Consider a wireless network where each communication link has a minimum bandwidth quality-of-service requirement. Certain pairs of wireless links interfere with each other due to being in the same vicinity, and this interference is modeled by a conflict graph. Given the conflict graph and link bandwidth requirements, the objective is to determine, using only localized information, whether the demands of all the links can be satisfied. At one extreme, each node knows the demands of only its neighbors; at the other extreme, there exists an optimal, centralized scheduler that has global information. The present work interpolates between these two extremes by quantifying the tradeoff between the degree of decentralization and the performance of the distributed algorithm. This open problem is resolved for the primary interference model, and the following general result is obtained: if each node knows the demands of all links in a ball of radius @math centered at the node, then there is a distributed algorithm whose performance is away from that of an optimal, centralized algorithm by a factor of at most @math . The tradeoff between performance and complexity of the distributed algorithm is also analyzed. It is shown that for line networks under the protocol interference model, the row constraints are a factor of at most @math away from optimal. Both bounds are best possible.
 Given a wireless network where some pairs of communication links interfere with each other, we study sufficient conditions for determining whether a given set of minimum bandwidth quality-of-service requirements can be satisfied. We are especially interested in algorithms which have low communication overhead and low processing complexity. The interference in the network is modeled using a conflict graph whose vertices correspond to the communication links in the network. Two links are adjacent in this graph if and only if they interfere with each other due to being in the same vicinity and hence cannot be simultaneously active. The problem of scheduling the transmission of the various links is then essentially a fractional, weighted vertex coloring problem, for which upper bounds on the fractional chromatic number are sought using only localized information. We recall some distributed algorithms for this problem, and then assess their worst-case performance. Our results on this fundamental problem imply that for some well known classes of networks and interference models, the performance of these distributed algorithms is within a bounded factor away from that of an optimal, centralized algorithm. The performance bounds are simple expressions in terms of graph invariants. It is seen that the induced star number of a network plays an important role in the design and performance of such networks. Wireless nodes within the same vicinity contend with each other for accessing the shared wireless medium. The contention constraints for sharing the medium depend on the medium access control (MAC) protocol that administers the accessibility of the network. In a previous work, we derived a set of sufficient conditions under which rates of all the flows are feasible given a MAC protocol. In this paper, we derive a new set of sufficient conditions that are better than those developed earlier. We show that these conditions are useful in solving many problems such as linear programming-based routing and admission control for QoS routing. We also evaluate, compare and discuss the performance of the derived sufficient conditions through simulation studies. The capacity of an arbitrary ad-hoc network is difficult to estimate due to interference between the links. We use a conflict graph that models this interference relationship to determine if a set of flow rates can be accommodated. Using the cliques (complete subgraphs) of the conflict graph, we derive constraints that are sufficient for a set of flow rates to be feasible, yet are guaranteed to be within a constant bound of the optimal. We also compute an alternate set of sufficient constraints that can be easily derived from the rows of the matrix representation of the conflict graph. These two sets of constraints are particularly useful because their construction and verification may be distributed across the nodes of a network. We also extend the ad-hoc network model to incorporate variations in the interference range, and obstructions in the network.