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The Parameterized Complexity of Geometric Graph Isomorphism

V. Arvind, Gaurav Rattan
2015 Algorithmica  
L A = {α 1 a 1 + · · · + α n a n | α i ∈ Z} Claim Let S A be the set of shortest vectors in L A . Then, S A is isomorphism-invariant. Proof.  ...  The lattice generated by a set A ∈ R k , denoted by L A , is the set of all integer linear combinations of the set A.  ... 
doi:10.1007/s00453-015-0024-8 fatcat:erjsbtuhjjbuxmpxtimbp2rxxq

Foreword: Special Issue on IPEC 2014

Marek Cygan, Pinar Heggernes
2016 Algorithmica  
This issue consists of nine papers, reviewed thoroughly according to the usual, high standard of the journal. In The Parameterized Complexity of Geometric Graph Isomorphism, V.  ...  Jannis Bulian and Anuj Dawar consider the Graph Isomorphism problem in Graph Isomorphism Parameterized by Elimination Distance to Bounded Degree.  ... 
doi:10.1007/s00453-016-0151-x fatcat:2xhmdtkgtzbbppmbxnhugehgr4

Recognition of Polymorphic Patterns in Parameterized Graphs for 3D Building Reconstruction [chapter]

R. Englert, A. B. Cremers, J. Seelmann-Eggebert
1998 Computing Supplement  
An approach for the recognition of polymorphic patterns by subgraph isomorphism computation of parameterized graphs will be presented.  ...  Parameterized graphs (short: p-graphs) are extensions of undirected graphs by parameter vectors at the nodes and edges.  ...  Acknowledgments The authors like to thank W. F orstner for his discussion. Furthermore they thank J. Zimmermann for comments on an earlier version.  ... 
doi:10.1007/978-3-7091-6487-7_2 dblp:conf/gbrpr/EnglertCS97 fatcat:shojunaytfeufjdqgir6dxsub4

Optimality and tight results in parameterized complexity (Dagstuhl Seminar 14451)

Stefan Kratsch, Daniel Lokshtanov, Dániel Marx, Peter Rossmanith, Marc Herbstritt
2015 Dagstuhl Reports  
Over the last two decades parameterized complexity has become one of the main tools for handling intractable problems.  ...  This report documents the program and the outcomes of Dagstuhl Seminar 14451 "Optimality and tight results in parameterized complexity".  ...  The parameterized complexity of MCPP with respect to treewidth was an open question of van Bevern et al.  ... 
doi:10.4230/dagrep.4.11.1 dblp:journals/dagstuhl-reports/KratschLMR14 fatcat:vwgmhttkgrf4pb34jpsb2rfvnm

The parameterized complexity of finding a 2-sphere in a simplicial complex [article]

Benjamin Burton and Sergio Cabello and Stefan Kratsch and William Pettersson
2018 arXiv   pre-print
We consider the problem of finding a subcomplex K' of a simplicial complex K such that K' is homeomorphic to the 2-dimensional sphere, S^2. We study two variants of this problem.  ...  The second problem is the dual of the first, and asks if K' can be found by removing at most k triangles from K.  ...  We are grateful to the other participants of the workshop and the Lorentz Center for their support.  ... 
arXiv:1802.07175v1 fatcat:3e2zlnzkovbopbzhdr5qprr3fy

Counting Restricted Homomorphisms via Möbius Inversion over Matroid Lattices [article]

Marc Roth
2017 arXiv   pre-print
We present a framework for the complexity classification of parameterized counting problems that can be formulated as the summation over the numbers of homomorphisms from small pattern graphs H_1,...  ...  states that the sign of the M\"obius function over a geometric lattice only depends on the rank of its arguments.  ...  Furthermore the author thanks Cornelius Brand for saying "Tutte Polynomial" every once in a while.  ... 
arXiv:1706.08414v1 fatcat:54q2ljvnp5ewboak3d67ij73oq

On the Parameterized Complexity of d-Dimensional Point Set Pattern Matching [chapter]

Sergio Cabello, Panos Giannopoulos, Christian Knauer
2006 Lecture Notes in Computer Science  
When the dimension d is unbounded, the problem is equivalent to graph isomorphism and is conjectured to be in FPT.  ...  When |A| = m < |B| = n, the problem becomes that of deciding whether A is congruent to a subset of B and is known to be NP-complete.  ...  The complexity of these two problems for point sets in unbounded dimensions has been already studied within the classical complexity theory: the former is graph-isomorphism-hard and the latter is NP-complete  ... 
doi:10.1007/11847250_16 fatcat:ftfickzctbccjdkdgxkf2hjmcy

