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Deciding whether graph G has page number one is in NC

Shigeru Masuyama, Shozo Naito
1992 Information Processing Letters  
Based on a forbidden subgraph characterization of a graph to have one page, we develop a polylog time algorithm to tell if page number of given graph $G$ is one with polynomial number of processors, clarifying  ...  this problem to be in NC.  ...  Deciding if a Graph has Page Number One is in NC We now introduce a linear time algorithm, by which we can decide, with respect to the number of edges, whether the given graph $G$ has page number one.  ... 
doi:10.1016/0020-0190(92)90247-s fatcat:qjgdoapjmrevfphcuzshuxkac4

Page 1198 of Mathematical Reviews Vol. , Issue 90B [page]

1990 Mathematical Reviews  
This means also that there is an NC algorithm for the problem whether a K;3-free graph has a perfect matching and whether it has an exact matching.  ...  In passing, it is also shown that the problems of testing whether a graph is K3;-free or Ks-minor-free are also in NC.  ... 

Circuits, Logic and Games (Dagstuhl Seminar 15401)

Mikolaj Bojanczyk, Meena Mahajan, Thomas Schwentick, Heribert Vollmer, Marc Herbstritt
2016 Dagstuhl Reports  
In recent years, there has been an impressive and sustained growth of interest and activity in the intersection of finite model theory and Boolean circuit complexity.  ...  on circuit lower bounds that trigger results in finite model theory like separations between logics New connections between uniformity conditions on circuit families and logical predicates Structural  ...  In [1] it was shown that deciding whether a perfect matching exists for constant width grid graphs can be decided in ACC 0 .  ... 
doi:10.4230/dagrep.5.9.105 dblp:journals/dagstuhl-reports/BojanczykMSV15 fatcat:pv6oxt7lnvhkbczugwxmvumdxq

Improved Bounds for Bipartite Matching on Surfaces

Samir Datta, Arjun Gopalan, Raghav Kulkarni, Raghunath Tewari, Marc Herbstritt
2012 Symposium on Theoretical Aspects of Computer Science  
(improves upon the SPL bound from [7]); (2) BPM in constant genus graphs is in NL (orthogonal to the SPL bound from [8]); (3) BPM in poly-logarithmic genus graphs is in NC; (extends the NC bound for O  ...  We exhibit the following new upper bounds on the space complexity and the parallel complexity of the Bipartite Perfect Matching (BPM) problem for graphs of small genus: (1) BPM in planar graphs is in UL  ...  Acknowledgement We would like to thank Prajakta Nimbhorkar for discussion in the initial stages of the work, in particular for pointing out that the Neg-Cycle problem is in NL.  ... 
doi:10.4230/lipics.stacs.2012.254 dblp:conf/stacs/DattaGKT12 fatcat:p2hinlmayfchffc4lvkmw77omu

A Gentle Introduction to Applications of Algorithmic Metatheorems for Space and Circuit Classes

Till Tantau
2016 Algorithms  
Now, 101 what about highly interconnected graphs that are not tree-like? Do their many edges somehow help 102 in deciding whether the graph has an even cycle?  ...  cycle problem, which just asks whether there is a cycle of even length in a graph (in the 98 graph the black vertices form the only even cycle).  ...  For each k, the set {G | G has tree width at most k and G is 3-colorable} can be decided in logarithmic space. Proof.  ... 
doi:10.3390/a9030044 fatcat:4njcekeavbeufbltvu5y4rxkxa

Introducing lop-kernels: a framework for kernelization lower bounds [article]

Júlio Araújo, Marin Bougeret, Victor A. Campos, Ignasi Sau
2021 arXiv   pre-print
In the Maximum Minimal Vertex Cover (MMVC) problem, we are given a graph G and a positive integer k, and the objective is to decide whether G contains a minimal vertex cover of size at least k.  ...  Back to the MMVC problem, given the (plausible) non-existence of subquadratic kernels for MMVC on general graphs, we provide subquadratic kernels on H-free graphs for several graphs H, such as the bull  ...  In fact, deciding whether a set S ⊆ V (G) can the extended to a minimal vertex cover of G is an NP-complete problem [20]. 7 Subquadratic kernels for MMVC on particular graph classes In this section  ... 
arXiv:2102.02484v3 fatcat:fzq4726v7feydmutjof6zvkik4

Distributed LTL Model Checking Based on Negative Cycle Detection [chapter]

