52,902 research outputs found
Tolerating multiple faults in multistage interconnection networks with minimal extra stages
Adams and Siegel (1982) proposed an extra stage cube interconnection network that tolerates one switch failure with one extra stage. We extend their results and discover a class of extra stage interconnection networks that tolerate multiple switch failures with a minimal number of extra stages. Adopting the same fault model as Adams and Siegel, the faulty switches can be bypassed by a pair of demultiplexer/multiplexer combinations. It is easy to show that, to maintain point to point and broadcast connectivities, there must be at least S extra stages to tolerate I switch failures. We present the first known construction of an extra stage interconnection network that meets this lower-bound. This 12-dimensional multistage interconnection network has n+f stages and tolerates I switch failures. An n-bit label called mask is used for each stage that indicates the bit differences between the two inputs coming into a common switch. We designed the fault-tolerant construction such that it repeatedly uses the singleton basis of the n-dimensional vector space as the stage mask vectors. This construction is further generalized and we prove that an n-dimensional multistage interconnection network is optimally fault-tolerant if and only if the mask vectors of every n consecutive stages span the n-dimensional vector space
Erasure Correction for Noisy Radio Networks
The radio network model is a well-studied model of wireless, multi-hop networks. However, radio networks make the strong assumption that messages are delivered deterministically. The recently introduced noisy radio network model relaxes this assumption by dropping messages independently at random.
In this work we quantify the relative computational power of noisy radio networks and classic radio networks. In particular, given a non-adaptive protocol for a fixed radio network we show how to reliably simulate this protocol if noise is introduced with a multiplicative cost of poly(log Delta, log log n) rounds where n is the number nodes in the network and Delta is the max degree. Moreover, we demonstrate that, even if the simulated protocol is not non-adaptive, it can be simulated with a multiplicative O(Delta log ^2 Delta) cost in the number of rounds. Lastly, we argue that simulations with a multiplicative overhead of o(log Delta) are unlikely to exist by proving that an Omega(log Delta) multiplicative round overhead is necessary under certain natural assumptions
Shortest, Fastest, and Foremost Broadcast in Dynamic Networks
Highly dynamic networks rarely offer end-to-end connectivity at a given time.
Yet, connectivity in these networks can be established over time and space,
based on temporal analogues of multi-hop paths (also called {\em journeys}).
Attempting to optimize the selection of the journeys in these networks
naturally leads to the study of three cases: shortest (minimum hop), fastest
(minimum duration), and foremost (earliest arrival) journeys. Efficient
centralized algorithms exists to compute all cases, when the full knowledge of
the network evolution is given.
In this paper, we study the {\em distributed} counterparts of these problems,
i.e. shortest, fastest, and foremost broadcast with termination detection
(TDB), with minimal knowledge on the topology.
We show that the feasibility of each of these problems requires distinct
features on the evolution, through identifying three classes of dynamic graphs
wherein the problems become gradually feasible: graphs in which the
re-appearance of edges is {\em recurrent} (class R), {\em bounded-recurrent}
(B), or {\em periodic} (P), together with specific knowledge that are
respectively (the number of nodes), (a bound on the recurrence
time), and (the period). In these classes it is not required that all pairs
of nodes get in contact -- only that the overall {\em footprint} of the graph
is connected over time.
Our results, together with the strict inclusion between , , and ,
implies a feasibility order among the three variants of the problem, i.e.
TDB[foremost] requires weaker assumptions on the topology dynamics than
TDB[shortest], which itself requires less than TDB[fastest]. Reversely, these
differences in feasibility imply that the computational powers of ,
, and also form a strict hierarchy
Secure Partial Repair in Wireless Caching Networks with Broadcast Channels
We study security in partial repair in wireless caching networks where parts
of the stored packets in the caching nodes are susceptible to be erased. Let us
denote a caching node that has lost parts of its stored packets as a sick
caching node and a caching node that has not lost any packet as a healthy
caching node. In partial repair, a set of caching nodes (among sick and healthy
caching nodes) broadcast information to other sick caching nodes to recover the
erased packets. The broadcast information from a caching node is assumed to be
received without any error by all other caching nodes. All the sick caching
nodes then are able to recover their erased packets, while using the broadcast
information and the nonerased packets in their storage as side information. In
this setting, if an eavesdropper overhears the broadcast channels, it might
obtain some information about the stored file. We thus study secure partial
repair in the senses of information-theoretically strong and weak security. In
both senses, we investigate the secrecy caching capacity, namely, the maximum
amount of information which can be stored in the caching network such that
there is no leakage of information during a partial repair process. We then
deduce the strong and weak secrecy caching capacities, and also derive the
sufficient finite field sizes for achieving the capacities. Finally, we propose
optimal secure codes for exact partial repair, in which the recovered packets
are exactly the same as erased packets.Comment: To Appear in IEEE Conference on Communication and Network Security
(CNS
- …