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An Algorithmic Meta-Theorem for Graph Modification to Planarity and FOL [article]

Fedor V. Fomin and Petr A. Golovach and Giannos Stamoulis and Dimitrios M. Thilikos
2021 arXiv   pre-print
We call the corresponding meta-problem Graph ⊠-Modification to Planarity and ϕ and prove the following algorithmic meta-theorem: there exists a function f:N^2→N such that, for every ⊠ and every FOL sentence  ...  the second is the use of Gaifman's Locality Theorem that is the theoretical base for the meta-algorithmic study of FOL-expressible problems.  ...  Given an FOL-sentence ϕ and some ∈ OP , we define the following meta-problem: Graph -Modification to Planarity and ϕ (In short: G MPϕ) Input: A graph G and a non-negative integer k.  ... 
arXiv:2106.03425v1 fatcat:2s3e7ngkonf4dfoumq64rte524

An Algorithmic Meta-Theorem for Graph Modification to Planarity and FOL

Fedor V. Fomin, Petr A. Golovach, Giannos Stamoulis, Dimitrios M. Thilikos, Peter Sanders, Fabrizio Grandoni, Grzegorz Herman
2020 European Symposium on Algorithms  
We call the corresponding meta-problem Graph ⊠-Modification to Planarity and ϕ and prove the following algorithmic meta-theorem: there exists a function f: ℕ² → ℕ such that, for every ⊠ and every FOL sentence  ...  the second is the use of Gaifman's Locality Theorem that is the theoretical base for the meta-algorithmic study of FOL-expressible problems.  ...  having a dominating 51:4 An Algorithmic Meta-Theorem for Graph Modification to Planarity and FOL set of constant size.  ... 
doi:10.4230/lipics.esa.2020.51 dblp:conf/esa/FominGST20 fatcat:isihu2it3vgx5ouzbxnjpyyeuq

Data-Compression for Parametrized Counting Problems on Sparse Graphs

Eun Jung Kim, Maria Serna, Dimitrios M. Thilikos, Michael Wagner
2018 International Symposium on Algorithms and Computation  
We study a family of vertex-certified counting problems on graphs that are MSOL-expressible; that is, for an MSOL-formula φ with one free set variable to be interpreted as a vertex subset, we want to count  ...  This implies the existence of an FPT-algorithm of running time O(n 2 k 2 ) + 2 O(k) .  ...  On the side of FOL, the problem condition of Corollary 2 is stronger than FOL, while its combinatorial applicability includes planar graphs or graphs of bounded genus where, the existing algorithmic meta-theorems  ... 
doi:10.4230/lipics.isaac.2018.20 dblp:conf/isaac/0002ST18 fatcat:xytw4ioxsbelxko3iv4tmutely

A Compound Logic for Modification Problems: Big Kingdoms Fall from Within [article]

Fedor V. Fomin and Petr A. Golovach and Ignasi Sau and Giannos Stamoulis and Dimitrios M. Thilikos
2021 arXiv   pre-print
This algorithmic meta-theorem encompasses, unifies, and extends all known meta-algorithmic results on minor-closed graph classes.  ...  We introduce a novel model-theoretic framework inspired from graph modification and based on the interplay between model theory and algorithmic graph minors.  ...  We wish to thank Stavros G. Kolliopoulos and Christophe Paul for their valuable remarks on earlier versions of this paper.  ... 
arXiv:2111.02755v1 fatcat:3sv32gmw3jbgpmrnuhg57mcyuq

Data-compression for Parametrized Counting Problems on Sparse graphs [article]

Eun Jung Kim, Maria Serna, Dimitrios M. Thilikos
2018 arXiv   pre-print
We study a family of vertex-certified counting problems on graphs that are MSOL-expressible; that is, for an MSOL-formula ϕ with one free set variable to be interpreted as a vertex subset, we want to count  ...  This implies the existence of an FPT-algorithm of running time O(n^2k^2)+2^O(k).  ...  This extends the applicability of our meta-algorithmic result to more problems but in more restricted graph classes.  ... 
arXiv:1809.08160v2 fatcat:dwejq5ok25dv5hto3moiejvjva

Harmless Sets in Sparse Classes [article]

Pål Grønås Drange, Irene Muzi, Felix Reidl
2022 arXiv   pre-print
The first question can be answered in the positive using existing meta-theorems on sparse classes, and we further show that HARMLESS SET not only admits a polynomial kernel, but that it can be solved in  ...  Specifically, we answer two open questions posed by the aforementioned authors, namely a) whether the problem is FPT on planar graphs and b) whether it is FPT parametrised by treewidth.  ...  XOR gadget We construct an XOR gadget for vertices u and v by adding a new forbidden vertex x with threshold two and adding the edges xu and xv to the graph.  ... 
arXiv:2111.11834v2 fatcat:w7g2i6rgdvd25msqkvqieizkru

Index—Volumes 1–89

1997 Artificial Intelligence  
, tool kit for -526 proofs for theorems, algorithm for -4 proofb for theorems of an axiomatic theory 4 construction of belief arguments 527 of delluctive systems 374 of invariants for 3D objects  ...  and structures 679 oriented view of abstraction 1359 parsing algorithm 582 pattern 1219 planar -302 graph representation 117.5, 1219 of problem spaces 930 graph resolution system 648 graph search  ...  1222,1339 reasoning abductive -684, 1175, 1222 logical -1124, 1217 machinery 58 1 management of evidential -328 mathematical -166,579 mathematics of non-monotonic-150 mechanism 381 mechanized formal -152 meta-level  ... 
doi:10.1016/s0004-3702(97)80122-1 fatcat:6az7xycuifaerl7kmv7l3x6rpm

