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.
When n identical randomly located nodes, each capable of transmitting at W bits per second and using a fixed range, form a wireless network, the throughput spl lambda (n) obtainable by each node for a randomly chosen destination is spl Theta (W spl radic (nlogn)) bits per second under a noninterference protocol. If the nodes are optimally placed in a disk of unit area, traffic patterns are optimally assigned, and each transmission's range is optimally chosen, the bit-distance product that can be transported by the network per second is spl Theta (W spl radic An) bit-meters per second. Thus even under optimal circumstances, the throughput is only spl Theta (W spl radic n) bits per second for each node for a destination nonvanishingly far away. Similar results also hold under an alternate physical model where a required signal-to-interference ratio is specified for successful receptions. Fundamentally, it is the need for every node all over the domain to share whatever portion of the channel it is utilizing with nodes in its local neighborhood that is the reason for the constriction in capacity. Splitting the channel into several subchannels does not change any of the results. Some implications may be worth considering by designers. Since the throughput furnished to each user diminishes to zero as the number of users is increased, perhaps networks connecting smaller numbers of users, or featuring connections mostly with nearby neighbors, may be more likely to be find acceptance. We define and study the scheduling complexity in wireless networks, which expresses the theoretically achievable efficiency of MAC layer protocols. Given a set of communication requests in arbitrary networks, the scheduling complexity describes the amount of time required to successfully schedule all requests. The most basic and important network structure in wireless networks being connectivity, we study the scheduling complexity of connectivity, i.e., the minimal amount of time required until a connected structure can be scheduled. In this paper, we prove that the scheduling complexity of connectivity grows only polylogarithmically in the number of nodes. Specifically, we present a novel scheduling algorithm that successfully schedules a strongly connected set of links in time O(logn) even in arbitrary worst-case networks. On the other hand, we prove that standard MAC layer or scheduling protocols can perform much worse. Particularly, any protocol that either employs uniform or linear (a node’s transmit power is proportional to the minimum power required to reach its intended receiver) power assignment has a Ω(n) scheduling complexity in the worst case, even for simple communication requests. In contrast, our polylogarithmic scheduling algorithm allows many concurrent transmission by using an explicitly formulated non-linear power assignment scheme. Our results show that even in large-scale worst-case networks, there is no theoretical scalability problem when it comes to scheduling transmission requests, thus giving an interesting complement to the more pessimistic bounds for the capacity in wireless networks. All results are based on the physical model of communication, which takes into account that the signal-tonoise plus interference ratio (SINR) at a receiver must be above a certain threshold if the transmission is to be received correctly.