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Tight Lower and Upper Bounds for the Complexity of Canonical Colour Refinement
[article]
2015
arXiv
pre-print
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We give an O((m+n) n) algorithm for finding a canonical version of such a stable colouring, on graphs with n vertices and m edges. ...
The goal of colour refinement is to find a stable colouring that uses a minimum number of colours. ...
Acknowledgements We thank Christof Löding for discussions and references regarding the lower bounds for bisimilarity and DFA-minimisation. ...
arXiv:1509.08251v1
fatcat:yb4j4tzoivaa3cep7msj5qptge
Tight Lower and Upper Bounds for the Complexity of Canonical Colour Refinement
[chapter]
2013
Lecture Notes in Computer Science
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We give an O((m + n) log n) algorithm for finding a canonical version of such a stable colouring, on graphs with n vertices and m edges. ...
The goal of colour refinement is to find a stable colouring that uses a minimum number of colours. ...
Acknowledgments We thank Christof Löding for discussions and references regarding the lower bounds for bisimilarity and DFA-minimisation. ...
doi:10.1007/978-3-642-40450-4_13
fatcat:fbyky6w3ovh2ricvb2spmvenkq
Tight Lower and Upper Bounds for the Complexity of Canonical Colour Refinement
2016
Theory of Computing Systems
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We give an O((m + n) log n) algorithm for finding a canonical version of such a stable colouring, on graphs with n vertices and m edges. ...
The goal of colour refinement is to find a stable colouring that uses a minimum number of colours. ...
We formulate the lower bound result for undirected graphs and noncanonical colour refinement, so that it also holds for digraphs, and canonical colour refinement. ...
doi:10.1007/s00224-016-9686-0
fatcat:dfrgsj2vgfc65dhlfknzcqythi
Circuits, Logic and Games (Dagstuhl Seminar 15401)
2016
Dagstuhl Reports
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There are tight connections between small-depth circuit classes and fragments and extensions of firstorder logic, and ideas from games and finite model theory have provided powerful lower bound techniques ...
complexity and circuit lower bounds inherently using methods from logic and algebra Proof systems with low circuit complexity Dynamic complexity: understanding the dynamic expressive power of small depth ...
By using the full spectrum of state-of-the-art circuit lower bounds, our new lower bound method leads to very strong lower bounds for QBF Frege systems: 1. exponential lower bounds and separations for ...
doi:10.4230/dagrep.5.9.105
dblp:journals/dagstuhl-reports/BojanczykMSV15
fatcat:pv6oxt7lnvhkbczugwxmvumdxq
The Graph Isomorphism Problem (Dagstuhl Seminar 15511)
2016
Dagstuhl Reports
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This report documents the program and the outcomes of Dagstuhl Seminar 15511 "The Graph Isomorphism Problem". ...
A highlight of the conference was the presentation of a new quasi-polynomial time algorithm for the Graph Isomorphism Problem, providing the first improvement since 1983. ...
However, the problem of characterizing and recognizing compact graphs in polynomial time remains an open question. We relate this approach to the classical color-refinement (CR) procedure. ...
doi:10.4230/dagrep.5.12.1
dblp:journals/dagstuhl-reports/BabaiDST15
fatcat:meig4kvcgffnjiq5wpa6wjs6am
Analysing local algorithms in location-aware quasi-unit-disk graphs
2011
Discrete Applied Mathematics
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We give tight bounds on the local horizon for a class of local algorithms for combinatorial problems on unit-disk graphs (UDGs). ...
The algorithms are applied to matching, independent set, graph colouring, vertex cover, and dominating set. ...
Hecse), by the Foundation of Nokia Corporation, and by the Finnish Cultural Foundation. ...
doi:10.1016/j.dam.2011.05.004
fatcat:hzufrsbw5ra2hciv5m45ltggwu
Query Complexity of Sampling and Small Geometric Partitions
2014
Combinatorics, probability & computing
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We will be mainly interested in the casek=n.DPP arises in an approach that we propose for proving lower bounds for the query complexity of generating random points from convex bodies. ...
We conjecture an asymptotically optimal partition for DPP and show that it is optimal in two cases: when the dimension is low (k=n= 2) and when the factors of the parts are structured, namely factors of ...
We also thank an anonymous reviewer for careful reading and useful comments.
Appendix: From sampling lower bound to the continuous partitioning problem ...
doi:10.1017/s0963548314000704
fatcat:z3jvv7gxmbegrbhxpbcu46m77i
Rules for the recognition of dilysine retrieval motifs by coatomer
2013
EMBO Journal
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We present crystal structures of a-COP and b 0 -COP bound to a series of naturally occurring retrieval motifs-encompassing KKxx, KxKxx and non-canonical RKxx and viral KxHxx sequences. ...
the tolerance of the acidic patches for non-lysine residues. ...
