One of the main problems in all-optical packetswitched networks is the lack of optical buffers, and currently the only known feasible technology for the constructions of optical buffers is to use optical crossbar Switches and fiber Delay Lines (SDLs). In this paper, we consider SDL constructions of optical queues with a limited number of recirculations through the optical switches and the fiber delay lines. Such a problem arises from practical feasibility considerations, such as crosstalk, power loss, amplified spontaneous emission from the Erbium doped fiber amplifiers, and the pattern effect of the optical switches. We first transform the design of the fiber delays in such SDL constructions into an equivalent integer representation problem. Specifically, given 1 ≤ k ≤ M, we seek for an M-sequence dM= (d1, d2, ..., dM) of positive integers to maximize the number of consecutive integers (starting from 0) that can be represented by the C-transform (a generalization of the well-known binary representation) with respect to dMsuch that there are at most k 1-entries in their C-transforms. Then, we propose a class of greedy constructions of dM, in which d1, d2, ..., dMare obtained recursively in a greedy manner so that the number of representable consecutive integers by using d1, d2, . .., diis larger than that by using d1, d2, . .., di-1for all i. Finally, we show that every optimal construction (in the sense of maximizing the number of representable consecutive integers) must be a greedy construction. As a result, the complexity of searching for an optimal construction can be greatly reduced from exponential time to polynomial time by only considering the greedy constructions rather than performing an exhaustive search. The solution of such an integer representation problem can be applied to the constructions of optical 2-to-1 FIFO multiplexers with a limited number of recirculations. Similar results can be obtained for the constructions of optical linear compressors/decompressors with a limited number of recirculations.

Two-stage constructions and banyan-type networks play important roles in designing high speed switch fabrics. Switch fabrics designed from two-stage constructions and banyan-type networks cannot realize all the permutations and are known as conditionally nonblocking switches. A renowned property for conditionally nonblocking switches is the closure property, i.e., if all the switches in a two-stage construction can realize a subset of permutations that satisfy a certain property P, then the switch resulted from the two-stage construction can also realize a subset of permutations that satisfy the same property P. However, such a closure property is mostly stated for the sufficient part in the literature and the necessary part of the statement is in general either not true or unknown. Finding such a necessary and sufficient result is of fundamental importance to two-stage constructions as it can completely characterize the permutations that are realizable by two-stage constructions. In this paper, we prove a necessary and sufficient closure property for two-stage constructions. For this, we consider uniform mapping permutations and define uniform mapping switches as switches that can only realize the set of uniform mapping permutations. We show that a switch constructed by a two-stage construction is a uniform mapping switch if and only if all the switches at the first stage and the second stage are uniform mapping switches. Such a necessary and sufficient result provides a complete characterization of the permutations that can be realized by two-stage constructions. Since banyan-type networks are constructed recursively by using two-stage constructions with 2 × 2 switches, we obtain a complete characterization for any realizable permutation of any banyan-type network as a composition of its trace, a uniform mapping permutation and its guide.

The effectiveness of epidemic routing for information dissemination in energy harvesting wireless sensor networks is examined in this work. Here, information is to be disseminated from a few nodes to a considerable fraction of all other nodes in the network. The use of epidemic routing is motivated by the fact that, when sensors are supported solely by harvested energy, the sensors' availability and the network topology may change dynamically due to the uncertainty of the energy arrival at the sensors. With epidemic routing, a node will receive and forward a packet to all other nodes in its neighborhood whenever it is able to do so. Each node will keep the packet only for a certain time duration depending on its recovery rate. By utilizing only energy harvested from the environment, the transmission radius of each sensor (and, thus, the network connectivity) is affected by its local energy arrival and the time in between transmissions. The less frequently it transmits, the further the distance it is able to reach. Two cases are examined in this work: 1) the case with identical transmission radius and 2) the case with identical inter-transmission time. The first case occurs when sensors transmit with fixed power and the second case occurs when the sensors operate under a fixed sleep-wake cycle or TDMA scheduling. The transmission radius and intertransmission time required to guarantee that a considerable fraction of nodes receive the information is derived for a given sensor density and recovery rate. Computer simulations are provided to validate our theoretical claims.