grant numbers 1421908, 1533797 to RA, MP); National Evolutionary Synthesis Center (NesCENT) (through a researcher fellowship  ... 
arXiv:1502.04239v3 fatcat:kmogzr7txffbhbfiyncflgtrmm

AmpliconReconstructor: Integrated analysis of NGS and optical mapping resolves the complex structures of focal amplifications in cancer [article]

Jens Luebeck, Ceyda Coruh, Siavash R. Dehkordi, Joshua T. Lange, Kristen M. Turner, Viraj Deshpande, Dave A. Pai, Chao Zhang, Utkrisht Rajkumar, Julie A. Law, Paul S. Mischel, Vineet Bafna
2020 bioRxiv   pre-print
AR uses an NGS-derived breakpoint graph alongside OM scaffolds to produce high-fidelity reconstructions.  ...  of the origins of fCNAs, and their functional consequences.  ...  1) Length (bp): Reports the length of a breakpoint graph path in base pair units. 2 ) 2 Nsegs: Reports the length of a breakpoint graph path in terms of the number of 845 graph segments (unbiased towards  ... 
doi:10.1101/2020.01.22.916031 fatcat:or6ymgr66jeqngiexwjwdq6osy

Skeletal graphs for efficient structure from motion

Noah Snavely, Steven M. Seitz, Richard Szeliski
2008 2008 IEEE Conference on Computer Vision and Pattern Recognition  
To compute a skeletal image set, we first estimate the accuracy of two-frame reconstructions between pairs of overlapping images, then use a graph algorithm to select a subset of images that, when reconstructed  ...  Our approach computes a small skeletal subset of images, reconstructs the skeletal set, and adds the remaining images using pose estimation.  ...  This work was supported in part by National Science Foundation grants IIS-0413198, IIS-0743635, and CNS-0321235, the Office of Naval Research, Microsoft, and an endowment by Rob Short and Emer Dooley.  ... 
doi:10.1109/cvpr.2008.4587678 dblp:conf/cvpr/SnavelySS08 fatcat:kg2fa3urojhutckbh5vl7nrzwm

Acyclic graphs with at least 2ℓ+1 vertices are ℓ-recognizable [article]

Alexandr V. Kostochka, Mina Nahvi, Douglas B. West, Dara Zirlin
2021 arXiv   pre-print
The (n-ℓ)-deck of an n-vertex graph is the multiset of subgraphs obtained from it by deleting ℓ vertices.  ...  A family of n-vertex graphs is ℓ-recognizable if every graph having the same (n-ℓ)-deck as a graph in the family is also in the family.  ...  Therefore, an enhancement of the Reconstruction Problem is to find for each graph the maximum ℓ such that it is ℓ-reconstructible.  ... 
arXiv:2103.12153v1 fatcat:3t7jdm5d7nf6thl3c3d5dukefm

On Learning a Hidden Directed Graph with Path Queries [article]

Mano Vikash Janardhanan, Lev Reyzin
2021 arXiv   pre-print
In this paper, we consider the problem of reconstructing a directed graph using path queries.  ...  In this query model of learning, a graph is hidden from the learner, and the learner can access information about it with path queries.  ...  In particular, a path query consists of an ordered pair of vertices (u, v) and the result of the query is 1 (or "yes") if the hidden graph has a directed path from u to v and 0 (or "no") otherwise.  ... 
arXiv:2002.11541v2 fatcat:e7zilyzdaval3hg4y4rmsoxcky

Assembly complexity of prokaryotic genomes using short reads

Carl Kingsford, Michael C Schatz, Mihai Pop
2010 BMC Bioinformatics  
We describe an application of de Bruijn graphs to analyze the global repeat structure of prokaryotic genomes.  ...  The analysis gives an upper-bound on the performance of genome assemblers for de novo reconstruction of genomes across a wide range of read lengths.  ...  Acknowledgements This work was supported in part by grant IIS-0812111 from the NSF to MP and CK, in part by grant #HU001-06-1-0015 from the Uniformed Services University of the Health Sciences administered  ... 
doi:10.1186/1471-2105-11-21 pmid:20064276 pmcid:PMC2821320 fatcat:ouceq3gytjbybhw4fnmlsvfq4y

