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Cutwidth of ther-dimensional Mesh ofd-ary Trees

Imrich Vrťo
2000 RAIRO - Theoretical Informatics and Applications  
We prove that the cutwidth of the r-dimensional mesh of d-ary trees is of order (d (r?1)n+1 ), which improves and generalizes the previous result of Barth 2].  ...  Resum e Nous provons que la largeur de coupe de la grille r-dimensionall d'arbres d-naires est d'ordre (d (r?1)n+1 ), que ameliore et generalise le resultat de Barth 2].  ...  We study the cutwidth of the r-dimensional mesh of d-ary trees MT(r; d; n), denoted by cw(MT(r; d; n)). This graph is de ned as follows.  ... 
doi:10.1051/ita:2000128 fatcat:goe4tylibzgmhgailg6ntradyq

Addenda to the Survey of Layout Problems

Jordi Petit
2011 Bulletin of the European Association for Theoretical Computer Science  
Serna and the author published "A Survey of Graph Layout Problems", which then was a complete view of the current state of the art of layout problems from an algorithmic point of view.  ...  The current review expands the contents of the original survey with updated results from these latest ten years and contributes an extensive bibliography.  ...  O(n) [Nakano, 1994] d-dimensional c-ary arrays O(n) [Nakano, 1994] d-dimensional c-ary cliques O(n) [Nakano, 1994] ordinary 2-and 3-dim. meshes O(n 2 ) [Rolim et al., 1995] toroidal and cylindrical  ... 
dblp:journals/eatcs/Petit11 fatcat:eh3cwodhybdyzdmbxxnmuv66nu

Page 2349 of Mathematical Reviews Vol. , Issue 2002D [page]

2002 Mathematical Reviews  
Summary: “We prove that the cutwidth of the r-dimensional mesh of d-ary trees is of order O(d‘"~'"*'), which improves and gen- eralizes previous results.” 2002d:05110 05C78 Yu, Ping (PRC-NJN; Nanjing)  ...  We investigate some basic properties of these transformation graphs.” 2002d:05109 05C78 68M07 68R10 90B18 Vrto, Imrich (SK-AOS; Bratislava) Cutwidth of the r-dimensional mesh of d-ary trees.  ... 

Minimal cutwidth linear arrangements of abelian Cayley graphs

Daniel Berend, Ephraim Korach, Vladimir Lipets
2008 Discrete Mathematics  
We find the minimal cutwidth and bisection width values for abelian Cayley graphs with up to 4 generators and present an algorithm for finding the corresponding optimal ordering.  ...  We also find minimal cuts of each order.  ...  Trees O(n log n) [28] Hypercubes O(n) + [21] d-dimensional c-ary cliques O(n) + [20] Max degree and treewidth k O(n k 2 ) [3] Ordinary two-and three-dimensional meshes O(n) + [26] Toroidal  ... 
doi:10.1016/j.disc.2007.08.083 fatcat:oljtm6uzzzamhlvpfdqmo7wog4

Subject index volumes 1–92

2000 Discrete Applied Mathematics  
, 2223 three axes theorem, 2 165 counterfeit coins problem, 1132 three dimensional assignment problem, 1767 configuration, 252 three dimensional matching, 2278 model, 2278 three dimensional planar  ...  I, .We also zero one (1,2)-tree, 806 (1 ,d)-tree, 143 1 -broadcasting, 1440 l-center problem, 1124 1 -component, 260 1 -edge star, 1843 , 108 1 test, 1017, 1882, 1896, 1979 computer aided design, 677  ...  , 1745 , 1768 , 1797 , 1988 , 1990 , 1995 ,2 167,22 IO, 2223 algorithm, 711, 853 method, 339, 561 procedure, 676, 7 11 result, 2206 rule, 1493 redundance, 1489 redundancy, 342,939, 1620 , 1643 , 1745 of  ... 
doi:10.1016/s0166-218x(00)00208-0 fatcat:3e5dfhyphbbchjttvqq4yalo7e

Page 1888 of Mathematical Reviews Vol. , Issue Subject Index [page]

Mathematical Reviews  
Russian summary) 2002m:65043 Vrio, Imrich Cutwidth of the r-dimensional mesh of d-ary trees.  ...  Efficient line broadcasting in a d- dimensional grid.  ... 

Page 2490 of Mathematical Reviews Vol. , Issue Subject Index [page]

Mathematical Reviews  
Estimation of the capacity of a local wireless network under a high load and noise. (Russian. Russian summary) 2002¢:90014 Vrto, Imrich Cutwidth of the r-dimensional mesh of d-ary trees.  ...  Porro, R. see Bonzani, I. Rambau, Jérg see Hauptmeier, D. et al., 2002f:90016 Rascle, M. An improved macroscopic model of traffic flow: derivation and links with the Lighthill-Whitham model.  ... 

