scholarly journals The exchange graph and variations of the ratio of the two Symanzik polynomials

2019 ◽  
Vol 6 (2) ◽  
pp. 155-197 ◽  
Author(s):  
Omid Amini
Keyword(s):  
Exchange Graph

Index-Shuffle Graphs

1997 ◽  
Vol 08 (03) ◽  
pp. 289-304 ◽  
Author(s):  
Marc Baumslag ◽  
Bojana Obrenić
Keyword(s):  
Interconnection Networks ◽  
Graph Embedding ◽  
Theoretical Framework ◽  
Parallel Computers ◽  
Bounded Degree ◽  
Exchange Graph ◽  
Comparative Advantages ◽  
On Line

Index-shuffle graphs are introduced as candidate interconnection networks for parallel computers. The comparative advantages of index-shuffle graphs over the standard bounded-degree "approximations" of the hypercube, namely butterfly-like and shuffle-like graphs, are demonstrated in the theoretical framework of graph embedding and network emulations. An N-node index-shuffle graph emulates: • an N-node shuffle-exchange graph with no slowdown, which the currently best emulations of shuffle-like graphs by hypercubes and butterflies incur a slowdown of Ω( log N). • its like-sized butterfly graph with a slowdown O( log log log N), while the currently best emulations of butterfly-like graphs by shuffle-like graphs incur a slowdown of Ω( log log N). • an N-node hypercube that executes an on-line leveled algorithm with a slowdown O( log log N), while the slowdown of currently best such emulations of the hypercube by its bounded-degree shuffle-like and butterfly-like derivatives remains Ω( log N). Our emulation is based on an embedding of an N-node hypercube into an N-node index-shuffle graph with dilation O( log log N), while the currently best embeddings of the hypercube into its bounded-degree shuffle-like and butterfly-like derivatives incur a dilation of Ω( log N).

New layouts for the shuffle-exchange graph(Extended Abstract)

1981 ◽  
Author(s):  
Daniel Kleitman ◽  
Frank Thomson Leighton ◽  
Margaret Lepley ◽  
Gary L. Miller
Keyword(s):  
Exchange Graph

AN APPLICATION OF ST-NUMBERING TO SECRET KEY AGREEMENT

2011 ◽  
Vol 22 (05) ◽  
pp. 1211-1227 ◽  
Author(s):  
TAKAAKI MIZUKI ◽  
SATORU NAKAYAMA ◽  
HIDEAKI SONE
Keyword(s):  
Probability Distribution ◽  
Key Agreement ◽  
Key Exchange ◽  
Secret Key ◽  
Exchange Graph ◽  
Secret Keys ◽  
Shared Secret ◽  
Secret Key Agreement

Assume that there are players and an eavesdropper Eve, where several pairs of players have shared secret keys beforehand. We regard each player as a vertex of a graph and regard each pair of players sharing a key as an edge. Consider the case where Eve knows some of the keys according to a certain probability distribution. In this paper, applying the technique of st-numbering, we propose a protocol which allows any two designated players to agree on a secret key through such a "partially leaked key exchange graph." Our protocol is optimal in the sense that Eve's knowledge about the secret key agreed on by the two players is as small as possible.

IMPROVED BOUNDS ON CUTWIDTHS OF SHUFFLE-EXCHANGE AND DE BRUIJN GRAPHS

2004 ◽  
Vol 14 (03n04) ◽  
pp. 361-366 ◽  
Author(s):  
BURKHARD MONIEN ◽  
IMRICH VRŤO
Keyword(s):  
Upper Bound ◽  
De Bruijn Graph ◽  
Best Constant ◽  
De Bruijn Graphs ◽  
Exchange Graph ◽  
De Bruijn

We prove that the cutwidth of the n-dimensional shuffle-exchange graph is at most ⌈2n+1/n⌉, for n≥10. This essentially improves on the previous best constant factors. As a consequence we obtain an improved upper bound for the cutwidth of the de Bruijn graph.

scholarly journals Cluster Automorphisms and the Marked Exchange Graphs of Skew-Symmetrizable Cluster Algebras

10.37236/6230 ◽  
2016 ◽  
Vol 23 (4) ◽  
Author(s):  
John W Lawson
Keyword(s):  
Mapping Class Groups ◽  
Cluster Algebras ◽  
Mapping Class ◽  
Symmetric Matrices ◽  
Class Groups ◽  
Exchange Graph ◽  
Symmetrizable Matrices

Cluster automorphisms have been shown to have links to the mapping class groups of surfaces, maximal green sequences and to exchange graph automorphisms for skew-symmetric cluster algebras. In this paper we generalise these results to the skew-symmetrizable case by introducing a marking on the exchange graph. Many skew-symmetrizable matrices unfold to skew-symmetric matrices and we consider how cluster automorphisms behave under this unfolding with applications to coverings of orbifolds by surfaces.

Layouts for the Shuffle-Exchange Graph Based on the Complex Plane Diagram

1984 ◽  
Vol 5 (2) ◽  
pp. 202-215 ◽  
Author(s):  
Frank Thomson Leighton ◽  
Margaret Lepley ◽  
Gary L. Miller
Keyword(s):  
Complex Plane ◽  
Exchange Graph

Malchain: Virtual Application Behaviour Profiling by Aggregated Microservice Data Exchange Graph

2020 ◽  
Author(s):  
Mohammad Mahdi Ghorbani ◽  
Fereydoun Farrahi Moghaddam ◽  
Mengyuan Zhang ◽  
Makan Pourzandi ◽  
Kim Khoa Nguyen ◽  
...  
Keyword(s):  
Data Exchange ◽  
Exchange Graph
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