Radhika Ramamurthi
(Department of Mathematics, California State University, San Marco)
Reliable Single Message Transmission and Graph Minors
Abstract
Reliable single message transmission considers the problem of sending a
message from a sender s to a receiver r through an asynchronous,
unreliable network, such as the Internet. In this talk, we consider the
specific problem of transmitting a single message from s to r through
a network in which edges may fail, but cannot recover. We assume that
there is at least one s,r-path without failing edges, and our aim is to
design a protocol that ensures that a message sent by s will be
received by r (no matter which edges fail) without generating an
infinite number of messages in the process.
We first give a structural characterization of graphs of networks
that permit successful single message transmission. This leads to an
explicit characterization of this family of networks in terms of forbidden
rooted minors, which in turn leads to a linear time recognition algorithm.
We also describe a protocol that ensures that the message is delivered
if the network does not contain one of the forbidden minors.
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