198 research outputs found
Latency Optimal Broadcasting in Noisy Wireless Mesh Networks
In this paper, we adopt a new noisy wireless network model introduced very
recently by Censor-Hillel et al. in [ACM PODC 2017, CHHZ17]. More specifically,
for a given noise parameter any sender has a probability of
of transmitting noise or any receiver of a single transmission in its
neighborhood has a probability of receiving noise.
In this paper, we first propose a new asymptotically latency-optimal
approximation algorithm (under faultless model) that can complete
single-message broadcasting task in time units/rounds in any
WMN of size and diameter . We then show this diameter-linear
broadcasting algorithm remains robust under the noisy wireless network model
and also improves the currently best known result in CHHZ17 by a
factor.
In this paper, we also further extend our robust single-message broadcasting
algorithm to multi-message broadcasting scenario and show it can broadcast
messages in time rounds. This new robust
multi-message broadcasting scheme is not only asymptotically optimal but also
answers affirmatively the problem left open in CHHZ17 on the existence of an
algorithm that is robust to sender and receiver faults and can broadcast
messages in time rounds.Comment: arXiv admin note: text overlap with arXiv:1705.07369 by other author
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
Information Gathering in Ad-Hoc Radio Networks with Tree Topology
We study the problem of information gathering in ad-hoc radio networks
without collision detection, focussing on the case when the network forms a
tree, with edges directed towards the root. Initially, each node has a piece of
information that we refer to as a rumor. Our goal is to design protocols that
deliver all rumors to the root of the tree as quickly as possible. The protocol
must complete this task within its allotted time even though the actual tree
topology is unknown when the computation starts. In the deterministic case,
assuming that the nodes are labeled with small integers, we give an O(n)-time
protocol that uses unbounded messages, and an O(n log n)-time protocol using
bounded messages, where any message can include only one rumor. We also
consider fire-and-forward protocols, in which a node can only transmit its own
rumor or the rumor received in the previous step. We give a deterministic
fire-and- forward protocol with running time O(n^1.5), and we show that it is
asymptotically optimal. We then study randomized algorithms where the nodes are
not labelled. In this model, we give an O(n log n)-time protocol and we prove
that this bound is asymptotically optimal
Message and time efficient multi-broadcast schemes
We consider message and time efficient broadcasting and multi-broadcasting in
wireless ad-hoc networks, where a subset of nodes, each with a unique rumor,
wish to broadcast their rumors to all destinations while minimizing the total
number of transmissions and total time until all rumors arrive to their
destination. Under centralized settings, we introduce a novel approximation
algorithm that provides almost optimal results with respect to the number of
transmissions and total time, separately. Later on, we show how to efficiently
implement this algorithm under distributed settings, where the nodes have only
local information about their surroundings. In addition, we show multiple
approximation techniques based on the network collision detection capabilities
and explain how to calibrate the algorithms' parameters to produce optimal
results for time and messages.Comment: In Proceedings FOMC 2013, arXiv:1310.459
Gossip Algorithms for Distributed Signal Processing
Gossip algorithms are attractive for in-network processing in sensor networks
because they do not require any specialized routing, there is no bottleneck or
single point of failure, and they are robust to unreliable wireless network
conditions. Recently, there has been a surge of activity in the computer
science, control, signal processing, and information theory communities,
developing faster and more robust gossip algorithms and deriving theoretical
performance guarantees. This article presents an overview of recent work in the
area. We describe convergence rate results, which are related to the number of
transmitted messages and thus the amount of energy consumed in the network for
gossiping. We discuss issues related to gossiping over wireless links,
including the effects of quantization and noise, and we illustrate the use of
gossip algorithms for canonical signal processing tasks including distributed
estimation, source localization, and compression.Comment: Submitted to Proceedings of the IEEE, 29 page
Some combinational optimization problems on radio network communication and machine scheduling
The combinatorial optimization problems coming from two areas are studied in this dissertation: network communication and machine scheduling.
In the network communication area, the complexity of distributed broadcasting and distributed gossiping is studied in the setting of random networks. Two different models are considered: one is random geometric networks, the main model used to study properties of sensor and ad-hoc networks, where ri points are randomly placed in a unit square and two points are connected by an edge if they are at most a certain fixed distance r from each other. The other model is the so-called line-of-sight networks, a new network model introduced recently by Frieze et al. (SODA\u2707). The nodes in this model are randomly placed (with probability p) on an n x n grid and a node can communicate with all the nodes that are in at most a certain fixed distance r and which are in the same row or column. It can be shown that in many scenarios of both models, the random structure of these networks makes it possible to perform distributed gossiping in asymptotically optimal time 0(D), where D is the diameter of the network. The simulation results show that most algorithms especially the randomized algorithm works very fast in practice.
In the scheduling area, the first problem is online scheduling a set of equal processing time tasks with precedence constraints so as to minimize the makespan. It can be shown that Hu \u27s algorithm yields an asymptotic competitive ratio of 3/2 for intree precedence constraints and an asymptotic competitive ratio of 1 for outtree precedences, and Coffinan-Graham algorithm yields an asymptotic competitive ratio of 1 for arbitrary precedence constraints and two machines.The second scheduling problem is the integrated production and delivery scheduling with disjoint windows. In this problem, each job is associated with a time window, and a profit. A job must be finished within its time window to get the profit. The objective is to pick a set ofjobs and schedule them to get the maximum total profit. For a single machine and unit profit, an optimal algorithm is proposed. For a single machine and arbitrary profit, a fully polynomial time approximation scheme(FPTAS) is proposed. These algorithms can be extended to multiple machines with approximation ratio less than e/(e - 1).
The third scheduling problem studied in this dissertation is the preemptive scheduling algorithms with nested and inclusive processing set restrictions. The objective is to minimize the makespan of the schedule. It can be shown that there is no optimal online algorithm even for the case of inclusive processing set. Then a linear time optimal algorithm is given for the case of nested processing set, where all jobs are available for processing at time t = 0. A more complicated algorithm with running time 0(n log ri) is given that produces not only optimal but also maximal schedules. When jobs have different release times, an optimal algorithm is given for the nested case and a faster optimal algorithm is given for the inclusive processing set case
Optimal Initialization and Gossiping Algorithms for Random Radio Networks
The initialization problem, also known as naming, consists to give a unique identifier ranging from to to a set of indistinguishable nodes in a given network. We consider a network where nodes (processors) are randomly deployed in a square (resp. cube) . We assume that the time is slotted and the network is synchronous, two nodes are able to communicate if they are within distance at most of of each other ( is the transmitting/receiving range). Moreover, if two or more neighbors of a processor transmit concurrently at the same time slot, then would not receive either messages. We suppose also that the anonymous nodes know neither the topology of the network nor the number of nodes in the network. Under this extremal scenario, we first show how the transmitting range of the deployed processors affects the typical characteristics of the network. Then, by allowing the nodes to transmit at various ranges we design sub-linear randomized initialization protocols~: In the two, resp. three, dimensional case, our randomized initialization algorithms run in , resp. , time slots. These latter protocols are based upon an optimal gossiping algorithm which is of independent interest
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