24,574 research outputs found
The Unreasonable Success of Local Search: Geometric Optimization
What is the effectiveness of local search algorithms for geometric problems
in the plane? We prove that local search with neighborhoods of magnitude
is an approximation scheme for the following problems in the
Euclidian plane: TSP with random inputs, Steiner tree with random inputs,
facility location (with worst case inputs), and bicriteria -median (also
with worst case inputs). The randomness assumption is necessary for TSP
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
Joint Pilot Design and Uplink Power Allocation in Multi-Cell Massive MIMO Systems
This paper considers pilot design to mitigate pilot contamination and provide
good service for everyone in multi-cell Massive multiple input multiple output
(MIMO) systems. Instead of modeling the pilot design as a combinatorial
assignment problem, as in prior works, we express the pilot signals using a
pilot basis and treat the associated power coefficients as continuous
optimization variables. We compute a lower bound on the uplink capacity for
Rayleigh fading channels with maximum ratio detection that applies with
arbitrary pilot signals. We further formulate the max-min fairness problem
under power budget constraints, with the pilot signals and data powers as
optimization variables. Because this optimization problem is non-deterministic
polynomial-time hard due to signomial constraints, we then propose an algorithm
to obtain a local optimum with polynomial complexity. Our framework serves as a
benchmark for pilot design in scenarios with either ideal or non-ideal
hardware. Numerical results manifest that the proposed optimization algorithms
are close to the optimal solution obtained by exhaustive search for different
pilot assignments and the new pilot structure and optimization bring large
gains over the state-of-the-art suboptimal pilot design.Comment: 16 pages, 8 figures. Accepted to publish at IEEE Transactions on
Wireless Communication
Target Assignment in Robotic Networks: Distance Optimality Guarantees and Hierarchical Strategies
We study the problem of multi-robot target assignment to minimize the total
distance traveled by the robots until they all reach an equal number of static
targets. In the first half of the paper, we present a necessary and sufficient
condition under which true distance optimality can be achieved for robots with
limited communication and target-sensing ranges. Moreover, we provide an
explicit, non-asymptotic formula for computing the number of robots needed to
achieve distance optimality in terms of the robots' communication and
target-sensing ranges with arbitrary guaranteed probabilities. The same bounds
are also shown to be asymptotically tight.
In the second half of the paper, we present suboptimal strategies for use
when the number of robots cannot be chosen freely. Assuming first that all
targets are known to all robots, we employ a hierarchical communication model
in which robots communicate only with other robots in the same partitioned
region. This hierarchical communication model leads to constant approximations
of true distance-optimal solutions under mild assumptions. We then revisit the
limited communication and sensing models. By combining simple rendezvous-based
strategies with a hierarchical communication model, we obtain decentralized
hierarchical strategies that achieve constant approximation ratios with respect
to true distance optimality. Results of simulation show that the approximation
ratio is as low as 1.4
On Wireless Scheduling Using the Mean Power Assignment
In this paper the problem of scheduling with power control in wireless
networks is studied: given a set of communication requests, one needs to assign
the powers of the network nodes, and schedule the transmissions so that they
can be done in a minimum time, taking into account the signal interference of
concurrently transmitting nodes. The signal interference is modeled by SINR
constraints. Approximation algorithms are given for this problem, which use the
mean power assignment. The problem of schduling with fixed mean power
assignment is also considered, and approximation guarantees are proven
Wireless Scheduling with Power Control
We consider the scheduling of arbitrary wireless links in the physical model
of interference to minimize the time for satisfying all requests. We study here
the combined problem of scheduling and power control, where we seek both an
assignment of power settings and a partition of the links so that each set
satisfies the signal-to-interference-plus-noise (SINR) constraints.
We give an algorithm that attains an approximation ratio of , where is the number of links and is the ratio
between the longest and the shortest link length. Under the natural assumption
that lengths are represented in binary, this gives the first approximation
ratio that is polylogarithmic in the size of the input. The algorithm has the
desirable property of using an oblivious power assignment, where the power
assigned to a sender depends only on the length of the link. We give evidence
that this dependence on is unavoidable, showing that any
reasonably-behaving oblivious power assignment results in a -approximation.
These results hold also for the (weighted) capacity problem of finding a
maximum (weighted) subset of links that can be scheduled in a single time slot.
In addition, we obtain improved approximation for a bidirectional variant of
the scheduling problem, give partial answers to questions about the utility of
graphs for modeling physical interference, and generalize the setting from the
standard 2-dimensional Euclidean plane to doubling metrics. Finally, we explore
the utility of graph models in capturing wireless interference.Comment: Revised full versio
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