129,509 research outputs found
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
Spatial networks with wireless applications
Many networks have nodes located in physical space, with links more common
between closely spaced pairs of nodes. For example, the nodes could be wireless
devices and links communication channels in a wireless mesh network. We
describe recent work involving such networks, considering effects due to the
geometry (convex,non-convex, and fractal), node distribution,
distance-dependent link probability, mobility, directivity and interference.Comment: Review article- an amended version with a new title from the origina
A PTAS for Bounded-Capacity Vehicle Routing in Planar Graphs
The Capacitated Vehicle Routing problem is to find a minimum-cost set of
tours that collectively cover clients in a graph, such that each tour starts
and ends at a specified depot and is subject to a capacity bound on the number
of clients it can serve. In this paper, we present a polynomial-time
approximation scheme (PTAS) for instances in which the input graph is planar
and the capacity is bounded. Previously, only a quasipolynomial-time
approximation scheme was known for these instances. To obtain this result, we
show how to embed planar graphs into bounded-treewidth graphs while preserving,
in expectation, the client-to-client distances up to a small additive error
proportional to client distances to the depot
A new graph perspective on max-min fairness in Gaussian parallel channels
In this work we are concerned with the problem of achieving max-min fairness
in Gaussian parallel channels with respect to a general performance function,
including channel capacity or decoding reliability as special cases. As our
central results, we characterize the laws which determine the value of the
achievable max-min fair performance as a function of channel sharing policy and
power allocation (to channels and users). In particular, we show that the
max-min fair performance behaves as a specialized version of the Lovasz
function, or Delsarte bound, of a certain graph induced by channel sharing
combinatorics. We also prove that, in addition to such graph, merely a certain
2-norm distance dependent on the allowable power allocations and used
performance functions, is sufficient for the characterization of max-min fair
performance up to some candidate interval. Our results show also a specific
role played by odd cycles in the graph induced by the channel sharing policy
and we present an interesting relation between max-min fairness in parallel
channels and optimal throughput in an associated interference channel.Comment: 41 pages, 8 figures. submitted to IEEE Transactions on Information
Theory on August the 6th, 200
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