Merging and Merge-Sort in a Single Hop Radio Network

Abstract. We present two merging algorithms on a single-channel single-hop radio network without collision detection. The simpler of these algorithms merges two sorted sequences of length n in time 4n with energetic cost for each station lg n. The energetic cost of broadcasting is constant. This yields the merge-sort for n elements in time 2n lg n, where the energetic cost for each station i

Energy Efficient Algorithms in Low-Energy Wireless Sensor Networks

Wireless sensor networks (WSNs) consist of small autonomous processors spatially distributed, typically with the goal of gathering physical data about the environment such as temperature, air pressure, and sound. WSNs have a wide range of applications including military use, health care monitoring, and environmental sensing. Because sensors are typically battery powered, algorithms for sensor network models should not only seek to minimize runtime but also energy utilization. Specifically, to maximize network lifetime, algorithms must minimize the energy usage of the sensors that use the most energy in the network. In extremely dense networks it may be inefficient for sensors to communicate with all neighboring sensors on a consistent basis, especially in mobile wireless sensor networks (MWSNs) where the topology of the network is constantly changing. Sensors conserve energy by going into a low-energy sleep state, and in our algorithms sensors will be asleep for the vast majority of the total runtime. Algorithms under these conditions face additional challenges because of the increased difficulty of coordinating between sensors. Because of the spatial nature of sensor networks, geometry problems are often of particular interest. For example, to detect outliers, data is often compared with the nearest neighboring sensors. In this dissertation we provide algorithmic techniques designed for divide-and-conquer solutions to computational geometry problems. We provide a technique for coordinating divide-and-conquer algorithms in a single-hop setting called breadth first recursion. We use this technique to sort data and to find the convex hull. Although most WSNs are multi-hop networks, locally very dense, expansive networks resemble single-hop networks. Thus we use algorithms for single-hop networks as a building blocks for multi-hop algorithms with α-consolidation algorithms. We then provide α-consolidation algorithms for all points k-nearest neighbors, the coverage boundary, and the Voronoi diagram. We also analyze the WSN problem of propagating data to a high-energy base station. Clustering approaches, such as low-energy adaptive clustering hierarchy (LEACH) and its multi-hop variant (MR-LEACH), are extremely popular for data propagation. The energy balanced protocol (EBP) is a clustering approach like MRLEACH where clusters pass data towards the base station but also, with some probability, send data long distances directly to the base station. We analytically and empirically show that EBP is close to optimal while approaches that do not use long hops like MR-LEACH are only close to optimal if sending messages long distances is prohibitively expensive.PHDComputer Science & EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/153370/1/timlewis_1.pd