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Modular counting of subgraphs: Matchings, matching-splittable graphs, and paths [article]

Radu Curticapean, Holger Dell, Thore Husfeldt
2021 arXiv   pre-print
Complementing our algorithm, we also give a simple and self-contained proof that counting $k$-matchings modulo odd integers $q$ is Mod_q-W[1]-complete and prove that counting $k$-paths modulo $2$ is Parity-W  ...  This shows that the known polynomial-time cases of subgraph detection (Jansen and Marx, SODA 2015) carry over into the setting of counting modulo $2^t$.  ...  We are ready to state the modular counting algorithm for s-matching-splittable subgraphs. ) Let C = 2 R ∪ 2 R 1 ∪ 2 R 2 .  ... 
arXiv:2107.00629v1 fatcat:6ch2zonbobgjdjrrkxdr4cz2je

Modular Counting of Subgraphs: Matchings, Matching-Splittable Graphs, and Paths

Radu Curticapean, Holger Dell, Thore Husfeldt, Grzegorz Herman, Rasmus Pagh, Petra Mutzel
2021
Complementing our algorithm, we also give a simple and self-contained proof that counting k-matchings modulo odd integers q is {Mod}_q W[1]-complete and prove that counting k-paths modulo 2 is ⊕W[1]-complete  ...  This shows that the known polynomial-time cases of subgraph detection (Jansen and Marx, SODA 2015) carry over into the setting of counting modulo 2^t.  ...  An appropriate transfer of the subgraph-homomorphism framework to modular counting is likely to help in settling this conjecture. Partial results towards this have been obtained by Peyerimhoff et al.  ... 
doi:10.4230/lipics.esa.2021.34 fatcat:qoi4icux7vgv3jzgy37yx5qqym

Fixed-Treewidth-Efficient Algorithms for Edge-Deletion to Intersection Graph Classes [article]

Toshiki Saitoh, Ryo Yoshinaka, Hans L. Bodlaender
2021 arXiv   pre-print
For a graph class 𝒞, the 𝒞-Edge-Deletion problem asks for a given graph G to delete the minimum number of edges from G in order to obtain a graph in 𝒞.  ...  We study the 𝒞-Edge-Deletion problem for 𝒞 the permutation graphs, interval graphs, and other related graph classes.  ...  This work was supported in part by JSPS KAKENHI Grant Numbers JP18H04091 and JP19K12098.  ... 
arXiv:2007.03859v2 fatcat:i7v6pgxr3fb3vcnuzc2y6oykhe

The monadic second-order logic of graphs XVI : Canonical graph decompositions

Bruno Courcelle, Erich Grädel
2006 Logical Methods in Computer Science  
canonical graph decompositions like the modular decomposition and the Tutte decomposition of 2-connected graphs into 3-connected components.  ...  As an application, we prove that the set of graphs having the same cycle matroid as a given 2-connected graph can be defined from this graph by Monadic Second-Order formulas.  ...  Acknowledgement The dissertation of F. de Montgolfier [19] contains a very good introduction to the articles by W. Cunnigham and J. Edmonds [18, 17] . Many thanks to A. Blumensath, S.  ... 
doi:10.2168/lmcs-2(2:2)2006 fatcat:k6twdcpho5blbcund2gbmocjwy

Describing shapes by geometrical-topological properties of real functions

S. Biasotti, L. De Floriani, B. Falcidieno, P. Frosini, D. Giorgi, C. Landi, L. Papaleo, M. Spagnuolo
2008 ACM Computing Surveys  
and attributes are crucial for characterizing specific instances of features, while topological properties are necessary to abstract and classify shapes according to invariant aspects of their geometry  ...  The mapping function plays the role of a lens through which we look at the properties of the shape, and different functions provide different insights.  ...  This work has been developed within the CNR research activities ICT-P03 and DG.RSTL.050.004, and with the support of the EU FP6 Network of Excellence AIM@SHAPE, contract number 506766, by the Italian National  ... 
doi:10.1145/1391729.1391731 fatcat:yg6k2lwerfd63nuhhxxypcnzju

A quantitative framework for software restructuring

Byung‐Kyoo Kang, James M. Bieman
1999 Journal of Software Maintenance: Research and Practice  
Restructuring is accomplished through a series of decomposition and composition operations which increase the cohesion and or decrease the coupling of individual system components.  ...  Criteria for comparing alternative design structures include measures of design-level cohesion and coupling.  ...  We thank the Journal's anonymous reviewers for their comments, which greatly improved both the content and presentation.  ... 
doi:10.1002/(sici)1096-908x(199907/08)11:4<245::aid-smr193>3.3.co;2-# fatcat:zwxy3ryy3zapzpziyrdv7i3joy

A quantitative framework for software restructuring

Byung-Kyoo Kang, James M. Bieman
1999 Journal of Software Maintenance: Research and Practice  
Restructuring is accomplished through a series of decomposition and composition operations which increase the cohesion and or decrease the coupling of individual system components.  ...  Criteria for comparing alternative design structures include measures of design-level cohesion and coupling.  ...  We thank the Journal's anonymous reviewers for their comments, which greatly improved both the content and presentation.  ... 
doi:10.1002/(sici)1096-908x(199907/08)11:4<245::aid-smr193>3.0.co;2-8 fatcat:bvux3memobdafkvtzxrmo75pui

