Design and Analysis of Algorithms for Graph Exploration and Resource Allocation Problems and Their Application to Energy Management

In this dissertation, we discuss the design and analysis of algorithms for graph exploration and resource allocation problems, and their application to energy management. Efficient use of energy has been a topic of great importance in various fields. For example, in the research fields on sensor networks and robotics, efficient energy control is decisive because available energy resources are generally limited. Therefore, there have been strong needs for energy-efficient control algorithms. Another example is a recent movement to construct new-generation power networks and power management systems, such as the evolving smart grid and frameworks of automated demand response. Especially, new power networks have been proposed based on the concept of Energy-on-Demand (EoD), where an energy management system automatically controls amounts of power supplied to appliances limiting total power consumption below a targeted value. There also have been novel concepts such as “optimal allocation of energy”, where a power network optimally allocates power from various kind of power sources to appliances considering Quality-of-Energy (QoEn), which represents characteristics of power that appliances require and sources supply. For realizing these concepts, we need efficient algorithms, devices and systems for power allocation. The first topic of this dissertation is the design and analysis of efficient online algorithms for the graph exploration problems. Algorithms for exploration of unknown terrains have been actively studied, and much research work focuses on exploration algorithms for minimizing the total moving distance by a searcher to obtain all the topological information of the terrains. Kalyanasundaram and Pruhs formulated the problem in an online problem on undirected edge-weighted graphs. In Chapter 3, we will discuss the design and analysis of graph exploration algorithms for cycles and unweighted graphs, and give tight bounds on competitive ratios. Second, the design and analysis of an approximation algorithm for resource allocation problems applicable to QoEn-based power allocation are described in Chapter