inria-00265297
https://inria.hal.science/inria-00265297
https://inria.hal.science/inria-00265297v2/document
https://inria.hal.science/inria-00265297v2/file/RR-6480.pdf
arxiv:0803.2759
[UNICE] Université Nice Sophia Antipolis
[CNRS] CNRS - Centre national de la recherche scientifique
[INRIA] INRIA - Institut National de Recherche en Informatique et en Automatique
[INRIA-SOPHIA] INRIA Sophia Antipolis - Méditerranée
[INRIA-RRRT] Rapports de recherche et Technique de l'Inria
[I3S] Laboratoire d'Informatique, Signaux et Systèmes de Sophia-Antipolis
[INSMI] CNRS-INSMI - INstitut des Sciences Mathématiques et de leurs Interactions
[INRIASO] INRIA-SOPHIA
[INRIA_TEST] INRIA - Institut National de Recherche en Informatique et en Automatique
[TESTALAIN1] TESTALAIN1
[INRIA2] INRIA 2
[LARA] LARA
[UNIV-COTEDAZUR] Université Côte d'Azur
$(\ell,k)$-Routing on Plane Grids
Amini, Omid
Huc, Florian
Zerovnik, Janez
[MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO]
REPORT
Packet routing
distributed algorithm
$(\ell
k)$-routing
plane grids
permutation routing
shortest path
oblivious algorithm
The packet routing problem plays an essential role in communication networks. It involves how to transfer data from some origins to some destinations within a reasonable amount of time. In the $(\ell,k)$-routing problem, each node can send at most $\ell$ packets and receive at most $k$ packets. Permutation routing is the particular case $\ell=k=1$. In the $r$-central routing problem, all nodes at distance at most $r$ from a fixed node $v$ want to send a packet to $v$. In this article we study the permutation routing, the $r$-central routing and the general $(\ell,k)$-routing problems on plane grids, that is square grids, triangular grids and hexagonal grids. We use the \emph{store-and-forward} $\Delta$-port model, and we consider both full and half-duplex networks. The main contributions are the following: \begin{itemize} \item[1.] Tight permutation routing algorithms on full-duplex hexagonal grids, and half duplex triangular and hexagonal grids. \item[2.] Tight $r$-central routing algorithms on triangular and hexagonal grids. \item[3.] Tight $(k,k)$-routing algorithms on square, triangular and hexagonal grids. \item[4.] Good approximation algorithms (in terms of running time) for $(\ell,k)$-routing on square, triangular and hexagonal grids, together with new lower bounds on the running time of any algorithm using shortest path routing. \end{itemize} \noindent All these algorithms are completely distributed, i.e. can be implemented independently at each node. Finally, we also formulate the $(\ell,k)$-routing problem as a \textsc{Weighted Edge Coloring} problem on bipartite graphs.
2008
2008-03-25
en