1 research outputs found
(l,k)-Routing on Plane Grids
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 -routing problem, each node can
send at most packets and receive at most packets. Permutation
routing is the particular case . In the -central routing problem,
all nodes at distance at most from a fixed node want to send a packet
to . In this article we study the permutation routing, the -central
routing and the general -routing problems on plane grids, that is
square grids, triangular grids and hexagonal grids. We use the
\emph{store-and-forward} -port model, and we consider both full and
half-duplex networks. We first survey the existing results in the literature
about packet routing, with special emphasis on -routing on plane
grids. Our main contributions are the following:
1. Tight permutation routing algorithms on full-duplex hexagonal grids, and
half duplex triangular and hexagonal grids.
2. Tight -central routing algorithms on triangular and hexagonal grids.
3. Tight -routing algorithms on square, triangular and hexagonal
grids.
4. Good approximation algorithms (in terms of running time) for
-routing on square, triangular and hexagonal grids, together with new
lower bounds on the running time of any algorithm using shortest path routing.
These algorithms are all completely distributed, i.e., can be implemented
independently at each node. Finally, we also formulate the -routing
problem as a \textsc{Weighted Edge Coloring} problem on bipartite graphs.Comment: Final versio