On the parameterized complexity of d-dimensional point set pattern matching

Sergio Cabello, Panos Giannopoulos, Christian Knauer
2008 Information Processing Letters  
When the dimension d is unbounded, the problem is equivalent to graph isomorphism and is conjectured to be in FPT.  ...  When |A| = m < |B| = n, the problem becomes that of deciding whether A is congruent to a subset of B and is known to be NP-complete.  ...  The complexity of these two problems for point sets in unbounded dimensions has been already studied within the classical complexity theory: the former is graph-isomorphism-hard and the latter is NP-complete  ... 
doi:10.1016/j.ipl.2007.08.003 fatcat:622yn35rrzgl3h6sucheftaugy

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.  ...  On Tinhofer's Linear Programming Approach to Isomorphism Testing Oleg Verbitsky ( Exploring a linear programming approach to Graph Isomorphism, Tinhofer [1] defined the concept of a compact graph: A graph  ... 
doi:10.4230/dagrep.5.12.1 dblp:journals/dagstuhl-reports/BabaiDST15 fatcat:meig4kvcgffnjiq5wpa6wjs6am

FO model checking on geometric graphs

Petr Hliněný, Filip Pokrývka, Bodhayan Roy
2019 Computational geometry  
We study the FO model checking problem for dense graph classes definable by geometric means (intersection and visibility graphs).  ...  for FO model checking of nowhere dense classes of graphs.  ...  parameterized complexity.  ... 
doi:10.1016/j.comgeo.2018.10.001 fatcat:4reekwyaqfez7idoh34lgyksoe

Parameterized Counting of Partially Injective Homomorphisms

Marc Roth
2021 Algorithmica  
As a consequence, we are able to fully classify its parameterized complexity depending on the class of allowed pattern graphs.  ...  AbstractWe study the parameterized complexity of the problem of counting graph homomorphisms with given partial injectivity constraints, i.e., inequalities between pairs of vertices, which subsumes counting  ...  Furthermore the author thanks Cornelius Brand for saying "Tutte Polynomial" every once in a while, and Philip Wellnitz for providing valuable feedback on early drafts of the full version of this work.  ... 
doi:10.1007/s00453-021-00805-y fatcat:oetq4yn2nnhy7ovyr47zgch6am

Automorphisms of procongruence curve and pants complexes [article]

Marco Boggi, Louis Funar
2021 arXiv   pre-print
Our main result is a rigidity theorem for the procongruence completion of the pants complex.  ...  In this paper we study the automorphism group of the procongruence mapping class group through its action on the associated procongruence curve and pants complexes.  ...  Geometric interpretation for the pants graph and its congruence completion.  ... 
arXiv:2004.04135v3 fatcat:ldyhtivk4zgprnu5yfngk7spcq

Lossless Compression of Structured Convolutional Models via Lifting [article]

Gustav Sourek, Filip Zelezny, Ondrej Kuzelka
2021 arXiv   pre-print
The computation graphs themselves then reflect the symmetries of the underlying data, similarly to the lifted graphical models.  ...  To address the irregular structure of the data, the models typically extrapolate on the idea of convolution, effectively introducing parameter sharing in their, dynamically unfolded, computation graphs  ...  We used the re-implemented LRNN framework to emulate all the models, and also compared with popular GNN frameworks of PyTorch Geometric (PyG) [6] and Deep Graph Library (DGL) [37] .  ... 
arXiv:2007.06567v2 fatcat:3ea3dzdeufd4bjnn5bsjwf5cgi

On the Role of Graph Theory Apparatus in a CAD Modeling Kernel

Sergey Slyadnev, Alexander Malyshev, Andrey Voevodin, Vadim Turlapov
2020 Proceedings of the 30th International Conference on Computer Graphics and Machine Vision (GraphiCon 2020). Part 2  
The set of topological and geometric heuristics backing the subgraph isomorphism algorithm is presented to achieve decent performance in our extensible feature recognition framework.  ...  We use the notion of face transition graph for the unfoldability analysis. The basic operations on hierarchical assembly graphs are formalized in terms of graph theory for handling CAD assemblies.  ...  At the higher level of abstraction, hierarchical assembly graphs serve to represent complex digital products.  ... 
doi:10.51130/graphicon-2020-2-3-70 fatcat:fcbvtybrojgi3mcdt2ok2ftqmu

Homological Coordinatization [article]

Andrew Tausz, Gunnar Carlsson
2011 arXiv   pre-print
In this paper, we review a method for computing and parameterizing the set of homotopy classes of chain maps between two chain complexes.  ...  This is then applied to finding topologically meaningful maps between simplicial complexes, which in the context of topological data analysis, can be viewed as an extension of conventional unsupervised  ...  Complexity theorists have created a class called GI which consists of those problems which are polynomial time reducible to the graph isomorphism problem.  ... 
arXiv:1107.0511v2 fatcat:zymzs4zo4rewrlkg44tkdyk4ba
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