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.
A commonly used model is the @math -hop link interference model, in which two links that are not within K-hops of each other can communicate simultaneously, and the capacity of a link is a constant value if there is no interference @cite_15 , @cite_13 , @cite_8 , @cite_1 , @cite_12 , @cite_10 . In @cite_15 , the Maximal Matching (MM) scheduling algorithm is used under the node exclusive interference model. This algorithm can operate in a distributed fashion and is proven to achieve at least one half of the achievable throughput. This has motivated subsequent research on distributed algorithms with provable performance @cite_13 , @cite_8 , @cite_10 , @cite_1 , @cite_12 .
@cite_8 @cite_10 @cite_1 @cite_15 @cite_13 @cite_12
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We consider the problem of throughput-optimal scheduling in wireless networks subject to interference constraints. We model the interference using a family of K -hop interference models. We define a K-hop interference model as one for which no two links within K hops can successfully transmit at the same time (Note that IEEE 802.11 DCF corresponds to a 2-hop interference model.) .For a given K, a throughput-optimal scheduler needs to solve a maximum weighted matching problem subject to the K-hop interference constraints. For K=1, the resulting problem is the classical Maximum Weighted Matching problem, that can be solved in polynomial time. However, we show that for K>1,the resulting problems are NP-Hard and cannot be approximated within a factor that grows polynomially with the number of nodes. Interestingly, we show that for specific kinds of graphs, that can be used to model the underlying connectivity graph of a wide range of wireless networks, the resulting problems admit polynomial time approximation schemes. We also show that a simple greedy matching algorithm provides a constant factor approximation to the scheduling problem for all K in this case. We then show that under a setting with single-hop traffic and no rate control, the maximal scheduling policy considered in recent related works can achieve a constant fraction of the capacity region for networks whose connectivity graph can be represented using one of the above classes of graphs. These results are encouraging as they suggest that one can develop distributed algorithms to achieve near optimal throughput in case of a wide range of wireless networks. In this paper, we characterize the performance of an important class of scheduling schemes, called greedy maximal scheduling (GMS), for multi-hop wireless networks. While a lower bound on the throughput performance of GMS is relatively well-known in the simple node-exclusive interference model, it has not been thoroughly explored in the more general K-hop interference model. Moreover, empirical observations suggest that the known bounds are quite loose, and that the performance of GMS is often close to optimal. In this paper, we provide a number of new analytic results characterizing the performance limits of GMS. We first provide an equivalent characterization of the efficiency ratio of GMS through a topological property called the local-pooling factor of the network graph. We then develop an iterative procedure to estimate the local-pooling factor under a large class of network topologies and interference models. We use these results to study the worst-case efficiency ratio of GMS on two classes of network topologies. First, we show how these results can be applied to tree networks to prove that GMS achieves the full capacity region in tree networks under the K-hop interference model. Second, we show that the worst-case efficiency ratio of GMS in geometric network graphs is between 1 6 and 1 3. 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 the 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 @W(I ([email protected])) steps, where @D denotes the aspect ratio of the metric. When restricting to the two-dimensional Euclidean space (as in the previous work) the bound improves to @W(I [email protected]). Alternatively, when restricting to linear power assignments, the lower bound improves even to @W(I). The lower bounds are complemented by an efficient algorithm computing a schedule for linear power assignments using only O(Ilogn) steps. A more sophisticated algorithm computes a schedule using even only O(I+log^2n) 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 O([email protected]). In addition, we extend these results for single-hop scheduling to multi-hop scheduling and combined scheduling and routing problems, where our analysis generalizes the previous results towards general metrics and improves on the previous approximation factors. 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. We propose the first scheduling algorithm with approximation guarantee independent of the topology of the network. The algorithm has a constant approximation guarantee for the problem of maximizing the number of links scheduled in one time-slot. Furthermore, we obtain a O(log n) approximation for the problem of minimizing the number of time slots needed to schedule a given set of requests. Simulation results indicate that our algorithm does not only have an exponentially better approximation ratio in theory, but also achieves superior performance in various practical network scenarios. Furthermore, we prove that the analysis of the algorithm is extendable to higher-dimensional Euclidean spaces, and to more realistic bounded-distortion spaces, induced by non-isotropic signal distortions. Finally, we show that it is NP-hard to approximate the scheduling problem to within n 1-epsiv factor, for any constant epsiv > 0, in the non-geometric SINR model, in which path-loss is independent of the Euclidean coordinates of the nodes.