6,859 research outputs found
On Approximating the Sum-Rate for Multiple-Unicasts
We study upper bounds on the sum-rate of multiple-unicasts. We approximate
the Generalized Network Sharing Bound (GNS cut) of the multiple-unicasts
network coding problem with independent sources. Our approximation
algorithm runs in polynomial time and yields an upper bound on the joint source
entropy rate, which is within an factor from the GNS cut. It
further yields a vector-linear network code that achieves joint source entropy
rate within an factor from the GNS cut, but \emph{not} with
independent sources: the code induces a correlation pattern among the sources.
Our second contribution is establishing a separation result for vector-linear
network codes: for any given field there exist networks for which
the optimum sum-rate supported by vector-linear codes over for
independent sources can be multiplicatively separated by a factor of
, for any constant , from the optimum joint entropy
rate supported by a code that allows correlation between sources. Finally, we
establish a similar separation result for the asymmetric optimum vector-linear
sum-rates achieved over two distinct fields and
for independent sources, revealing that the choice of field
can heavily impact the performance of a linear network code.Comment: 10 pages; Shorter version appeared at ISIT (International Symposium
on Information Theory) 2015; some typos correcte
Network Coding for Speedup in Switches
We present a graph theoretic upper bound on speedup needed to achieve 100%
throughput in a multicast switch using network coding. By bounding speedup, we
show the equivalence between network coding and speedup in multicast switches -
i.e. network coding, which is usually implemented using software, can in many
cases substitute speedup, which is often achieved by adding extra switch
fabrics. This bound is based on an approach to network coding problems called
the "enhanced conflict graph". We show that the "imperfection ratio" of the
enhanced conflict graph gives an upper bound on speedup. In particular, we
apply this result to K-by-N switches with traffic patterns consisting of
unicasts and broadcasts only to obtain an upper bound of min{(2K-1)/K,
2N/(N+1)}.Comment: 5 pages, 4 figures, IEEE ISIT 200
Relaxed Byzantine Vector Consensus
Exact Byzantine consensus problem requires that non-faulty processes reach
agreement on a decision (or output) that is in the convex hull of the inputs at
the non-faulty processes. It is well-known that exact consensus is impossible
in an asynchronous system in presence of faults, and in a synchronous system,
n>=3f+1 is tight on the number of processes to achieve exact Byzantine
consensus with scalar inputs, in presence of up to f Byzantine faulty
processes. Recent work has shown that when the inputs are d-dimensional vectors
of reals, n>=max(3f+1,(d+1)f+1) is tight to achieve exact Byzantine consensus
in synchronous systems, and n>= (d+2)f+1 for approximate Byzantine consensus in
asynchronous systems.
Due to the dependence of the lower bound on vector dimension d, the number of
processes necessary becomes large when the vector dimension is large. With the
hope of reducing the lower bound on n, we consider two relaxed versions of
Byzantine vector consensus: k-Relaxed Byzantine vector consensus and
(delta,p)-Relaxed Byzantine vector consensus. In k-relaxed consensus, the
validity condition requires that the output must be in the convex hull of
projection of the inputs onto any subset of k-dimensions of the vectors. For
(delta,p)-consensus the validity condition requires that the output must be
within distance delta of the convex hull of the inputs of the non-faulty
processes, where L_p norm is used as the distance metric. For
(delta,p)-consensus, we consider two versions: in one version, delta is a
constant, and in the second version, delta is a function of the inputs
themselves.
We show that for k-relaxed consensus and (delta,p)-consensus with constant
delta>=0, the bound on n is identical to the bound stated above for the
original vector consensus problem. On the other hand, when delta depends on the
inputs, we show that the bound on n is smaller when d>=3
Data Dissemination in Unified Dynamic Wireless Networks
We give efficient algorithms for the fundamental problems of Broadcast and
Local Broadcast in dynamic wireless networks. We propose a general model of
communication which captures and includes both fading models (like SINR) and
graph-based models (such as quasi unit disc graphs, bounded-independence
graphs, and protocol model). The only requirement is that the nodes can be
embedded in a bounded growth quasi-metric, which is the weakest condition known
to ensure distributed operability. Both the nodes and the links of the network
are dynamic: nodes can come and go, while the signal strength on links can go
up or down.
The results improve some of the known bounds even in the static setting,
including an optimal algorithm for local broadcasting in the SINR model, which
is additionally uniform (independent of network size). An essential component
is a procedure for balancing contention, which has potentially wide
applicability. The results illustrate the importance of carrier sensing, a
stock feature of wireless nodes today, which we encapsulate in primitives to
better explore its uses and usefulness.Comment: 28 pages, 2 figure
Time-relaxed broadcasting in communication networks
AbstractBroadcasting is the process of information dissemination in communication networks (modelled as graphs) whereby a message originating at one vertex becomes known to all members under the constraint that each call requires one unit of time and at every step any member can call at most one of its neighbours. A broadcast graph on n vertices is a network in which message can be broadcast in the minimum possible (=⌊log2n⌋) time regardless of the originator. Broadcast graphs having the smallest number of edges are called minimum broadcast graphs, and are subjects of intensive study. On the other hand, in Shastri (1995) we have considered how quickly broadcasting can be done in trees. In this paper, we study how the number of edges in a minimum broadcast graphs decrease, as we allow addition time over ⌊log2 n⌋, until we get a tree. In particular, the sparsest possible time-relaxed broadcast graphs are constructed for small n(⩽15) and very sparse time-relaxed broadcast graphs are given for larger n(⩽65). General constructions are also provided putting bounds which hold for all n. Some of these constructions make use of the techniques developed in Bermond et al. (1995, 1992) and Chau and Liestman (1985)
- …