Alexander Fanghänel

Improved Algorithms for Latency Minimization in Wireless Networks

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

Online capacity maximization in wireless networks

\mathcal O(I \log n)

Scheduling and Power Assignments in the Physical Model

steps. A more sophisticated algorithm computes a schedule using even only

Who should pay for forwarding packets

\mathcal O(I + \log^2 n)

Oblivious interference scheduling

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

Improved algorithms for latency minimization in wireless networks

\mathcal O(\log \Delta)

Who Should Pay for Forwarding Packets

. 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.

Scheduling in wireless networks with oblivious power assignments

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 Ω(Γ⋅Δd/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)+ε)-competitive, for any constant ε>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⋅Γ1/k′⋅Δ(d/2k″)+ε) 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 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 the interference scheduling problem, one is given a set of n communication requests each of which corresponds to a sender and a receiver in a multipoint radio network. Each request must be assigned a power level and a color such that signals in each color class can be transmitted simultaneously. 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 modeling interference in the engineering community. The objective is to minimize the schedule length corresponding to the number of colors needed to schedule all requests. We study oblivious power assignments in which the power value of a request only depends on the path loss between the sender and the receiver, e.g., in a linear fashion. At first, we present a measure of interference giving lower bounds for the schedule length with respect to linear and other power assignments. Based on this measure, we devise distributed scheduling algorithms for the linear power assignment achieving the minimal schedule length up to small factors. In addition, we study a power assignment in which the signal strength is set to the square root of the path loss. We show that this power assignment leads to improved approximation guarantees in two kinds of problem instances defined by directed and bidirectional communication request. Finally, we study the limitations of oblivious power assignments by proving lower bounds for this class of algorithms.

Deliverable 4.3.4 Evolutionary approaches to coalition formation in dynamic nets

We present a game theoretic study of hybrid communication networks in which mobile devices can connect in an ad hoc fashion to a base station, possibly via a few hops using other mobile devices as intermediate nodes. The maximal number of allowed hops might be bounded with the motivation to guarantee small latency. We introduce hybrid connectivity games to study the impact of selfishness on this kind of infrastructure. Mobile devices are represented by selfish players, each of which aims at establishing an uplink path to the base station minimizing its individual cost. Our model assumes that intermediate nodes on an uplink path are reimbursed for transmitting the packets of other devices. The reimbursements can be paid either by a benevolent network operator or by the senders of the packets using micropayments via a clearing agency that possibly collects a small percentage as commission. These different ways to implement the payments lead to different variants of the hybrid connectivity game. Our main findings are: (1) If there is no constraint on the number of allowed hops on the path to the base station, then the existence of equilibria is guaranteed regardless of whether the network operator or the senders pay for forwarding packets. (2) If the network operator pays, then the existence of equilibria is guaranteed only if at most one intermediate node is allowed, i.e., for at most two hops on the uplink path of a device, but not if the maximal number of allowed hops is three or larger. (3) In contrast, if the senders pay for forwarding their packets, then equilibria are guaranteed to exist given any bound on the number of allowed hops. The equilibrium analysis presented in this paper gives a first game theoretical motivation for the implementation of micropayment schemes in which senders pay for forwarding their packets. We further support this evidence by giving an upper bound on the Price of Anarchy for this kind of hybrid connectivity games that is independent of the number of nodes, but only depends on the number of hops and the power gradient.