Power Aware Routing in Mobile Ad Hoc Networks

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) Ω(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, existing approaches work well together with the algorithm allowing it to be used in singlehop and multi-hop scheduling scenarios. Here, we also get polylog n approximations.

https://epubs.siam.org/doi/pdf/10.1137/1.9781611973082.120

A constant-factor approximation for wireless capacity maximization with power control in the SINR model

We present and analyze simple distributed contention resolution protocols for wireless networks. In our setting, one is given n pairs of senders and receivers located in a metric space. Each sender wants to transmit a signal to its receiver at a prespecified power level, e. g., all senders use the same, uniform power level as it is typically implemented in practice. Our analysis is based on the physical model in which the success of a transmission depends on the Signal-to-Interference-plus-Noise-Ratio (SINR). The objective is to minimize the number of time slots until all signals are successfully transmitted.

Our main technical contribution is the introduction of a measure called maximum average affectance enabling us to analyze random contention-resolution algorithms in which each packet is transmitted in each step with a fixed probability depending on the maximum average affectance. We prove that the schedule generated this way is only an O(log2 n) factor longer than the optimal one, provided that the prespecified power levels satisfy natural monontonicity properties. By modifying the algorithm, senders need not to know the maximum average affectance in advance but only static information about the network. In addition, we extend our approach to multi-hop communication achieving the same appoximation factor.

/pdf/distributed-contention-resolution-in-wireless-networks-41hdr6yd95.pdf

Distributed contention resolution in wireless networks

The capacity of a wireless network is the maximum possible amount of simultaneous communication, taking interference into account. Formally, we treat the following problem. Given is a set of links, each a sender-receiver pair located in a metric space, and an assignment of power to the senders. We seek a maximum subset of links that are feasible in the SINR model: namely, the signal received on each link should be larger than the sum of the interferences from the other links. We give a constant-factor approximation that holds for any length-monotone, sub-linear power assignment and any distance metric.We use this to give essentially tight characterizations of capacity maximization under power control using oblivious power assignments. Specifically, we show that the mean power assignment is optimal for capacity maximization of bi-directional links, and give a tight θ(log n)-approximation of scheduling bi-directional links with power control using oblivious power. For uni-directional links we give a nearly optimal O(log n + log log Δ)-approximation to the power control problem using mean power, where Δ is the ratio of longest and shortest links. Combined, these results clarify significantly the centralized complexity of wireless communication problems.

https://epubs.siam.org/doi/pdf/10.1137/1.9781611973082.119

Wireless capacity with oblivious power in general metrics

In the interference scheduling problem, one is given a set of n communication requests described by pairs of points from a metric space. The points correspond to devices in a wireless network. In the directed version of the problem, each pair of points consists of a dedicated sending and a dedicated receiving device. In the bidirectional version the devices within a pair shall be able to exchange signals in both directions. In both versions, each pair must be assigned a power level and a color such that the pairs in each color class (representing pairs communicating in the same time slot) can communicate simultaneously at the specified power levels. The feasibility of simultaneous communication within a color class is defined in terms of the Signal to Interference Plus Noise Ratio (SINR) that compares the strength of a signal at a receiver to the sum of the strengths of other signals. This is commonly referred to as the "physical model" and is the established way of modelling interference in the engineering community. The objective is to minimize the number of colors as this corresponds to the time needed to schedule all requests.We study oblivious power assignments in which the power value of a pair only depends on the distance between the points of this pair. We prove that oblivious power assignments cannot yield approximation ratios better than Ω(n) for the directed version of the problem, which is the worst possible performance guarantee as there is a straightforward algorithm that achieves an O(n)-approximation. For the bidirectional version, however, we can show the existence of a universally good oblivious power assignment: For any set of n bidirectional communication requests, the so-called "square root assignment" admits a coloring with at most polylog(n) times the minimal number of colors. The proof for the existence of this coloring is non-constructive. We complement it by an approximation algorithm for the coloring problem under the square root assignment. This way, we obtain the first polynomial time algorithm with approximation ratio polylog(n) for interference scheduling in the physical model.

/pdf/oblivious-interference-scheduling-1wa5kipjb9.pdf

Oblivious interference scheduling

In the interference scheduling problem , one is given a set of n communication requests described by source-destination pairs of nodes from a metric space. The nodes correspond to devices in a wireless network. Each pair must be assigned a power level and a color such that the pairs in each color class can communicate simultaneously at the specified power levels. The feasibility of simultaneous communication within a color class is defined in terms of the Signal to Interference plus Noise Ratio (SINR) that compares the strength of a signal at a receiver to the sum of the strengths of other signals. The objective is to minimize the number of colors as this corresponds to the time needed to schedule all requests.

