This paper considers the interaction between channel assignment and distributed scheduling in multi-channel multiradio Wireless Mesh Networks (WMNs). Recently, a number of distributed scheduling algorithms for wireless networks have emerged. Due to their distributed operation, these algorithms can achieve only a fraction of the maximum possible throughput. As an alternative to increasing the throughput fraction by designing new algorithms, in this paper we present a novel approach that takes advantage of the inherent multi-radio capability of WMNs. We show that this capability can enable partitioning of the network into subnetworks in which simple distributed scheduling algorithms can achieve 100% throughput. The partitioning is based on the recently introduced notion of Local Pooling. Using this notion, we characterize topologies in which 100% throughput can be achieved distributedly. These topologies are used in order to develop a number of channel assignment algorithms that are based on a matroid intersection algorithm. These algorithms partition a network in a manner that not only expands the capacity regions of the subnetworks but also allows distributed algorithms to achieve these capacity regions. Finally, we evaluate the performance of the algorithms via simulation and show that they significantly increase the distributedly achievable capacity region.

Abstract-Efficient operation of wireless networks requires distributed routing and scheduling algorithms that take into account interference constraints. Recently, a few algorithms for networks with primary-or secondary-interference constraints have been developed. Due to their distributed operation, these algorithms can achieve only a guaranteed fraction of the maximum possible throughput. It was also recently shown that if a set of conditions (known as Local Pooling) is satisfied, simple distributed scheduling algorithms achieve 100% throughput. However, previous work regarding Local Pooling focused mostly on obtaining abstract conditions and on networks with single-hop interference or singlehop traffic. In this paper, we identify several graph classes that satisfy the Local Pooling conditions, thereby enabling the use of such graphs in network design algorithms. Then, we study the multihop implications of Local Pooling. We show that in many cases, as the interference degree increases, the Local Pooling conditions are more likely to hold. Consequently, although increased interference reduces the maximum achievable throughput of the network, it tends to enable distributed algorithms to achieve 100% of this throughput. Regarding multihop traffic, we show that if the network satisfies only the single-hop Local Pooling conditions, distributed joint routing and scheduling algorithms are not guaranteed to achieve maximum throughput. Therefore, we present new conditions for Multihop Local Pooling, under which distributed algorithms achieve 100% throughout. Finally, we identify network topologies in which the conditions hold and discuss the algorithmic implications of the results.

Interference lithography is an attractive technique for the creation of three dimensional photonic crystals. Structures with potential for photonic applications are fabricated in a photoresist through concurrent exposure with four coherent beams of laser radiation. The polymer-air templates are used to create higher refractive index contrast photonic crystals by infilling using atomic layer deposition followed by chemical vapor deposition. These photonic crystals exhibit excellent optical properties with strong reflectance peaks at the calculated band gap frequencies. Two-photon polymerization is used to demonstrate the ability to create designed defect structures such as waveguides in silicon-air photonic crystals.

Abstract-We seek to maximize the average data throughput of a single transmitter sending data over a fading channel to a single user class. The transmitter has a fixed amount of energy and a limited amount of time to send data. Given that the channel state determines the throughput obtained per unit of energy expended, the goal is to obtain a policy for scheduling transmissions that maximizes the expected data throughput. We develop a dynamic programming formulation that leads to an optimal transmission schedule, first where the present channel state is known just before transmission, and then to the case where the current channel state is unknown before transmission, but observed after transmission and evolves according to a Markov process. We then extend our approach to the problem of minimizing the expected energy required to send a fixed amount of data over a fading channel given deadline constraints.

We describe the fabrication of silicon three dimensional photonic crystals using polymer templates defined by a single step, two-photon exposure through a layer of photopolymer with relief molded on its surface. The resulting crystals exhibit high structural quality over large areas, displaying geometries consistent with calculation. Spectroscopic measurements of transmission and reflection through the silicon and polymer structures reveal excellent optical properties, approaching properties predicted by simulations that assume ideal layouts.