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### NLC2-DECOMPOSITION IN POLYNOMIAL TIME

ÖJVIND JOHANSSON
2000 International Journal of Foundations of Computer Science
In this paper, an algorithm is presented that works for k = 2. It runs in O(n 4 log n) time and uses O(n 2 ) space. Related concepts: clique-decomposition, cliquewidth.  ...  It is unknown though whether arbitrary graphs of NLC-width at most k can be decomposed with k labels in polynomial time. So far this has been possible only for k = 1, which corresponds to cographs.  ...  With the algorithm in  , this takes O(|V(G)| 2 ) time and space. NLC 2 -Decomposition in Polynomial Time In this section we solve the NLC k -decomposition problem for k = 2.  ...

### NLC2-Decomposition in Polynomial Time [chapter]

Öjvind Johansson
1999 Lecture Notes in Computer Science
In this paper, an algorithm is presented that works for k = 2. It runs in O(n 4 log n) time and uses O(n 2 ) space. Related concepts: clique-decomposition, cliquewidth.  ...  It is unknown though whether arbitrary graphs of NLC-width at most k can be decomposed with k labels in polynomial time. So far this has been possible only for k = 1, which corresponds to cographs.  ...  With the algorithm in  , this takes O(|V(G)| 2 ) time and space. NLC 2 -Decomposition in Polynomial Time In this section we solve the NLC k -decomposition problem for k = 2.  ...

### Page 3340 of Mathematical Reviews Vol. , Issue 2001E [page]

2001 Mathematical Reviews
Reed], An improved algorithm for finding tree decompositions of small width (365- 371); Ojvind Johansson, NLC2-decomposition in polynomial time (373-395); Anne Berry, Jean-Paul Bordat and Olivier Cogis  ...  , Gen- erating all the minimal separators of a graph (397-403); Anna Accornero, Massimo Ancona and Sonia Varini, All separating triangles in a plane graph can be optimally “broken” in polyno- mial time  ...

### Quantifying Tripartite Spatial and Energy-Time Entanglement in Nonlinear Optics [article]

James Schneeloch, Richard J. Birrittella, Christopher C. Tison, Gregory A. Howland, Michael L. Fanto, Paul M. Alsing
2021 arXiv   pre-print
Furthermore, we predict its effectiveness in quantifying the tripartite spatial and energy-time entanglement in photon triplets generated in cascaded spontaneous parametric down-conversion (SPDC), and  ...  In this work, we provide a means to quantify genuine tripartite entanglement in arbitrary (pure and mixed) continuous-variable states as measured by the Tripartite Entanglement of formation -- a resource-based  ...  In this decomposition, θ n (x B , x C ) is an n-th order polynomial double-Gaussian wavefunction, defined here as the product of a Gaussian wavefunction in the rotated coordinate (x B −x C ) and an n-th  ...

### Page 1984 of Mathematical Reviews Vol. , Issue Subject Index [page]

Mathematical Reviews
(English summary) 2001b:68100 Johansson, Ojvind NLC2-decomposition in polynomial time. (English summary) 2001h:68121 Kajitani, Yoji see Kubo, Yukiko et al.  ...  Approximating the independence number and the chromatic number in expected polynomial time.  ...

### Affine highest weight categories and affine quasihereditary algebras

Alexander S. Kleshchev
2015 Proceedings of the London Mathematical Society
In particular, we prove an affine analogue of the Cline-Parshall-Scott Theorem. We also develop stratified versions of these notions.  ...  This additional property is reminiscent of the properties of quasihereditary algebras of Cline-Parshall-Scott in a finite dimensional situation.  ...  In general, let C ⊇ C 1 ⊇ C 2 ⊇ . . . be a filtration as in (NLC2). Since C/C n is finite length, it suffices to prove that ext i (C n , L) = 0 for n sufficiently large.  ...

### A study of single laser interferometry-based sensing and measuring technique in robot manipulator control and guidance. Volume 1

Pek Loo Teoh
2017
Acknowledgements The research presented in this thesis was conducted in the Robotics  ...  *nLC2*v_m + c; Bptr[l] = -nLC2*nLCl*v_m; Bptr = -nLCl*2*d; Bptr[l] = Bptr ; Bptrtl]  = nIiCl*nLCl*v_m + c; Bptr[l] = -nLC2*2*d; Bptr = -Bptr; Bptr[l] = -Bptr  ...  The object-orientated programming architecture in C++ enables decomposition and abstraction of the subsystem's operations into object modules.  ...

### Fungal and bacterial contributions to hyphosphere enzyme activity

Denise Dowdy Brooks
2010
in areas of low phosphatase activity.  ...  Visualization of phosphatase activity across a chronosequence forest stands demonstrated a change in the pattern of in-situ soil phosphatase activity; areas of phosphatase activity were smaller in stands  ...  in soil over time.  ...