1 research outputs found
Shortest Paths in a Hybrid Network Model
We introduce a communication model for hybrid networks, where nodes have
access to two different communication modes: a local mode where communication
is only possible between specific pairs of nodes, and a global mode where
communication between any pair of nodes is possible. This can be motivated, for
instance, by wireless networks in which we combine direct device-to-device
communication (e.g., using WiFi) with communication via a shared infrastructure
(like base stations, the cellular network, or satellites).
Typically, communication over short-range connections is cheaper and can be
done at a much higher rate. Hence, we are focusing here on the LOCAL model (in
which the nodes can exchange an unbounded amount of information in each round)
for the local connections while for the global communication we assume the
so-called node-capacitated clique model, where in each round every node can
exchange only -bit messages with just other nodes.
In order to explore the power of combining local and global communication, we
study the impact of hybrid communication on the complexity of computing
shortest paths in the graph given by the local connections. Specifically, for
the all-pairs shortest paths problem (APSP), we show that an exact solution can
be computed in time and that approximate solutions
can be computed in time . For the
single-source shortest paths problem (SSSP), we show that an exact solution can
be computed in time , where
denotes the shortest path diameter. We further show that a
-approximate solution can be computed in time . Additionally, we show that for every constant
, it is possible to compute an -approximate solution in
time