The Price of Local Power Control in Wireless Scheduling

2010

Abstract Shortest link scheduling (SLS) in multihop wireless networks under physical interference model is notoriously hard to resolve and been studied only recently by a few works. Most of the obtained approximation bounds grow linearly with the number of links, and many are only valid with single-hop wireless networks, and some claimed approximation bounds are even false. This paper conducts a rigorous algorithmic study of SLS with power control under the physical interference model.

Proceedings of the 12th …, 2006

1995

We study the transmission power control in wireless networks where the cochannel interfering users are random. Examples of such systems are Frequency Hopping and Direct-Sequence CDMA cellular networks, Packet Radio Networks, and Voice connections with Silent Detection. We derive a simple algorithm to control the power, which converges to a unique set of powers, under synchronous or asynchronous power updates. When all the connections can be supported, these powers meet the SIR requirement of all connections, with a minimum power level. It is shown how to precisely implement the algorithm in a xed stationary packet radio network, and how to implement it distributively, in a frequency hopping cellular network. Two distributed implementations are presented, which are based on local measurements taken by each receiver during a time window where powers are kept constant. Each transmitter adjusts its power level at the end of every window, based on percentile, or mean interference estimators. The distributed implementations are e cient in the sense that they derive the desired theoretical powers, if the number of measurements in each window approaches in nity.

IEEE Transactions on Wireless Communications, 2010

This paper studies the problem of finding a minimum-length schedule of a power-controlled wireless network subject to traffic demands and SINR (signal-to-interferenceplus-noise ratio) constraints. We propose a column generation based algorithm that finds the optimal schedules and transmit powers. The column generation method decomposes a complex linear optimization problem into a restricted master problem and a pricing problem. We develop a new formulation of the pricing problem using the Perron-Frobenius eigenvalue condition, which enables us to integrate link scheduling with power control in a single framework. This new formulation reduces the complexity of the pricing problem, and thus improves the overall efficiency of the column generation method significantly -for example, the average runtime is reduced by 99.86% in 18link networks compared with the traditional column generation method. Furthermore, we propose a branch-and-price method that combines column generation with the branch-and-bound technique to tackle the integer constraints on time slot allocation. We develop a new branching rule in the branch-and-price method that maintains the size of the pricing problem after each branching. Our branch-and-price method can obtain optimal integer solutions efficiently -for example, the average runtime is reduced by 99.72% in 18-link networks compared with the traditional branch-and-price method. We further suggest efficient heuristic algorithms based on the structure of the optimal algorithms. Simulation results show that the heuristic algorithms can reach solutions within 10% of optimality for networks with less than 30 links.

Mathematical Programming, 2007

Given a graph with costs on the edges, the power of a node is the maximum cost of an edge leaving it, and the power of the graph is the sum of the powers of the nodes of this graph. Motivated by applications in wireless multi-hop networks, we consider four fundamental problems under the power minimization criteria: the Min-Power b-Edge-Cover problem (MPb-EC) where the goal is to find a min-power subgraph so that the degree of every node v is at least some given integer b(v), the Min-Power k-node Connected Spanning Subgraph problem (MPk-CSS), Min-Power k-edge Connected Spanning Subgraph problem (MPk-ECSS), and finally the Min-Power k-Edge-Disjoint Paths problem in directed graphs (MPk-EDP). We give an O(log 4 n)-approximation algorithm for MPb-EC. This gives an O(log 4 n)-approximation algorithm for MPk-CSS for most values of k, improving the best previously known O(k)-approximation guarantee. In contrast, we obtain an O( √ n) approximation algorithm for MPk-ECSS, and for its variant in directed graphs (i.e., MPk-EDP), we establish the following inapproximability threshold: MPk-EDP cannot be approximated within O(2 log 1−ε n ) for any fixed ε > 0, unless NP-hard problems can be solved in quasi-polynomial time.

ACM Transactions on Algorithms, 2012

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.