Luboš Brim, Ivana Černá, Pavel Krčál, Radek Pelánek
2001 Lecture Notes in Computer Science  
We come up with entirely different approach which is dependent on locating cycles with negative length in a directed graph with real number length of edges.  ...  All the known methods for automata based model checking are based on depth first traversal of the state space which is difficult to parallelise as the ordering in which vertices are visited plays an important  ...  The SSSP problem is to decide whether, for a given triple (G, s, l), the graph G is feasible and if it is then to compute shortest paths from the source vertex s to all vertices v ∈ V .  ... 
doi:10.1007/3-540-45294-x_9 fatcat:jvkeecahyrefjnzgmcisltthmm

The Complexity of Bisimulation and Simulation on Finite Systems [article]

Moses Ganardi, Stefan Göller, Markus Lohrey
2018 arXiv   pre-print
Furthermore, if only one of the input graphs is required to be a tree, the bisimulation (simulation) problem is contained in AC^1 (LogCFL).  ...  In contrast, it is also shown that the simulation problem is P-complete already for graphs of bounded path-width.  ...  Whether the bisimulation problem on graphs of bounded tree-width is in NC remains open.  ... 
arXiv:1806.00256v1 fatcat:3qmsuonnurb2jpystyfioqtlli

Structured objects in owl

Boris Motik, Bernardo Cuenca Grau, Ulrike Sattler
2008 Proceeding of the 17th international conference on World Wide Web - WWW '08  
Based on an observation about the nature of structured objects, we ensure decidability of our formalism.  ...  Applications of semantic technologies often require the representation of and reasoning with structured objects-that is, objects composed of parts connected in complex ways.  ...  Decidability of the formalism is now ensured by the separation of the roles into tree and graph ones.  ... 
doi:10.1145/1367497.1367573 dblp:conf/www/MotikGS08 fatcat:6ma64pxqqjdhzcxjimsi4u25ki

A simple parallel algorithm for the maximal independent set problem

M Luby
1985 Proceedings of the seventeenth annual ACM symposium on Theory of computing - STOC '85  
' described in section 3.1.  ...  I thank Allan Borodin for introducing me to the work on connectionist models.  ...  on the following page.  ... 
doi:10.1145/22145.22146 dblp:conf/stoc/Luby85 fatcat:d3e5wbdpu5cfbi7cxidqeann4u

A Simple Parallel Algorithm for the Maximal Independent Set Problem

Michael Luby
1986 SIAM journal on computing (Print)  
' described in section 3.1.  ...  I thank Allan Borodin for introducing me to the work on connectionist models.  ...  on the following page.  ... 
doi:10.1137/0215074 fatcat:ns3swdjid5fzlniemwtdnwfeem

An empirical study on compressed sensing MRI using fast composite splitting algorithm and combined sparsifying transforms

Wangli Hao, Jianwu Li, Zhengchao Dong, Qihong Li, Kaitao Yu
2015 International journal of imaging systems and technology (Print)  
' described in section 3.1.  ...  I thank Allan Borodin for introducing me to the work on connectionist models.  ...  on the following page.  ... 
doi:10.1002/ima.22146 fatcat:dbh5mctlevd35a4qjdkgpbxxom

D5.2 Policy-based Language Data Management

Víctor Rodríguez-Doncel, Pablo Calleja
2020 Zenodo  
A portal has been published where all the information is presented (  ...  Integration with parts of Linghub shall be reported in D5.3 "Prêt-à-LLOD Language Resource Discover Portal", in June 2020 -Linghub is a portal providing harmonized access to language resource metadata,  ...  may assign the undefined graph to the accessible or to the non-accesible graphs -ultimately the Graph Matcher decides whether a resource (RDF triple) is authorised or not.  ... 
doi:10.5281/zenodo.5744693 fatcat:itbpyxwai5agdbeptab27a772a

A Quest for Structure in Complexity

Vikraman Arvind, Meena Mahajan
2017 Bulletin of the European Association for Theoretical Computer Science  
In particular, it shows that reachability on layered grid graphs can be decided in ULOG.  ...  Counting perfect matchings in planar graphs is in P and even NC, whereas in general graphs deciding existence via shallow circuits so far seems to need non-uniformity or quasi-polynomial size.  ... 
dblp:journals/eatcs/ArvindM17 fatcat:axk2knwgpbh6nfdz3bespdpqom

Page 4092 of Mathematical Reviews Vol. , Issue 2004e [page]

2004 Mathematical Reviews  
, NC) Optimal one-page tree embeddings in linear time.  ...  In fact, after a sufficient number of steps, the quality improvement provided by the paral- lel approach over the sequential one is superlinear in the number of processors used by the parallel model.”  ... 
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