76 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
The Price of Local Power Control in Wireless Scheduling
We consider the problem of scheduling wireless links in the physical model, where we seek an assignment of power levels and a partition of the given set of links into the minimum number of subsets satisfying the signal-to-interference-and-noise-ratio (SINR) constraints. Specifically, we are interested in the efficiency of local power assignment schemes, or oblivious power schemes, in approximating wireless scheduling. Oblivious power schemes are motivated by networking scenarios when power levels must be decided in advance, and not as part of the scheduling computation.
We present the first O(log log Delta)-approximation algorithm, which is known to be best possible (in terms of Delta) for oblivious power schemes, where Delta is the longest to shortest link length ratio. We achieve this by representing interference by a conflict graph, which allows the application of graph-theoretic results for a variety of related problems, including the weighted capacity problem. We explore further the contours of approximability and find the choice of power assignment matters; that not all metric spaces are equal; and that the presence of weak links makes the problem harder. Combined, our results resolve the price of local power for wireless scheduling, or the value of allowing unfettered power control
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
A Constant-Factor Approximation for Wireless Capacity Maximization with Power Control in the SINR Model
In modern wireless networks, devices are able to set the power for each
transmission carried out. Experimental but also theoretical results indicate
that such power control can improve the network capacity significantly. We
study this problem in the physical interference model using SINR constraints.
In the SINR capacity maximization problem, we are given n pairs of senders
and receivers, located in a metric space (usually a so-called fading metric).
The algorithm shall select a subset of these pairs and choose a power level for
each of them with the objective of maximizing the number of simultaneous
communications. This is, the selected pairs have to satisfy the SINR
constraints with respect to the chosen powers.
We present the first algorithm achieving a constant-factor approximation in
fading metrics. The best previous results depend on further network parameters
such as the ratio of the maximum and the minimum distance between a sender and
its receiver. Expressed only in terms of n, they are (trivial) Omega(n)
approximations.
Our algorithm still achieves an O(log n) approximation if we only assume to
have a general metric space rather than a fading metric. Furthermore, by using
standard techniques the algorithm can also be used in single-hop and multi-hop
scheduling scenarios. Here, we also get polylog(n) approximations.Comment: 17 page
Spanning Trees With Edge Conflicts and Wireless Connectivity
We introduce the problem of finding a spanning tree along with a partition of the tree edges into fewest number of feasible sets, where constraints on the edges define feasibility. The motivation comes from wireless networking, where we seek to model the irregularities seen in actual wireless environments. Not all node pairs may be able to communicate, even if geographically close - thus, the available pairs are specified with a link graph {L}=(V,E). Also, signal attenuation need not follow a nice geometric formula - hence, interference is modeled by a conflict (hyper)graph {C}=(E,F) on the links. The objective is to maximize the efficiency of the communication, or equivalently, to minimize the length of a schedule of the tree edges in the form of a coloring.
We find that in spite of all this generality, the problem can be approximated linearly in terms of a versatile parameter, the inductive independence of the interference graph. Specifically, we give a simple algorithm that attains a O(rho log n)-approximation, where n is the number of nodes and rho is the inductive independence, and show that near-linear dependence on rho is also necessary. We also treat an extension to Steiner trees, modeling multicasting, and obtain a comparable result.
Our results suggest that several canonical assumptions of geometry, regularity and "niceness" in wireless settings can sometimes be relaxed without a significant hit in algorithm performance
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