Knowledge Augmented Machine Learning with Applications in Autonomous Driving: A Survey [article]

Julian Wörmann, Daniel Bogdoll, Etienne Bührle, Han Chen, Evaristus Fuh Chuo, Kostadin Cvejoski, Ludger van Elst, Tobias Gleißner, Philip Gottschall, Stefan Griesche, Christian Hellert, Christian Hesels (+34 others)
2022 arXiv   pre-print
The reasons for this are manifold and range from time and cost constraints to ethical considerations.  ...  This work provides an overview of existing techniques and methods in the literature that combine data-based models with existing knowledge.  ...  In the associated meta-learning stage, the meta algorithm updates the base algorithm, i.e., the algorithm used to learn the base model.  ... 
arXiv:2205.04712v1 fatcat:u2bgxr2ctnfdjcdbruzrtjwot4

Elliptic multiple zeta values, modular graph functions and genus 1 superstring scattering amplitudes [article]

Federico Zerbini
2018 arXiv   pre-print
In this PhD thesis we study holomorphic and non-holomorphic elliptic analogues of multiple zeta values, namely elliptic multiple zeta values and modular graph functions.  ...  In particular, we obtain new results on the asymptotic expansion of these functions that allow us to perform explicit computations and point out analogies between genus zero and genus one amplitudes.  ...  Lemma 4.1.1), and we used it to prove that we get MZVs for an infinite family of modular graph functions (cf. Theorem 4.3.3).  ... 
arXiv:1804.07989v1 fatcat:6ehkjho2b5eyzjeygnu7pbcb3m

Dynamic graph algorithms and graph sparsification

Gramoz Goranci
2019 unpublished
In particular we obtain the following results: * The first dynamic algorithm for maintaining approximate solutions to Laplacian systems in sub-linear update and query time and an extension of the technique  ...  algorithms and graph sparsification.  ...  Our second contribution is new algorithms for constructing quality-1 (exact) cut, flow and distance sparsifiers for k-terminal planar graphs, where all the terminals are assumed to lie on the same face  ... 
doi:10.25365/thesis.57574 fatcat:ags5zcmgmfhy5gkhurvox2rvn4

URSI National Committee Report: Commission 6. Radio Waves and Circuits. Part 1. Information Theory and Coding

P. Elias
1960 Journal of Research of the National Bureau of Standards Section D Radio Propagation  
However a recent paper [Blaclnyell, Breimann, and Thomasian, ] 959], ha presented an interesting new problem, defining capacity and proving a coding theorem for a channel whose parameters are not known  ...  lier work Huffman [1956J had shown a coding and decoding procedure for the HamminO" code which was simple to implement and Green ~nd SanSoucie [1958] have shown an easy 'implementation for a short multiple-el  ...  The authors thank Mary Lee Bllschkottcr for diligent effort in correctin g and typin g the manuscript.  ... 
doi:10.6028/jres.064d.076 fatcat:as4o4awtpzaevjutixsygjqbpm

Computation and its limits

2012 ChoiceReviews  
A graph of this kind is called an indicator diagram for the system (see Figure 5 .8).  ...  said to be meta-stable.  ...  By itself this is not entirely germane, since the human mathematician has paper as an aide memoir and the tape of the TM is explicitly introduced as an analogy with the squared paper of the mathematician  ... 
doi:10.5860/choice.50-2108 fatcat:cfmueij4tvetlm4tzgft2aepzm

Strategy Generation and Evaluation for Meta-Game Playing

Barney Pell
2011 Künstliche Intelligenz  
Meta-Game Playing (Metagame) is a new paradigm for research in game-playing in which we design programs to take in the rules of unknown games and play those games without human assistance.  ...  , and the board for this game is planar, the piece is constrained to ride as far as possible in the selected direction.  ...  This method of representation is extremely general and flexible, and facilitates the entry and modification of knowledge.  ... 
doi:10.1007/s13218-010-0082-7 fatcat:ngz2pwwy4bguvpgwditnvgzbfm

Artificial intelligence and molecular biology

1994 ChoiceReviews  
See [Baddeley, 1986] for an overview of algorithms for two-dimensional segmentation.  ...  Carol Miernicki Steeg and Sarah Lesher for proofreading and helpful discussions and to Desirée Sy for editing and formatting help.  ...  of grammars for rapid prototyping and modification of such algorithms.  ... 
doi:10.5860/choice.31-3826 fatcat:5jmryy7mkbcrvifz6ahlbbdceu

Dagstuhl Reports, Volume 9, Issue 9, September 2019, Complete Issue

2020
The 4-term relations for graphs were introduced in [3] . E. Krasilnikov constructed an extension of this graph invariant to all graphs with up to 8 vertices and proved uniqueness of the extension.  ...  For example, a graph theory application of a service change classifier algorithm assigning change labels to a web service's call graph representing calls between operations and procedures, which helped  ...  If G is planar then G * is also a planar graph and we may take H = G * . In this case, the answer to the question is Yes: it's just the Four Colour Theorem.  ... 
doi:10.4230/dagrep.9.9 fatcat:yxieovrp4zbxvhjyyiah6znqxm
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