We thank all the members of our laboratory for advice and insights on coatomer behaviour and protein biochemistry experiments. ...
doi:10.1038/emboj.2013.41
pmid:23481256
pmcid:PMC3616288
fatcat:fgwxsndwvvbovacxl5y2nmnygq
Skolemising Blank Nodes while Preserving Isomorphism
2015
Proceedings of the 24th International Conference on World Wide Web - WWW '15
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In this paper, we propose and evaluate a scheme to produce canonical labels for blank nodes in RDF graphs. ...
These labels can be used as the basis for a Skolemisation scheme that gets rid of the blank nodes in an RDF graph by mapping them to globally canonical IRIs. ...
The tight asymptotic bound is given, for example, by the 1 2 · |B| + 1 iterations needed for a regular path graph. ...
doi:10.1145/2736277.2741653
dblp:conf/www/Hogan15
fatcat:ya3v6f5zmfaa5pqaize5wof6ri
Structural and functional analyses of the interaction of archaeal RNA polymerase with DNA
2012
Nucleic Acids Research
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Here, we report crystal structures of the DNA-bound and free form of the aRNAP from Sulfolobus shibatae. ...
These interactions map on our RNAP-DNA binary complex on the downstream DNA at the far end of the DNA entry channel. ...
We acknowledge the Swiss Light Synchrotron (SLS), the European Synchrotron Radiation Facility (ESRF) and Diamond Light Source for provision of synchrotron facilities. ...
doi:10.1093/nar/gks692
pmid:22848102
pmcid:PMC3479171
fatcat:simhwbjbdrccxanavoi2i2ycfi
A novel and unified two-metal mechanism for DNA cleavage by type II and IA topoisomerases
2010
Nature
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Type II topoisomerases are required for the management of DNA tangles and supercoils1, and are targets of clinical antibiotics and anti-cancer agents2. ...
, for the purposes of academic research, subject always to the full Conditions of use: ...
(Upper) Upward movement of the active-site tyrosine upon becoming attached to the DNA. (Lower) Concomitant inward movement of the coiled-coil joint through a conserved salt bridge network. ...
doi:10.1038/nature08974
pmid:20485342
pmcid:PMC2882514
fatcat:mgsueonal5cabpiu3zflm7zx7q
Near-Optimal Lower Bounds on Quantifier Depth and Weisfeiler-Leman Refinement Steps
[article]
2016
arXiv
pre-print
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Our trade-offs also apply to first-order counting logic, and by the known connection to the k-dimensional Weisfeiler--Leman algorithm imply near-optimal lower bounds on the number of refinement iterations ...
A key component in our proof is the hardness condensation technique recently introduced by [Razborov '16] in the context of proof complexity. ...
We also want to thank Neil Immerman for helping us find relevant references to previous works and explaining some of the finer details in [Imm81] . ...
arXiv:1608.08704v2
fatcat:zwcbr43z2vglviqttnobu2jkyu
Detecting and Counting Small Subgraphs, and Evaluating a Parameterized Tutte Polynomial: Lower Bounds via Toroidal Grids and Cayley Graph Expanders
[article]
2021
arXiv
pre-print
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Additionally, most of our hardness results come with an almost tight conditional lower bound under the so-called Exponential Time Hypothesis, ruling out algorithms for #𝙴𝚍𝚐𝚎𝚂𝚞𝚋(Φ) that run in time ...
Specifically, we study the parameterized complexity of 𝙴𝚍𝚐𝚎𝚂𝚞𝚋(Φ) and of its counting problem #𝙴𝚍𝚐𝚎𝚂𝚞𝚋(Φ) with respect to both approximate and exact counting. ...
The second author was supported by the SNF early postdoc mobility grant 184245 and thanks the Max Planck Institute for Mathematics in Bonn for its hospitality. ...
arXiv:2011.03433v2
fatcat:7aauf7xejvfx5atw3n7s6sefsa
Structure of the full-length HCV IRES in solution
2013
Nature Communications
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occurring in the (IRES) molecule upon formation of the initiation complex. ...
Until now, the structural characterization of the entire (IRES) remained limited to cryo-electron microscopy reconstructions of the (IRES) bound to different cellular partners. ...
Franck for providing the electron microscopy map of the IRES-eIF3 complex and Dr G. Schoehn for his help in preparing Fig. 7 . We thank Dr. A. Round and Dr. L. ...
doi:10.1038/ncomms2611
pmid:23511476
fatcat:fcl46ohseneo3dztv2srkafmue
Contractible, hyperbolic but non-CAT(0) complexes
2020
Geometric and Functional Analysis
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We also show the analogous statement for all but finitely many disc complexes of handlebodies and free splitting complexes of free groups. The obstruction is combinatorial. ...
These complexes are all hyperbolic and contractible but despite this we show that they satisfy no combinatorial isoperimetric inequality: for any n there is a loop of length 4 that only bounds discs consisting ...
We thank the anonymous referee for helpful mathematical comments and suggestions that have improved the paper. ...
doi:10.1007/s00039-020-00552-2
fatcat:peac4srmnng33muadgwij5f2hm
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