Routing permutations and 2–1 routing requests in the hypercube

Routing permutations and 2-1 routing requests in the hypercube

Routing Permutations in the Hypercube

Olivier Baudon y, Guillaume Fertin y and Ivan Havel z y LaBRI U.M.R. CNRS 5800, Universit e Bordeaux I 351 Cours de la Lib eration, F33405 Talence Cedex z Faculty of Mathematics and Physics, Charles University Malostransk e n am. 25, 118 00 Praha, Czech Republic fbaudon,[email protected], [email protected] Abstract We study an n-dimensional directed symmetric hypercube Hn, in which e...

QoS Routing in Hypercube Multicomputers

"!$# &% %' )( +*, -%.($ /! 0 12 . 354 !$# 12 ! 10 % ! .($ 76 198 : 1 ( 4 ! ;1 <#/= %' )($ >' 4 ? ! 1 4 % ! )($ @ # A 12 3B4 !$# 12 5>C D1 E? 1/ ?; F G ? 3 1 ($ !$# 4 * # )($ < #D 12 /! )(H ! *5 !$# ! 3 # >'1 ($ ! 1 3 !$# )(I6 1/8J 1 ( 4 ! 1 K8.%' ) MLC ?;? = #N 12 . 4 /! O P6 1/8GQ ! 1 (<* # )($ !$# SR :T!$# )?; 4 /! ($ )% ($ /! !$# 3 C (H /! U6 198V%' )( 1 ( 4 ! 1W W ! :

Deflection routing in hypercube networks

An approximate analysis of the transient and steady state behavior of deflection routing in hypercube networks is presented, under a uniform traffic model. In deflection routing congestion causes packets admitted to the network to be temporarily misrouted rather than buffered or dropped. Our approximations show that deflection routing performs remarkably well in hypercube networks, for small as...

Extremal Permutations in Routing Cycles

Let G be a graph whose vertices are labeled 1, . . . , n, and π be a permutation on [n] := {1, 2, . . . , n}. A pebble pi that is initially placed at the vertex i has destination π(i) for each i ∈ [n]. At each step, we choose a matching and swap the two pebbles on each of the edges. Let rt(G, π), the routing number for π, be the minimum number of steps necessary for the pebbles to reach their d...