IEEE Transactions on Wireless Communications, 2018

Considering a multiuser interference network with an eavesdropper, this paper aims at the power allocation to optimize the worst secrecy throughput among the network links or the secure energy efficiency in terms of achieved secrecy throughput per Joule under link security requirements. Three scenarios for the access of channel state information are considered: the perfect channel state information, partial channel state information with channels from the transmitters to the eavesdropper exponentially distributed, and not perfectly known channels between the transmitters and the users with exponentially distributed errors. The paper develops various pathfollowing procedures of low complexity and rapid convergence for the optimal power allocation. Their effectiveness and viability are illustrated through numerical examples. The power allocation schemes are shown to achieve both high secrecy throughput and energy efficiency.

INFOCOM 2009, …, 2009

In this work we study the problem of determining the throughput capacity of a wireless network. We propose a scheduling algorithm to achieve this capacity within an approximation factor. Our analysis is performed in the physical interference model, where nodes are arbitrarily distributed in Euclidean space. We consider the problem separately from the routing problem and the power control problem, i.e., all requests are single-hop, and all nodes transmit at a fixed power level. The existing solutions to this problem have either concentrated on special-case topologies, or presented optimality guarantees which become arbitrarily bad (linear in the number of nodes) depending on the network's topology.

Discrete Applied Mathematics, 2006

Motivated by topology control in ad hoc wireless networks, Power Assignment is a family of problems, each defined by a certain connectivity constraint (such as strong connectivity). The input consists of a directed complete weighted digraph G = (V , c) (that is, c : V × V → R +). The power of a vertex u in a directed spanning subgraph H is given by p H (u) = max uv∈E(H) c(uv), and corresponds to the energy consumption required for node u to transmit to all nodes v with uv ∈ E(H). The power of H is given by p(H) = u∈V p H (u). Power Assignment seeks to minimize p(H) while H satisfies the given connectivity constraint. Min-Power Bounded-Hops Broadcast is a power assignment problem which has as additional input a positive integer d and a r ∈ V. The output H must be a r-rooted outgoing arborescence of depth at most d. We give an (O(log n), O(log n)) bicriteria approximation algorithm for Min-Power Bounded-Hops Broadcast: that is, our output has depth at most O(d log n) and power at most O(log n) times the optimum solution. For the Euclidean case, when c(u, v) = c(v, u) = u, v (here u, v is the Euclidean distance and is a constant between 2 and 5), the output of our algorithm can be modified to give a O((log n)) approximation ratio. Previous results for Min-Power Bounded-Hops Broadcast are only exact algorithms based on dynamic programming for the case when the nodes lie on the line and c(u, v) = c(v, u) = u, v. Our bicriteria results extend to Min-Power Bounded-Hops Strong Connectivity, where H must have a path of at most d edges in between any two nodes. Previous work for Min-Power Bounded-Hops Strong Connectivity consists only of constant or better approximation for special cases of the Euclidean case.

2011 Proceedings IEEE INFOCOM, 2011

We consider the capacity problem (or, the single slot scheduling problem) in wireless networks. Our goal is to maximize the number of successful connections in arbitrary wireless networks where a transmission is successful only if the signal-to-interference-plus-noise ratio at the receiver is greater than some threshold. We study a game theoretic approach towards capacity maximization introduced by Andrews and Dinitz (INFOCOM 2009) and Dinitz (INFOCOM 2010). We prove vastly improved bounds for the game theoretic algorithm. In doing so, we achieve the first distributed constant factor approximation algorithm for capacity maximization for the uniform power assignment. When compared to the optimum where links may use an arbitrary power assignment, we prove a O(log ∆) approximation, where ∆ is the ratio between the largest and the smallest link in the network. This is an exponential improvement of the approximation factor compared to existing results for distributed algorithms. All our results work for links located in any metric space. In addition, we provide simulation studies clarifying the picture on distributed algorithms for capacity maximization.