886 research outputs found
Fast Structuring of Radio Networks for Multi-Message Communications
We introduce collision free layerings as a powerful way to structure radio
networks. These layerings can replace hard-to-compute BFS-trees in many
contexts while having an efficient randomized distributed construction. We
demonstrate their versatility by using them to provide near optimal distributed
algorithms for several multi-message communication primitives.
Designing efficient communication primitives for radio networks has a rich
history that began 25 years ago when Bar-Yehuda et al. introduced fast
randomized algorithms for broadcasting and for constructing BFS-trees. Their
BFS-tree construction time was rounds, where is the network
diameter and is the number of nodes. Since then, the complexity of a
broadcast has been resolved to be rounds. On the other hand, BFS-trees have been used as a crucial building
block for many communication primitives and their construction time remained a
bottleneck for these primitives.
We introduce collision free layerings that can be used in place of BFS-trees
and we give a randomized construction of these layerings that runs in nearly
broadcast time, that is, w.h.p. in rounds for any constant . We then use these
layerings to obtain: (1) A randomized algorithm for gathering messages
running w.h.p. in rounds. (2) A randomized -message
broadcast algorithm running w.h.p. in rounds. These
algorithms are optimal up to the small difference in the additive
poly-logarithmic term between and . Moreover, they imply the
first optimal round randomized gossip algorithm
Computing in Additive Networks with Bounded-Information Codes
This paper studies the theory of the additive wireless network model, in
which the received signal is abstracted as an addition of the transmitted
signals. Our central observation is that the crucial challenge for computing in
this model is not high contention, as assumed previously, but rather
guaranteeing a bounded amount of \emph{information} in each neighborhood per
round, a property that we show is achievable using a new random coding
technique.
Technically, we provide efficient algorithms for fundamental distributed
tasks in additive networks, such as solving various symmetry breaking problems,
approximating network parameters, and solving an \emph{asymmetry revealing}
problem such as computing a maximal input.
The key method used is a novel random coding technique that allows a node to
successfully decode the received information, as long as it does not contain
too many distinct values. We then design our algorithms to produce a limited
amount of information in each neighborhood in order to leverage our enriched
toolbox for computing in additive networks
Multicommodity Multicast, Wireless and Fast
We study rumor spreading in graphs, specifically multicommodity multicast problem under the wireless model: given source-destination pairs in the graph, one needs to find the fastest schedule to transfer information from each source to the corresponding destination. Under the wireless model, nodes can transmit to any subset of their neighbors in synchronous time steps, as long as they either transmit or receive from at most one transmitter during the same time step. We improve approximation ratio for this problem from O~(n^(2/3)) to O~(n^((1/2) + epsilon)) on n-node graphs. We also design an algorithm that satisfies p given demand pairs in O(OPT + p) steps, where OPT is the length of an optimal schedule, by reducing it to the well-studied packet routing problem. In the case where underlying graph is an n-node tree, we improve the previously best-known approximation ratio of O((log n)/(log log n)) to 3. One consequence of our proof is a simple constructive rule for optimal broadcasting in a tree under a widely studied telephone model
Energy Complexity of Distance Computation in Multi-hop Networks
Energy efficiency is a critical issue for wireless devices operated under
stringent power constraint (e.g., battery). Following prior works, we measure
the energy cost of a device by its transceiver usage, and define the energy
complexity of an algorithm as the maximum number of time slots a device
transmits or listens, over all devices. In a recent paper of Chang et al. (PODC
2018), it was shown that broadcasting in a multi-hop network of unknown
topology can be done in energy. In this paper, we continue
this line of research, and investigate the energy complexity of other
fundamental graph problems in multi-hop networks. Our results are summarized as
follows.
1. To avoid spending energy, the broadcasting protocols of Chang
et al. (PODC 2018) do not send the message along a BFS tree, and it is open
whether BFS could be computed in energy, for sufficiently large . In
this paper we devise an algorithm that attains energy
cost.
