No abstract

Abstract-Wireless networks have historically considered support for mobile elements as an extra overhead. However, recent research has provided the means by which a network can take advantage of mobile elements. Particularly in the case of wireless sensor networks, mobile elements can be deliberately built into the system to improve the lifetime of the network and act as mechanical carriers of data. The mobile element, whose mobility is controlled, visits the nodes to collect their data before their buffers are full. In general, the spatio-temporal dynamics of the sensed phenomenon may require sensor nodes to collect samples at different rates, in which case, some nodes need to be visited more frequently than others. This work formulates the problem of scheduling the mobile element in the network so that there is no data loss due to buffer overflow. The problem is shown to be NP-complete and an IntegerLinear-Programming formulation is given. Finally, some computationally practical algorithms for a single mobile and for the case of multiple mobiles are presented and their performances compared.

Abstract-Content delivery networks often employ caching to reduce transmission rates from the central server to the end users. Recently, the technique of coded caching was introduced whereby coding in the caches and coded transmission signals from the central server are considered. Prior results in this area demonstrate that (a) carefully designing placement of content in the caches and (b) designing appropriate coded delivery signals allow for a system where the delivery rates can be significantly smaller than conventional schemes. However, matching upper and lower bounds on the transmission rates have not yet been obtained. In this work, we derive tighter lower bounds on coded caching rates than were known previously. We demonstrate that this problem can equivalently be posed as one of optimally labeling the leaves of a directed tree. Several examples that demonstrate the utility of our bounds are presented.

Abstract-We study the maximum flow possible between a single-source and multiple terminals in a weighted random graph (modeling a wired network) and a weighted random geometric graph (modeling an ad-hoc wireless network) using network coding. For the weighted random graph model, we show that the network coding capacity concentrates around the expected number of nearest neighbors of the source and the terminals. Specifically, for a network with a single source, terminals, and relay nodes such that the link capacities between any two nodes is independent and identically distributed (i.i.d.), the maximum flow between the source and the terminals is approximately [ ] with high probability. For the weighted random geometric graph model where two nodes are connected if they are within a certain distance of each other we show that with high probability the network coding capacity is greater than or equal to the expected number of nearest neighbors of the node with the least coverage area.

Abstract-Content delivery networks often employ caching to reduce transmission rates from the central server to the end users. Recently, the technique of coded caching was introduced whereby coding in the caches and coded transmission signals from the central server are considered. Prior results in this area demonstrate that (a) carefully designing placement of content in the caches and (b) designing appropriate coded delivery signals allow for a system where the delivery rates can be significantly smaller than conventional schemes. However, matching upper and lower bounds on the transmission rates have not yet been obtained. In this work, we derive tighter lower bounds on coded caching rates than were known previously. We demonstrate that this problem can equivalently be posed as one of optimally labeling the leaves of a directed tree. Several examples that demonstrate the utility of our bounds are presented.