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Cutwidth of ther-dimensional Mesh ofd-ary Trees

2000
*
RAIRO - Theoretical Informatics and Applications
*

We prove that

doi:10.1051/ita:2000128
fatcat:goe4tylibzgmhgailg6ntradyq
*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. ...##
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Addenda to the Survey of Layout Problems

2011
*
Bulletin of the European Association for Theoretical Computer Science
*

Serna and

dblp:journals/eatcs/Petit11
fatcat:eh3cwodhybdyzdmbxxnmuv66nu
*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 ...##
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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*. ...##
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Minimal cutwidth linear arrangements of abelian Cayley graphs

2008
*
Discrete Mathematics
*

We find

doi:10.1016/j.disc.2007.08.083
fatcat:oljtm6uzzzamhlvpfdqmo7wog4
*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 ...##
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Subject index volumes 1–92

2000
*
Discrete Applied Mathematics
*

, 2223
three
axes theorem, 2 165
counterfeit coins problem, 1132
three

doi:10.1016/s0166-218x(00)00208-0
fatcat:3e5dfhyphbbchjttvqq4yalo7e
*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*...##
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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*. ...##
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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. ...##
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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. ...##
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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. ...##
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Multi-grid cellular genetic algorithm for optimizing variable ordering of ROBDDs

2012
*
2012 IEEE Congress on Evolutionary Computation
*

A similarity based communication protocol between clusters

doi:10.1109/cec.2012.6256590
dblp:conf/cec/RotaruB12
fatcat:4ly3nrktw5habc6lf5err7d5py
*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. ...##
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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)

unpublished

They use

fatcat:iz3co5xisfejfbnx2t6ptrorfm
*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 ...##
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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)

2014
unpublished

This report documents

fatcat:k3cugkqpf5btlba2hklfxyujdq
*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. ...