285,643 research outputs found
Leveraging Physical Layer Capabilites: Distributed Scheduling in Interference Networks with Local Views
In most wireless networks, nodes have only limited local information about
the state of the network, which includes connectivity and channel state
information. With limited local information about the network, each node's
knowledge is mismatched; therefore, they must make distributed decisions. In
this paper, we pose the following question - if every node has network state
information only about a small neighborhood, how and when should nodes choose
to transmit? While link scheduling answers the above question for
point-to-point physical layers which are designed for an interference-avoidance
paradigm, we look for answers in cases when interference can be embraced by
advanced PHY layer design, as suggested by results in network information
theory.
To make progress on this challenging problem, we propose a constructive
distributed algorithm that achieves rates higher than link scheduling based on
interference avoidance, especially if each node knows more than one hop of
network state information. We compare our new aggressive algorithm to a
conservative algorithm we have presented in [1]. Both algorithms schedule
sub-networks such that each sub-network can employ advanced
interference-embracing coding schemes to achieve higher rates. Our innovation
is in the identification, selection and scheduling of sub-networks, especially
when sub-networks are larger than a single link.Comment: 14 pages, Submitted to IEEE/ACM Transactions on Networking, October
201
On the Connectivity of Unions of Random Graphs
Graph-theoretic tools and techniques have seen wide use in the multi-agent
systems literature, and the unpredictable nature of some multi-agent
communications has been successfully modeled using random communication graphs.
Across both network control and network optimization, a common assumption is
that the union of agents' communication graphs is connected across any finite
interval of some prescribed length, and some convergence results explicitly
depend upon this length. Despite the prevalence of this assumption and the
prevalence of random graphs in studying multi-agent systems, to the best of our
knowledge, there has not been a study dedicated to determining how many random
graphs must be in a union before it is connected. To address this point, this
paper solves two related problems. The first bounds the number of random graphs
required in a union before its expected algebraic connectivity exceeds the
minimum needed for connectedness. The second bounds the probability that a
union of random graphs is connected. The random graph model used is the
Erd\H{o}s-R\'enyi model, and, in solving these problems, we also bound the
expectation and variance of the algebraic connectivity of unions of such
graphs. Numerical results for several use cases are given to supplement the
theoretical developments made.Comment: 16 pages, 3 tables; accepted to 2017 IEEE Conference on Decision and
Control (CDC
Solving k-Set Agreement with Stable Skeleton Graphs
In this paper we consider the k-set agreement problem in distributed
message-passing systems using a round-based approach: Both synchrony of
communication and failures are captured just by means of the messages that
arrive within a round, resulting in round-by-round communication graphs that
can be characterized by simple communication predicates. We introduce the weak
communication predicate PSources(k) and show that it is tight for k-set
agreement, in the following sense: We (i) prove that there is no algorithm for
solving (k-1)-set agreement in systems characterized by PSources(k), and (ii)
present a novel distributed algorithm that achieves k-set agreement in runs
where PSources(k) holds. Our algorithm uses local approximations of the stable
skeleton graph, which reflects the underlying perpetual synchrony of a run. We
prove that this approximation is correct in all runs, regardless of the
communication predicate, and show that graph-theoretic properties of the stable
skeleton graph can be used to solve k-set agreement if PSources(k) holds.Comment: to appear in 16th IEEE Workshop on Dependable Parallel, Distributed
and Network-Centric System
Synchronisation Properties of Trees in the Kuramoto Model
We consider the Kuramoto model of coupled oscillators, specifically the case
of tree networks, for which we prove a simple closed-form expression for the
critical coupling. For several classes of tree, and for both uniform and
Gaussian vertex frequency distributions, we provide tight closed form bounds
and empirical expressions for the expected value of the critical coupling. We
also provide several bounds on the expected value of the critical coupling for
all trees. Finally, we show that for a given set of vertex frequencies, there
is a rearrangement of oscillator frequencies for which the critical coupling is
bounded by the spread of frequencies.Comment: 21 pages, 19 Figure
Distributed Queuing in Dynamic Networks
We consider the problem of forming a distributed queue in the adversarial
dynamic network model of Kuhn, Lynch, and Oshman (STOC 2010) in which the
network topology changes from round to round but the network stays connected.
This is a synchronous model in which network nodes are assumed to be fixed, the
communication links for each round are chosen by an adversary, and nodes do not
know who their neighbors are for the current round before they broadcast their
messages. Queue requests may arrive over rounds at arbitrary nodes and the goal
is to eventually enqueue them in a distributed queue. We present two algorithms
that give a total distributed ordering of queue requests in this model. We
measure the performance of our algorithms through round complexity, which is
the total number of rounds needed to solve the distributed queuing problem. We
show that in 1-interval connected graphs, where the communication links change
arbitrarily between every round, it is possible to solve the distributed
queueing problem in O(nk) rounds using O(log n) size messages, where n is the
number of nodes in the network and k <= n is the number of queue requests.
Further, we show that for more stable graphs, e.g. T-interval connected graphs
where the communication links change in every T rounds, the distributed queuing
problem can be solved in O(n+ (nk/min(alpha,T))) rounds using the same O(log n)
size messages, where alpha > 0 is the concurrency level parameter that captures
the minimum number of active queue requests in the system in any round. These
results hold in any arbitrary (sequential, one-shot concurrent, or dynamic)
arrival of k queue requests in the system. Moreover, our algorithms ensure
correctness in the sense that each queue request is eventually enqueued in the
distributed queue after it is issued and each queue request is enqueued exactly
once. We also provide an impossibility result for this distributed queuing
problem in this model. To the best of our knowledge, these are the first
solutions to the distributed queuing problem in adversarial dynamic networks.Comment: In Proceedings FOMC 2013, arXiv:1310.459
Phase Transitions in Edge-Weighted Exponential Random Graphs: Near-Degeneracy and Universality
Conventionally used exponential random graphs cannot directly model weighted
networks as the underlying probability space consists of simple graphs only.
Since many substantively important networks are weighted, this limitation is
especially problematic. We extend the existing exponential framework by
proposing a generic common distribution for the edge weights. Minimal
assumptions are placed on the distribution, that is, it is non-degenerate and
supported on the unit interval. By doing so, we recognize the essential
properties associated with near-degeneracy and universality in edge-weighted
exponential random graphs.Comment: 15 pages, 4 figures. This article extends arXiv:1607.04084, which
derives general formulas for the normalization constant and characterizes
phase transitions in exponential random graphs with uniformly distributed
edge weights. The present article places minimal assumptions on the
edge-weight distribution, thereby recognizing essential properties associated
with near-degeneracy and universalit
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