Some work towards the proof of the reconstruction conjecture

S.K. Gupta, Pankaj Mangal, Vineet Paliwal
2003 Discrete Mathematics  
In this paper we de2ne 2ve families of simple graphs {fi,f 2 ,f^,t^ and F= 5 ) such that the reconstruction conjecture is true if reconstruction is proved for either the families $[,$2 m & % or the families  ...  The reconstruction conjecture is thus reduced to showing weak reconstructibility for either of the two sets of families.  ...  The authors are thankful to Prof. Amitabh Tripathi and Dinesh Kumar of Department of Mathematics at IIT-Delhi for their help and useful comments. The authors are grateful to Prof. P.K.  ... 
doi:10.1016/s0012-365x(03)00198-5 fatcat:3poesxtdk5chdedgon7fyx5ucy

Structural and Complexity Aspects of Line Systems of Graphs [chapter]

Jozef Jirásek, Pavel Klavík
2010 Lecture Notes in Computer Science  
Similarly to the Graph Reconstruction Problem, we question the reconstructability of graphs from their line systems.  ...  We call a pair of graphs isolinear if their line systems are isomorphic. We prove that deciding isolinearity of graphs is polynomially equivalent to the Graph Isomorphism Problem.  ...  We would also like to thank Martin Loebl for pointing out possible relations with the Graph Reconstruction Conjecture.  ... 
doi:10.1007/978-3-642-17517-6_16 fatcat:yth5a6wb3reklibdxvpqwdmglq

Whole Genome Phylogenetic Tree Reconstruction using Colored de Bruijn Graphs [article]

Cole Lyman
2017 Figshare  
We introduce the algorithm that kleuren uses to accomplish this task, and show its performance on reconstructing the phylogenetic tree of 12 Drosophila species. kleuren reconstructed the established phylogenetic  ...  We present kleuren, a novel assembly-free method to reconstruct phylogenetic trees using the Colored de Bruijn Graph. kleuren works by constructing the Colored de Bruijn Graph and then traversing it, finding  ...  common to use only a small portion of the genome to reconstruct a tree. → Alignment-free methods can provide the means to reconstruct phylogenetic trees using NGS data.  ... 
doi:10.6084/m9.figshare.5532751.v1 fatcat:3vsm7woscjef3h2vtheef2qpdy

NEW CASES OF RECONSTRUCTIBILITY OF SBT GRAPHS

M. Dowd
2015 International Journal of Pure and Applied Mathematics  
In earlier papers the author showed that all graphs which are not single-block trunk (SBT) graphs are reconstructible, and that two families of SBT graphs are reconstructible.  ...  Here some further families of SBT graphs are shown to be reconstructible.  ...  B m is a cycle iff, for any E-vertex v, MPG(G T v ) is a path, where for a graph G G T denotes the trunk of G. Suppose for the rest of the section that G is an SBT graph with B m a cycle.  ... 
doi:10.12732/ijpam.v103i4.11 fatcat:saefifvznncrjbclnpy3piot6e

Reconstructing a Bounded-Degree Directed Tree Using Path Queries [article]

Zhaosen Wang, Jean Honorio
2017 arXiv   pre-print
We present a randomized algorithm for reconstructing directed rooted trees of n nodes and node degree at most d, by asking at most O(dn^2 n) path queries.  ...  Each path query takes as input an origin node and a target node, and answers whether there is a directed path from the origin to the target.  ...  This process can be seen as the task of reconstructing a graph (i.e., finding the hidden edges of a graph) by asking queries to an oracle.  ... 
arXiv:1606.05183v3 fatcat:thzx62zvcfaszceuf5l25zedhe

Constructing Street Networks from GPS Trajectories [chapter]

Mahmuda Ahmed, Carola Wenk
2012 Lecture Notes in Computer Science  
Data Model We model the original graph and a reconstructed graph as embedded undirected graphs in R 2 . We model error associated with each trajectory by a precision parameter ǫ.  ...  Ahmed Our Observation We are interested to maximize the matched portion on curve. That allows the desired path to go through the black region along the graph without adding additional cost.  ... 
doi:10.1007/978-3-642-33090-2_7 fatcat:vuebwobbcfbifigo7idi4tpw44
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