2. We show that the framework of the round lower bound proof
for computing diameter in CONGEST of Abboud et al. (DISC 2017) can be adapted
to give an energy lower bound in the wireless network model
(with no message size constraint), and this lower bound applies to -arboricity graphs. From the upper bound side, we show that the energy
complexity of can be attained for bounded-genus graphs
(which includes planar graphs).
3. Our upper bounds for computing diameter can be extended to other graph
problems. We show that exact global minimum cut or approximate -- minimum
cut can be computed in energy for bounded-genus graphs
Low-complexity dominance-based Sphere Decoder for MIMO Systems
The sphere decoder (SD) is an attractive low-complexity alternative to
maximum likelihood (ML) detection in a variety of communication systems. It is
also employed in multiple-input multiple-output (MIMO) systems where the
computational complexity of the optimum detector grows exponentially with the
number of transmit antennas. We propose an enhanced version of the SD based on
an additional cost function derived from conditions on worst case interference,
that we call dominance conditions. The proposed detector, the king sphere
decoder (KSD), has a computational complexity that results to be not larger
than the complexity of the sphere decoder and numerical simulations show that
the complexity reduction is usually quite significant
An Almost Singularly Optimal Asynchronous Distributed MST Algorithm
A singularly (near) optimal distributed algorithm is one that is (near)
optimal in \emph{two} criteria, namely, its time and message complexities. For
\emph{synchronous} CONGEST networks, such algorithms are known for fundamental
distributed computing problems such as leader election [Kutten et al., JACM
2015] and Minimum Spanning Tree (MST) construction [Pandurangan et al., STOC
2017, Elkin, PODC 2017]. However, it is open whether a singularly (near)
optimal bound can be obtained for the MST construction problem in general
\emph{asynchronous} CONGEST networks.
We present a randomized distributed MST algorithm that, with high
probability, computes an MST in \emph{asynchronous} CONGEST networks and takes
time and messages, where
is the number of nodes, the number of edges, is the diameter of the
network, and is an arbitrarily small constant (both time and
message bounds hold with high probability). Our algorithm is message optimal
(up to a polylog factor) and almost time optimal (except for a
factor). Our result answers an open question raised in Mashregi
and King [DISC 2019] by giving the first known asynchronous MST algorithm that
has sublinear time (for all ) and uses
messages. Using a result of Mashregi and King [DISC 2019], this also yields the
first asynchronous MST algorithm that is sublinear in both time and messages in
the CONGEST model.
A key tool in our algorithm is the construction of a low diameter rooted
spanning tree in asynchronous CONGEST that has depth
(for an arbitrarily small constant )
in time and messages. To the best of
our knowledge, this is the first such construction that is almost singularly
optimal in the asynchronous setting.Comment: 27 pages, accepted to DISC 202
Data Collection and Capacity Analysis in Large-scale Wireless Sensor Networks
In this dissertation, we study data collection and its achievable network capacity in Wireless Sensor Networks (WSNs). Firstly, we investigate the data collection issue in dual-radio multi-channel WSNs under the protocol interference model. We propose a multi-path scheduling algorithm for snapshot data collection, which has a tighter capacity bound than the existing best result, and a novel continuous data collection algorithm with comprehensive capacity analysis. Secondly, considering most existing works for the capacity issue are based on the ideal deterministic network model, we study the data collection problem for practical probabilistic WSNs. We design a cell-based path scheduling algorithm and a zone-based pipeline scheduling algorithm for snapshot and continuous data collection in probabilistic WSNs, respectively. By analysis, we show that the proposed algorithms have competitive capacity performance compared with existing works. Thirdly, most of the existing works studying the data collection capacity issue are for centralized synchronous WSNs. However, wireless networks are more likely to be distributed asynchronous systems. Therefore, we investigate the achievable data collection capacity of realistic distributed asynchronous WSNs and propose a data collection algorithm with fairness consideration. Theoretical analysis of the proposed algorithm shows that its achievable network capacity is order-optimal as centralized and synchronized algorithms do and independent of network size. Finally, for completeness, we study the data aggregation issue for realistic probabilistic WSNs. We propose order-optimal scheduling algorithms for snapshot and continuous data aggregation under the physical interference model
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