An overarching issue in resource management of wireless networks is assessing their capacity: How much communication can be achieved in a network, utilizing all the tools available: power control, scheduling, routing, channel assignment and rate adjustment? We propose the first framework for approximation algorithms in the physical model of wireless interference that addresses these questions in full. The approximations obtained are at most doubly logarithmic in the link length and rate diversity. Where previous bounds are known, this gives an exponential improvement (or better). A key contribution is showing that the complex interference relationship of the physical model can be simplified, at a small cost, into a novel type of amenable conflict graphs. We also show that the approximation obtained is provably the best possible for any conflict graph formulation.
In this paper the problem of wireless transmissions scheduling in the path-loss SINR model is considered for different fixed power schemes. The lower bounds for the optimum schedule length proven by Kesselheim and Voecking are considered. It is shown that the lower bound for the linear power scheme is tight, by presenting a constant-factor approximation algorithm. On the other hand, it is shown that the lower bounds proven for many other interesting power schemes can be essentially far from the optima. We give algorithms with constant-factor performance guarantees for several capacity and throughput problems in the SINR model. The algorithms are all based on a novel LP formulation for capacity problems. First, we give a new constant-factor approximation algorithm for selecting the maximum subset of links that can be scheduled simultaneously, under any non-decreasing and sublinear power assignment. For the case of uniform power, we extend this to the case of variable QoS requirements and link-dependent noise terms. Second, we approximate a problem related to cognitive radio: find a maximum set of links that can be simultaneously scheduled without affecting a given set of previously assigned links. Finally, we obtain constant-factor approximation of weighted capacity under linear power assignment. Multihop infrastructure wireless mesh networks offer increased reliability, coverage, and reduced equipment costs over their single-hop counterpart, wireless local area networks. Equipping wireless routers with multiple radios further improves the capacity by transmitting over multiple radios simultaneously using orthogonal channels. Efficient channel assignment and routing is essential for throughput optimization of mesh clients. Efficient channel assignment schemes can greatly relieve the interference effect of close-by transmissions; effective routing schemes can alleviate potential congestion on any gateways to the Internet, thereby improving per-client throughput. Unlike previous heuristic approaches, we mathematically formulate the joint channel assignment and routing problem, taking into account the interference constraints, the number of channels in the network, and the number of radios available at each mesh router. We then use this formulation to develop a solution for our problem that optimizes the overall network throughput subject to fairness constraints on allocation of scarce wireless capacity among mobile clients. We show that the performance of our algorithms is within a constant factor of that of any optimal algorithm for the joint channel assignment and routing problem. Our evaluation demonstrates that our algorithm can effectively exploit the increased number of channels and radios, and it performs much better than the theoretical worst case bounds We study combinatorial auctions for secondary spectrum markets, where short-term communication licenses are sold to wireless nodes. Channels can be assigned to multiple bidders according to interference constraints captured by a conflict graph. We suggest a novel approach to such combinatorial auctions using a graph parameter called inductive independence number. We achieve good approximation results by showing that interference constraints for wireless networks imply a bounded inductive independence number. For example, in the physical model the factor becomes O(√k log2 n) for n bidders and k channels. Our algorithms can be turned into incentive-compatible mechanisms for bidders with arbitrary valuations. This paper considers two inter-related questions: (i) Given a wireless ad-hoc network and a collection of source-destination pairs (s i ,t i ) , what is the maximum throughput capacity of the network, i.e. the rate at which data from the sources to their corresponding destinations can be transferred in the network? (ii) Can network protocols be designed that jointly route the packets and schedule transmissions at rates close to the maximum throughput capacity? Much of the earlier work focused on random instances and proved analytical lower and upper bounds on the maximum throughput capacity. Here, in contrast, we consider arbitrary wireless networks. Further, we study the algorithmic aspects of the above questions: the goal is to design provably good algorithms for arbitrary instances. We develop analytical performance evaluation models and distributed algorithms for routing and scheduling which incorporate fairness, energy and dilation (path-length) requirements and provide a unified framework for utilizing the network close to its maximum throughput capacity.Motivated by certain popular wireless protocols used in practice, we also explore "shortest-path like" path selection strategies which maximize the network throughput. The theoretical results naturally suggest an interesting class of congestion aware link metrics which can be directly plugged into several existing routing protocols such as AODV, DSR, etc. We complement the theoretical analysis with extensive simulations. The results indicate that routes obtained using our congestion aware link metrics consistently yield higher throughput than hop-count based shortest path metrics. This paper considers the problem of determining the achievable rates in multi-hop wireless networks. We consider the problem of jointly routing the flows and scheduling transmissions to achieve a given rate vector. We develop tight necessary and sufficient conditions for the achievability of the rate vector. We develop efficient and easy to implement Fully Polynomial Time Approximation Schemes for solving the routing problem. The scheduling problem is a solved as a graph edge-coloring problem. We show that this approach guarantees that the solution obtained is within 67 of the optimal solution in the worst case and, in practice, is typically within about 80 of the optimal solution. The approach that we use is quite flexible and is a promising method to handle more sophisticated interference conditions, multiple channels, multiple antennas, and routing with diversity requirements. 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 paper we study the following optimization problem in a plane multihop wireless network under the physical interference model. Given a multihop wireless network and a positive link weight (or demand) function, select a set of independent links whose total weight is maximized. This problem is known to be NP-hard. The best known approximation algorithm for this problem achieves logarithmic factor approximation with power control. In this work, we present a constant-approximation algorithm for the problem with the power assignment specified in this paper when the link weight-to-length ratio is bounded. Moreover, our constant-approximation bound is valid regardless of the value of the noise power and the lengths of the communication links.  We study truthful auctions for secondary spectrum usage in wireless networks. In this scenario, n communication requests need to be allocated to k available channels that are subject to interference and noise. We present the first truthful mechanisms for secondary spectrum auctions with symmetric or submodular valuations. Our approach to model interference uses an edge-weighted conflict graph, and our algorithms provide asymptotically almost optimal approximation bounds for conflict graphs with a small inductive independence number ρ 