arXiv subjects

Magnus M. Halldorsson

Publications and source records attributed to Magnus M. Halldorsson.

24 records · Page 2Linked to original sources

arXiv2012

Wireless Network Stability in the SINR Model

We study the stability of wireless networks under stochastic arrival processes of packets, and design efficient, distributed algorithms that achieve stability in the SINR (Signal to Interference and Noise Ratio) interference model. Specifically, we make the following contributions. We give a distributed algorithm that achieves $Ω(\frac{1}{\log^2 n})$-efficiency on all networks (where $n$ is the number of links in the network), for all length monotone, sub-linear power assignments. For the power control version of the problem, we give a distributed algorithm with $Ω(\frac{1}{\log n(\log n + \log \log Δ)})$-efficiency (where $Δ$ is the length diversity of the link set).

cs.NI↗

arXiv2012

A Fully Distributed Algorithm for Throughput Performance in Wireless Networks

We study link scheduling in wireless networks under stochastic arrival processes of packets, and give an algorithm that achieves stability in the physical (SINR) interference model. The efficiency of such an algorithm is the fraction of the maximum feasible traffic that the algorithm can handle without queues growing indefinitely. Our algorithm achieves two important goals: (i) efficiency is independent of the size of the network, and (ii) the algorithm is fully distributed, i.e., individual nodes need no information about the overall network topology, not even local information.

cs.NI↗

arXiv2012

Wireless Capacity and Admission Control in Cognitive Radio

We give algorithms with constant-factor performance guarantees for several capacity and throughput problems in the SINR model. The algorithms are all based on a novel LP formulation for capacity problems. First, we give a new constant-factor approximation algorithm for selecting the maximum subset of links that can be scheduled simultaneously, under any non-decreasing and sublinear power assignment. For the case of uniform power, we extend this to the case of variable QoS requirements and link-dependent noise terms. Second, we approximate a problem related to cognitive radio: find a maximum set of links that can be simultaneously scheduled without affecting a given set of previously assigned links. Finally, we obtain constant-factor approximation of weighted capacity under linear power assignment.

cs.DS↗

arXiv2011

Wireless Connectivity and Capacity

Given $n$ wireless transceivers located in a plane, a fundamental problem in wireless communications is to construct a strongly connected digraph on them such that the constituent links can be scheduled in fewest possible time slots, assuming the SINR model of interference. In this paper, we provide an algorithm that connects an arbitrary point set in $O(\log n)$ slots, improving on the previous best bound of $O(\log^2 n)$ due to Moscibroda. This is complemented with a super-constant lower bound on our approach to connectivity. An important feature is that the algorithms allow for bi-directional (half-duplex) communication. One implication of this result is an improved bound of $Ω(1/\log n)$ on the worst-case capacity of wireless networks, matching the best bound known for the extensively studied average-case. We explore the utility of oblivious power assignments, and show that essentially all such assignments result in a worst case bound of $Ω(n)$ slots for connectivity. This rules out a recent claim of a $O(\log n)$ bound using oblivious power. On the other hand, using our result we show that $O(\min(\log Δ, \log n \cdot (\log n + \log \log Δ)))$ slots suffice, where $Δ$ is the ratio between the largest and the smallest links in a minimum spanning tree of the points. Our results extend to the related problem of minimum latency aggregation scheduling, where we show that aggregation scheduling with $O(\log n)$ latency is possible, improving upon the previous best known latency of $O(\log^3 n)$. We also initiate the study of network design problems in the SINR model beyond strong connectivity, obtaining similar bounds for biconnected and $k$-edge connected structures.

cs.DS↗

arXiv2011

Wireless Capacity With Arbitrary Gain Matrix

Given a set of wireless links, a fundamental problem is to find the largest subset that can transmit simultaneously, within the SINR model of interference. Significant progress on this problem has been made in recent years. In this note, we study the problem in the setting where we are given a fixed set of arbitrary powers each sender must use, and an arbitrary gain matrix defining how signals fade. This variation of the problem appears immune to most algorithmic approaches studied in the literature. Indeed it is very hard to approximate since it generalizes the max independent set problem. Here, we propose a simple semi-definite programming approach to the problem that yields constant factor approximation, if the optimal solution is strictly larger than half of the input size.

cs.DS↗

arXiv2011

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 $O(\log n \cdot \log\log Δ)$, where $n$ is the number of links and $Δ$ 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 $Δ$ is unavoidable, showing that any reasonably-behaving oblivious power assignment results in a $Ω(\log\log Δ)$-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.

cs.NI↗