We consider the problem of scheduling in multihop wireless networks subject to interference constraints. We consider a graph based representation of wireless networks, where scheduled links adhere to the K-hop link interference model. We develop a distributed greedy heuristic for this scheduling problem. Further, we show that this distributed greedy heuristic computes the exact same schedule as the centralized greedy heuristic.
Scheduling algorithms under different SINR interference models have been studied in the literature @cite_5 , @cite_9 , @cite_3 , @cite_14 , @cite_11 . In @cite_5 , the authors have proposed a simple and distributed scheduling algorithm, that is an approximation to the optimal centralized algorithm. In @cite_9 , for the logarithmic SINR interference model, the author has proposed a distributed algorithm that is distributed and optimal when SINR values are high. The authors in @cite_3 and @cite_14 have also proposed heuristic algorithms under the target SINR interference model where the capacity of a link is a constant value when the received SINR exceeds a threshold, or zero otherwise. In @cite_11 , the authors have explore localized distributed scheduling for linear and logarithmic SINR model.
@cite_14 @cite_9 @cite_3 @cite_5 @cite_11
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We study the wireless scheduling problem in the SINR model. More specifically, given a set of @math links, each a sender-receiver pair, we wish to partition (or ) the links into the minimum number of slots, each satisfying interference constraints allowing simultaneous transmission. In the basic problem, all senders transmit with the same uniform power. We give a distributed @math -approximation algorithm for the scheduling problem, matching the best ratio known for centralized algorithms. It holds in arbitrary metric space and for every length-monotone and sublinear power assignment. It is based on an algorithm of Kesselheim and V "ocking, whose analysis we improve by a logarithmic factor. We show that every distributed algorithm uses @math slots to schedule certain instances that require only two slots, which implies that the best possible absolute performance guarantee is logarithmic. In this paper, we consider the classical problem of link scheduling in wireless networks under an accurate interference model, in which correct packet reception at a receiver node depends on the signa-to-interference-plus-noise ratio (SINR). While most previous work on wireless networks has addressed the scheduling problem using simplistic graph-based or distance-based interference models, a few recent papers have investigated scheduling with SINR-based interference models. However, these papers have either used approximations to the SINR model or have ignored important aspects of the problem. We study the problem of wireless link scheduling under the exact SINR model and present the first known true approximation algorithms for transmission scheduling under the exact model. We also introduce an algorithm with a proven approximation bound with respect to the length of the optimal schedule under primary interference. As an aside, our study identifies a class of "difficult to schedule" links, which hinder the derivation of tighter approximation bounds. Furthermore, we characterize conditions under which scheduling under SINR-based interference is within a constant factor from optimal under primary interference, which implies that secondary interference only degrades performance by a constant factor in these situations. We study the problem of distributed scheduling in multi-hop MIMO networks. We first develop a MIMO-pipe" model that provides the upper layers a set of rates and SINR requirements, which capture the rate-reliability tradeoff in MIMO communications. The main thrust of this study is then dedicated to developing CSMA-based MIMO-pipe scheduling under the SINR model. We choose the SINR model over the extensively studied matching or protocol-based interference models because it more naturally captures the impact of interference in wireless networks. The coupling among the links caused by the interference makes the problem of devising distributed scheduling algorithms particularly challenging. To that end, we explore CSMA-based MIMO-pipe scheduling, from two perspectives. First, we consider an idealized continuous time CSMA network. We propose a dual-band approach in which control messages are exchanged instantaneously over a channel separate from the data channel, and show that CSMA-based scheduling can achieve throughput optimality under the SINR model. Next, we consider a discrete time CSMA network. To tackle the challenge due to the coupling caused by interference, we propose a conservative" scheduling algorithm in which more stringent SINR constraints are imposed based on the MIMO-pipe model. We show that this suboptimal distributed scheduling can achieve an efficiency ratio bounded from below. 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 ċ 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.