Page 181 of Mathematical Reviews Vol. , Issue Subject Index [page]

Mathematical Reviews  
., 2002h:05147 Vasuki, R. see Avadayappan, Selvam et al., 2002):05128 Vrfo, Imrich Cutwidth of the r-dimensional mesh of d-ary trees. (English summary) 20024:05109 Wallis, W. D.  ...  181 2002 Han, Pei You (with Cui, Zhen Wen) About the conjecture of felicitous trees. (English and Chinese summaries) — (with Yao, Hui) A new proof that two big classes of trees are felicitous trees.  ... 

Page 1482 of Mathematical Reviews Vol. , Issue Index [page]

Mathematical Reviews  
(English summary) 97j:68102 Ishigami, Yoshiyasu The wide-diameter of the n-dimensional toroidal mesh.  ...  A-order generation of k-ary trees with a 4k — 4 letter alphabet.  ... 

Page 2088 of Mathematical Reviews Vol. , Issue Author Index [page]

Mathematical Reviews  
(Summary) 2002g:68109 68R10 (05C85) — Cutwidth of the r-dimensional mesh of d-ary trees. (English summary) Theor. Inform. Appl. 34 (2000), no. 6, 515-519.  ...  From certain Lagrangian minimal submanifolds of the 3-dimensional complex projective space to minimal surfaces in the 5-sphere.  ... 

Page 1919 of Mathematical Reviews Vol. , Issue Subject Index [page]

Mathematical Reviews  
Optimally balanced spanning tree of the star network.  ...  ., (2001d:68026) Schréder, Heiko (with Sykora, Ondrej; Vrio, Imrich) Cyclic cutwidth of the mesh. (English summary) 2001f:68018 Schréder, Klaus see Cole, Richard J. et al., (2001d:68026) Shende, S.  ... 

Multi-grid cellular genetic algorithm for optimizing variable ordering of ROBDDs

Cristian Rotaru, Octav Brudaru
2012 2012 IEEE Congress on Evolutionary Computation  
A similarity based communication protocol between clusters of individuals from parallel grids is defined. The exchange of genetic material proves to considerably boost the quality of the solution.  ...  The extensive experimental evaluation uses difficult classical benchmarks and proves the efficiency and the stability of the algorithm.  ...  D. de Almeida, Renata M. C. R. Souza and Ana L. B.  ... 
doi:10.1109/cec.2012.6256590 dblp:conf/cec/RotaruB12 fatcat:4ly3nrktw5habc6lf5err7d5py

Reinforcement Learning (Dagstuhl Seminar 13321) The Critical Internet Infrastructure (Dagstuhl Seminar 13322) Coding Theory (Dagstuhl Seminar 13351) Interaction with Information for Visual Reasoning (Dagstuhl Seminar 13352)

Peter Auer, Marcus Hutter, Laurent, Georg Carle, Jochen Schiller, Steve Uhlig, Walter Willinger, Matthias Wählisch, Thore Husfeldt, Ramamohan Paturi, Gregory Sorkin, Ryan Williams (+14 others)
They use the same technology as IBM's ink-jet printer from 50 years ago, high dimensional and high throughput, measuring the intensity of the fluorescence (proportional to the number of certain proteins  ...  Acknowledgments The editors of this report would like to thank all participants for very fruitful and open-minded discussions! In particular, we thank the operators for sharing practical insights.  ...  model the access structures) and give rise to multiple of s-ary (where s is the power of 2 to the r and r being a divisor of m) simplex linear codes (whose the dual are the perfect s-ary Hamming codes  ... 

Combinatorics and Algorithmics of Strings (Dagstuhl Seminar 14111) Computational Complexity of Discrete Problems (Dagstuhl Seminar 14121) Computational Models of Cultural Behavior for Human-Agent Interaction (Dagstuhl Seminar 14131) Interaction and Collective Movement Processing (Dagstuhl Seminar 14132) Spatial reference in the Semantic Web and in Robotics (Dagstuhl Seminar 14142)

Johannes Fürnkranz, Eyke Hüllermeier, Cynthia Rudin, Scott Sanner, Roman Słowiński, Maxime Crochemore, James Currie, Gregory Kucherov, Dirk Nowotka, Pierre Dillenbourg, Claude Kirchner, John Mitchell (+25 others)
2014 unpublished
This report documents the program and the outcomes of Dagstuhl Seminar 14101 "Preference Learning".  ...  The motivation for this seminar was to showcase recent progress in these different areas with the goal of working towards a common basis of understanding, which should help to facilitate future synergies  ...  This yields both an implicit characterization of polynomial time in terms of ordinary differential equations, and a completeness result on the reachability problems for the corresponding class.  ...