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Tight Lower and Upper Bounds for the Complexity of Canonical Colour Refinement [article]

Christoph Berkholz, Paul Bonsma, Martin Grohe
2015 arXiv   pre-print
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]

Christoph Berkholz, Paul Bonsma, Martin Grohe
2013 Lecture Notes in Computer Science  
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

Christoph Berkholz, Paul Bonsma, Martin Grohe
2016 Theory of Computing Systems  
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)

Mikolaj Bojanczyk, Meena Mahajan, Thomas Schwentick, Heribert Vollmer, Marc Herbstritt
2016 Dagstuhl Reports  
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)

László Babai, Anuj Dawar, Pascal Schweitzer, Jacobo Torán, Marc Herbstritt
2016 Dagstuhl Reports  
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

Marja Hassinen, Joel Kaasinen, Evangelos Kranakis, Valentin Polishchuk, Jukka Suomela, Andreas Wiese
2011 Discrete Applied Mathematics  
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

NAVIN GOYAL, LUIS RADEMACHER, SANTOSH VEMPALA
2014 Combinatorics, probability & computing  
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

Wenfu Ma, Jonathan Goldberg
2013 EMBO Journal  
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

Aidan Hogan
2015 Proceedings of the 24th International Conference on World Wide Web - WWW '15  
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

Magdalena N. Wojtas, Maria Mogni, Oscar Millet, Stephen D. Bell, Nicola G. A. Abrescia
2012 Nucleic Acids Research  
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

Bryan H. Schmidt, Alex B. Burgin, Joseph E. Deweese, Neil Osheroff, James M. Berger
2010 Nature  
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]

Christoph Berkholz, Jakob Nordström
2016 arXiv   pre-print
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]

Marc Roth, Johannes Schmitt, Philip Wellnitz
2021 arXiv   pre-print
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

Julien Pérard, Cédric Leyrat, Florence Baudin, Emmanuel Drouet, Marc Jamin
2013 Nature Communications  
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

Richard C. H. Webb
2020 Geometric and Functional Analysis  
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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