On Dynamic Graph Partitioning and Graph Clustering using Diffusion

Henning Meyerhenke, Joachim Gehweiler
unpublished
Experiments with graph sequences that imitate adaptive numerical simulations demonstrate the applicability and high quality of DIBAP for load balancing by repartitioning.  ...  State-of-the-art libraries for this problem are based on graph repartitioning.  ...  Figure 1 illustrates how this principle works for a path graph and k = 3.  ... 
fatcat:2zc2exfdtrc2nnk55hqduhywei

CloudNet embeddings [article]

Carlo Fürst, Anja Feldmann, Technische Universität Berlin, Technische Universität Berlin
2016
In this work, we analyze two of these requirements and improve the way in which CloudNets are embedded to provide more options towards the tenant and increase the overall resource utilization of the provider  ...  We show that this subproblem of the CloudNet embedding problem is, contrary to previous beliefs, computationally tractable and show that it can even be solved taking data locality into account.  ...  The runtime consists of two parts: the construction of the matching graph and the actual matching computation.  ... 
doi:10.14279/depositonce-5340 fatcat:5x5yhlxpiffepptrguoamj5ynq

Analysis of large biological data: metabolic network modularization and prediction of N-terminal acetylation

Christophe Charpilloz, Bastien Chopard
2015
For example if a match count as 1 and a gap is penalized by 0.1, the alignments produce in order the scores: 2, 1.8, 1.9, 1.7 and 1.4.  ...  Also module can be found by searching for the partition that maximizes the network's modularity. The modularity measure the strength of division of a network into modules.  ...  The stop function is an implementation of a stop criterion depending on the instances set and the depth of the tree. Ensure: The root of a decision tree.  ... 
doi:10.13097/archive-ouverte/unige:86046 fatcat:bptdtg2lincitjoytls53f2rgq

Specification and optimization of analytical data flows

Fabian Hüske, Volker Markl, Technische Universität Berlin, Technische Universität Berlin
2016
The large number and diversity of data analysis techniques as well as the lack of data structure determine the use of user-defined functions and data types.  ...  The success of the SQL query language has shown the advantages of declarative query specification, such as potential for optimization and ease of use.  ...  Since then, Volker has been my most important mentor and encouraged and helped me to follow the academic path.  ... 
doi:10.14279/depositonce-5150 fatcat:5hdok3skcrddjdcodvmvgekbli

Game-theoretic and other Algorithmic Aspects of Mobile Crowdsensing

Julia Buwaya, Jose Rolim
2021
the induced subgraph E(Q).  ...  Overall there were 114 fields and we counted the preferences of 27 agents.  ... 
doi:10.13097/archive-ouverte/unige:157618 fatcat:gk6msq7fhbd3tfn3xkvqmu74wq

Formal Methods for Coordinating Multi-Agent Systems (Dagstuhl Seminar 14332) Next Generation Static Software Analysis Tools (Dagstuhl Seminar 14352) Computational Aspects of Fabrication (Dagstuhl Seminar 14361) Augmenting Human Memory-Capture and Recall in the Era of Lifelogging (Dagstuhl Seminar 14362)

Michael Benedikt, Carsten Lutz, Thomas Ågotnes, Nils Bulling, Daniel Kroening, Thomas Reps, Sanjit Seshia, Aditya Thakur, Patrick Cousot, Daniel Kroening, Carsten Sinz, Marc Alexa (+7 others)
2014 Querying and Reasoning Under Expressive Constraints   unpublished
The entailment regimes are specified in a very general way by extending SPARQL's standard query evaluation mechanism (simple entailment/subgraph matching).  ...  SMT solvers in a modular and flexible design.  ...  matches it.  ... 
fatcat:xufggsvrynatbg2tlxe5gt7tei

Capacitated Network Design - Multi-Commodity Flow Formulations, Cutting Planes, and Demand Uncertainty [article]

Christian Raack, Martin Grötschel, Technische Universität Berlin, Technische Universität Berlin
2012
More precisely, we identify multi-commodity (MCF) network sub-matrices and resolve the isomorphisms of the commodity blocks as well as the original graph structure.  ...  Providing theoretical and computational evidence for the efficacy of inequalities based on network cuts, we extend existing theory and algorithmic work in different directions.  ...  one (commodity) graph is contained in another or to maximize the largest common subgraph of two given (commodity) graphs.  ... 
doi:10.14279/depositonce-3291 fatcat:ag4junbmt5fglmkyvcyaxylm5u

Nonmonotonic Inductive Logic Programming as Abductive Search

Domenico Corapi, Emil Lupu, Alessandra Russo
2012
On the other hand, integration of negation and nonmonotonic reasoning in logic programming is common and important for a number of problems.  ...  negation, recursion and the definition of elements of the domain that are not directly observed.  ...  The dependency graph D P for a normal program P is a directed graph with signed positive and negative edges.  ... 
doi:10.25560/9814 fatcat:vcxuuya7vbegjifrtqj6kjrjcu