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Reconstruction of the Path Graph
[article]

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. ...

##
###
SOME RESULTS ON RECONSTRUCTIBILITY OF COLORED GRAPHS

2014
*
International Journal of Pure and Applied Mathematics
*

In an earlier paper

doi:10.12732/ijpam.v95i2.14
fatcat:2dvlx67zgbhhjgudgkjorff7h4
*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*. ...##
###
Graph Reconstruction from Path Correlation Data
[article]

2018
*
arXiv
*
pre-print

Network tomography aims to infer these edge weights from their pathwise versions measured on a set

arXiv:1804.04574v1
fatcat:fhwv6277cba3ffuzc5z2f2xhbq
*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. ...##
###
Maximum Likelihood de novo reconstruction of viral populations using paired end sequencing data
[article]

2016
*
arXiv
*
pre-print

Using

arXiv:1502.04239v3
fatcat:kmogzr7txffbhbfiyncflgtrmm
*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 ...##
###
AmpliconReconstructor: Integrated analysis of NGS and optical mapping resolves the complex structures of focal amplifications in cancer
[article]

2020
*
bioRxiv
*
pre-print

AR uses an NGS-derived breakpoint

doi:10.1101/2020.01.22.916031
fatcat:or6ymgr66jeqngiexwjwdq6osy
*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 ...##
###
Skeletal graphs for efficient structure from motion

2008
*
2008 IEEE Conference on Computer Vision and Pattern Recognition
*

To compute a skeletal image set, we first estimate

doi:10.1109/cvpr.2008.4587678
dblp:conf/cvpr/SnavelySS08
fatcat:kg2fa3urojhutckbh5vl7nrzwm
*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. ...##
###
Acyclic graphs with at least 2ℓ+1 vertices are ℓ-recognizable
[article]

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*. ...

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

2021
*
arXiv
*
pre-print

In this paper, we consider

arXiv:2002.11541v2
fatcat:e7zilyzdaval3hg4y4rmsoxcky
*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. ...##
###
Assembly complexity of prokaryotic genomes using short reads

2010
*
BMC Bioinformatics
*

We describe an application

doi:10.1186/1471-2105-11-21
pmid:20064276
pmcid:PMC2821320
fatcat:ouceq3gytjbybhw4fnmlsvfq4y
*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 ...##
###
Some work towards the proof of the reconstruction conjecture

2003
*
Discrete Mathematics
*

In this paper we de2ne 2ve families

doi:10.1016/s0012-365x(03)00198-5
fatcat:3poesxtdk5chdedgon7fyx5ucy
*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. ...##
###
Structural and Complexity Aspects of Line Systems of Graphs
[chapter]

2010
*
Lecture Notes in Computer Science
*

Similarly to

doi:10.1007/978-3-642-17517-6_16
fatcat:yth5a6wb3reklibdxvpqwdmglq
*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. ...##
###
Whole Genome Phylogenetic Tree Reconstruction using Colored de Bruijn Graphs
[article]

2017
*
Figshare
*

We introduce

doi:10.6084/m9.figshare.5532751.v1
fatcat:3vsm7woscjef3h2vtheef2qpdy
*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. ...##
###
NEW CASES OF RECONSTRUCTIBILITY OF SBT GRAPHS

2015
*
International Journal of Pure and Applied Mathematics
*

In earlier papers

doi:10.12732/ijpam.v103i4.11
fatcat:saefifvznncrjbclnpy3piot6e
*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. ...##
###
Reconstructing a Bounded-Degree Directed Tree Using Path Queries
[article]

2017
*
arXiv
*
pre-print

We present a randomized algorithm for

arXiv:1606.05183v3
fatcat:thzx62zvcfaszceuf5l25zedhe
*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. ...##
###
Constructing Street Networks from GPS Trajectories
[chapter]

2012
*
Lecture Notes in Computer Science
*

Data Model We model

doi:10.1007/978-3-642-33090-2_7
fatcat:vuebwobbcfbifigo7idi4tpw44
*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. ...
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