10 research outputs found
On Distributed Computation in Noisy Random Planar Networks
We consider distributed computation of functions of distributed data in
random planar networks with noisy wireless links. We present a new algorithm
for computation of the maximum value which is order optimal in the number of
transmissions and computation time.We also adapt the histogram computation
algorithm of Ying et al to make the histogram computation time optimal.Comment: 5 pages, 2 figure
Broadcasting in Noisy Radio Networks
The widely-studied radio network model [Chlamtac and Kutten, 1985] is a
graph-based description that captures the inherent impact of collisions in
wireless communication. In this model, the strong assumption is made that node
receives a message from a neighbor if and only if exactly one of its
neighbors broadcasts.
We relax this assumption by introducing a new noisy radio network model in
which random faults occur at senders or receivers. Specifically, for a constant
noise parameter , either every sender has probability of
transmitting noise or every receiver of a single transmission in its
neighborhood has probability of receiving noise.
We first study single-message broadcast algorithms in noisy radio networks
and show that the Decay algorithm [Bar-Yehuda et al., 1992] remains robust in
the noisy model while the diameter-linear algorithm of Gasieniec et al., 2007
does not. We give a modified version of the algorithm of Gasieniec et al., 2007
that is robust to sender and receiver faults, and extend both this modified
algorithm and the Decay algorithm to robust multi-message broadcast algorithms.
We next investigate the extent to which (network) coding improves throughput
in noisy radio networks. We address the previously perplexing result of Alon et
al. 2014 that worst case coding throughput is no better than worst case routing
throughput up to constants: we show that the worst case throughput performance
of coding is, in fact, superior to that of routing -- by a
gap -- provided receiver faults are introduced. However, we show that any
coding or routing scheme for the noiseless setting can be transformed to be
robust to sender faults with only a constant throughput overhead. These
transformations imply that the results of Alon et al., 2014 carry over to noisy
radio networks with sender faults.Comment: Principles of Distributed Computing 201
On network coding for sum-networks
A directed acyclic network is considered where all the terminals need to
recover the sum of the symbols generated at all the sources. We call such a
network a sum-network. It is shown that there exists a solvably (and linear
solvably) equivalent sum-network for any multiple-unicast network, and thus for
any directed acyclic communication network. It is also shown that there exists
a linear solvably equivalent multiple-unicast network for every sum-network. It
is shown that for any set of polynomials having integer coefficients, there
exists a sum-network which is scalar linear solvable over a finite field F if
and only if the polynomials have a common root in F. For any finite or cofinite
set of prime numbers, a network is constructed which has a vector linear
solution of any length if and only if the characteristic of the alphabet field
is in the given set. The insufficiency of linear network coding and
unachievability of the network coding capacity are proved for sum-networks by
using similar known results for communication networks. Under fractional vector
linear network coding, a sum-network and its reverse network are shown to be
equivalent. However, under non-linear coding, it is shown that there exists a
solvable sum-network whose reverse network is not solvable.Comment: Accepted to IEEE Transactions on Information Theor