9,530 research outputs found
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
Beyond Geometry : Towards Fully Realistic Wireless Models
Signal-strength models of wireless communications capture the gradual fading
of signals and the additivity of interference. As such, they are closer to
reality than other models. However, nearly all theoretic work in the SINR model
depends on the assumption of smooth geometric decay, one that is true in free
space but is far off in actual environments. The challenge is to model
realistic environments, including walls, obstacles, reflections and anisotropic
antennas, without making the models algorithmically impractical or analytically
intractable.
We present a simple solution that allows the modeling of arbitrary static
situations by moving from geometry to arbitrary decay spaces. The complexity of
a setting is captured by a metricity parameter Z that indicates how far the
decay space is from satisfying the triangular inequality. All results that hold
in the SINR model in general metrics carry over to decay spaces, with the
resulting time complexity and approximation depending on Z in the same way that
the original results depends on the path loss term alpha. For distributed
algorithms, that to date have appeared to necessarily depend on the planarity,
we indicate how they can be adapted to arbitrary decay spaces.
Finally, we explore the dependence on Z in the approximability of core
problems. In particular, we observe that the capacity maximization problem has
exponential upper and lower bounds in terms of Z in general decay spaces. In
Euclidean metrics and related growth-bounded decay spaces, the performance
depends on the exact metricity definition, with a polynomial upper bound in
terms of Z, but an exponential lower bound in terms of a variant parameter phi.
On the plane, the upper bound result actually yields the first approximation of
a capacity-type SINR problem that is subexponential in alpha
Efficient Approximation Algorithms for Multi-Antennae Largest Weight Data Retrieval
In a mobile network, wireless data broadcast over channels (frequencies)
is a powerful means for distributed dissemination of data to clients who access
the channels through multi-antennae equipped on their mobile devices. The
-antennae largest weight data retrieval (ALWDR) problem is to
compute a schedule for downloading a subset of data items that has a maximum
total weight using antennae in a given time interval. In this paper,
we propose a ratio approximation algorithm for the
-antennae largest weight data retrieval (ALWDR) problem that
has the same ratio as the known result but a significantly improved time
complexity of from
when
\cite{lu2014data}. To our knowledge, our algorithm represents the first ratio
approximation solution to ALWDR for the
general case of arbitrary . To achieve this, we first give a ratio
algorithm for the -separated ALWDR
(ALWDR) with runtime , under the assumption
that every data item appears at most once in each segment of
ALWDR, for any input of maximum length on channels in
time slots. Then, we show that we can retain the same ratio for
ALWDR without this assumption at the cost of increased time
complexity to . This result immediately yields an
approximation solution of same ratio and time complexity for ALWDR,
presenting a significant improvement of the known time complexity of ratio
approximation to the problem
Towards Optimal Distributed Node Scheduling in a Multihop Wireless Network through Local Voting
In a multihop wireless network, it is crucial but challenging to schedule
transmissions in an efficient and fair manner. In this paper, a novel
distributed node scheduling algorithm, called Local Voting, is proposed. This
algorithm tries to semi-equalize the load (defined as the ratio of the queue
length over the number of allocated slots) through slot reallocation based on
local information exchange. The algorithm stems from the finding that the
shortest delivery time or delay is obtained when the load is semi-equalized
throughout the network. In addition, we prove that, with Local Voting, the
network system converges asymptotically towards the optimal scheduling.
Moreover, through extensive simulations, the performance of Local Voting is
further investigated in comparison with several representative scheduling
algorithms from the literature. Simulation results show that the proposed
algorithm achieves better performance than the other distributed algorithms in
terms of average delay, maximum delay, and fairness. Despite being distributed,
the performance of Local Voting is also found to be very close to a centralized
algorithm that is deemed to have the optimal performance
Scheduling under Linear Constraints
We introduce a parallel machine scheduling problem in which the processing
times of jobs are not given in advance but are determined by a system of linear
constraints. The objective is to minimize the makespan, i.e., the maximum job
completion time among all feasible choices. This novel problem is motivated by
various real-world application scenarios. We discuss the computational
complexity and algorithms for various settings of this problem. In particular,
we show that if there is only one machine with an arbitrary number of linear
constraints, or there is an arbitrary number of machines with no more than two
linear constraints, or both the number of machines and the number of linear
constraints are fixed constants, then the problem is polynomial-time solvable
via solving a series of linear programming problems. If both the number of
machines and the number of constraints are inputs of the problem instance, then
the problem is NP-Hard. We further propose several approximation algorithms for
the latter case.Comment: 21 page
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