We introduce an instance-based measure of interference, denoted by I , that enables us to improve on previous results for the interference scheduling problem. We prove upper and lower bounds in terms of I on the number of steps needed for scheduling a set of requests. For general power assignments, we prove a lower bound of *** (I / (log Δ log n)) steps, where Δ denotes the aspect ratio of the metric. When restricting to the two-dimensional Euclidean space (as previous work) the bound improves to *** (I (logΔ ). Alternatively, when restricting to linear power assignments, the lower bound improves even to *** (I ). The lower bounds are complemented by an efficient algorithm computing a schedule for linear power assignments using only $\mathcal O(I \log n)$ steps. A more sophisticated algorithm computes a schedule using even only $\mathcal O(I + \log^2 n)$ steps. For dense instances in the two-dimensional Euclidean space, this gives a constant factor approximation for scheduling under linear power assignments, which shows that the price for using linear (and, hence, energy-efficient) power assignments is bounded by a factor of $\mathcal O(\log \Delta)$.

In addition, we extend these results for single-hop scheduling to multi-hop scheduling and combined scheduling and routing problems, where our analysis generalizes previous results towards general metrics and improves on the previous approximation factors.

Improved Algorithms for Latency Minimization in Wireless Networks

http://www.thomas-kesselheim.de/science/ImprovedAlgorithmsForLatencyMinimization.pdf

Improved algorithms for latency minimization in wireless networks

In this paper we study a dynamic version of capacity maximization is the physical model of wireless communication. In our model, requests for connections between pairs of points in Euclidean space of constant dimension d arrive iteratively over time. When a new request arrives, an online algorithm needs to decide whether or not to accept the request and to assign one out of k channels and a transmission power to the channel. Accepted requests must satisfy constraints on the signal-to-interference-plus-noise (SINR) ratio. The objective is to maximize the number of accepted requests.Using competitive analysis we study algorithms using distance-based power assignments, for which the power of a request relies only on the distance between the points. Such assignments are inherently local and particularly useful in distributed settings. We first focus on the case of a single channel. For request sets with spatial lengths in [1, Δ] and duration in [1, Γ] we derive a lower bound of Ω(Γ ⋅ Δ d/2) on the competitive ratio of any deterministic online algorithm using a distance-based power assignment. Our main result is a near-optimal deterministic algorithm that is O(Γ ⋅ Δ (d/2)+e)-competitive, for any constant e > 0.Our algorithm for a single channel can be generalized to k channels. It can be adjusted to yield a competitive ratio of O(k ⋅ Γ 1/k' ⋅ Δ(d/2k")+e) for any factorization (k', k") such that k' ⋅ k'' = k. This illustrates the effectiveness of multiple channels when dealing wite unknown request sequences. In particular, for Θ(log Γ ⋅ log Δ) channels this yields an O(log Γ ⋅ log Δ)-competitive algorithm. Additionally, we show how this approach can be turned into a randomized algorithm, which is O(log Γ ⋅ log Δ)-competitive even for a single channel.

Online capacity maximization in wireless networks

In this paper we study a dynamic version of capacity maximization in the physical model of wireless communication. In our model, requests for connections between pairs of points in Euclidean space of constant dimension d arrive iteratively over time. When a new request arrives, an online algorithm needs to decide whether or not to accept the request and to assign one out of k channels and a transmission power to the request. Accepted requests must satisfy constraints on the signal-to-interference-plus-noise (SINR) ratio. The objective is to maximize the number of accepted requests.

Using competitive analysis we study algorithms using distance-based power assignments, for which the power of a request relies only on the distance between the points. Such assignments are inherently local and particularly useful in distributed settings. We first focus on the case of a single channel. For request sets with spatial lengths in [1,Δ] and duration in [1,Γ] we derive a lower bound of ?(Γ?Δ d/2) on the competitive ratio of any deterministic online algorithm using a distance-based power assignment. Our main result is a near-optimal deterministic algorithm that is O(Γ?Δ(d/2)+? )-competitive, for any constant ?>0.

Our algorithm for a single channel can be generalized to k channels. It can be adjusted to yield a competitive ratio of O(k?Γ 1/k??Δ(d/2k?)+? ) for any factorization (k?,k?) such that k??k?=k. This illustrates the effectiveness of multiple channels when dealing with unknown request sequences. In particular, for ?(log?Γ?log?Δ) channels this yields an O(log?Γ?log?Δ)-competitive algorithm. Additionally, we show how this approach can be turned into a randomized algorithm, which is O(log?Γ?log?Δ)-competitive even for a single channel.

Alexander Fanghänel

Papers

Oblivious interference scheduling

Improved Algorithms for Latency Minimization in Wireless Networks

Improved algorithms for latency minimization in wireless networks

Online capacity maximization in wireless networks

Online capacity maximization in wireless networks