This thesis is concerned with caching algorithms. We investigate three variations of the caching problem: web caching in the Torng framework, relative competitiveness and caching with request reordering. <br /><br /> In the first variation we define different cost models involving page sizes and page costs. We also present the Torng cost framework introduced by Torng in [29]. Next we analyze the competitive ratio of online deterministic marking algorithms in the BIT cost model combined with the Torng framework. We show that given some specific restrictions on the set of possible request sequences, any marking algorithm is 2-competitive. <br /><br /> The second variation consists in using the relative competitiveness ratio on an access graph as a complexity measure. We use the concept of access graphs introduced by Borodin [11] to define our own concept of relative competitive ratio. We demonstrate results regarding the relative competitiveness of two cache eviction policies in both the basic and the Torng framework combined with the CLASSICAL cost model. <br /><br /> The third variation is caching with request reordering. Two reordering models are defined. We prove some important results about the value of a move and number of orderings, then demonstrate results about the approximation factor and competitive ratio of offline and online reordering schemes, respectively.

We consider the scheduling problem of minimizing the average weighted completion time on identical parallel machines when jobs are arriving over time. For both the preemptive and the nonpreemptive setting, we show that straightforward extensions of Smith's ratio rule yield smaller competitive ratios compared to the previously best-known deterministic on-line algorithms, which are (4+epsilon)-competitive in either case. Our preemptive algorithm is 2-competitive, which actually meets the competitive ratio of the currently best randomized on-line algorithm for this scenario. Our nonpreemptive algorithm has a competitive ratio of 3.28. Both results are characterized by a surprisingly simple analysis; moreover, the preemptive algorithm also works in the less clairvoyant environment in which only the ratio of weight to processing time of a job becomes known at its release date, but neither its actual weight nor its processing time. In the corresponding nonpreemptive situation, every on-line algorithm has an unbounded competitive ratio

This thesis is concerned with caching algorithms. We investigate three variations of the caching problem: web caching in the Torng framework, relative competitiveness and caching with request reordering. <br /><br /> In the first variation we define different cost models involving page sizes and page costs. We also present the Torng cost framework introduced by Torng in [29]. Next we analyze the competitive ratio of online deterministic marking algorithms in the BIT cost model combined with the Torng framework. We show that given some specific restrictions on the set of possible request sequences, any marking algorithm is 2-competitive. <br /><br /> The second variation consists in using the relative competitiveness ratio on an access graph as a complexity measure. We use the concept of access graphs introduced by Borodin [11] to define our own concept of relative competitive ratio. We demonstrate results regarding the relative competitiveness of two cache eviction policies in both the basic and the Torng framework combined with the CLASSICAL cost model. <br /><br /> The third variation is caching with request reordering. Two reordering models are defined. We prove some important results about the value of a move and number of orderings, then demonstrate results about the approximation factor and competitive ratio of offline and online reordering schemes, respectively.

In various business and military settings, there is an expectation of on-demand delivery of supplies and services. Typically, several delivery vehicles (also called servers) carry these supplies. Requests arrive one at a time and when a request arrives, a server is assigned to this request at a cost that is proportional to the distance between the server and the request. Bad assignments will not only lead to larger costs but will also create bottlenecks by increasing delivery time. There is, therefore, a need to design decision-making algorithms that produce cost-effective assignments of servers to requests in real-time. In this thesis, we consider the online bipartite matching problem where each server can serve exactly one request. In the online minimum metric bipartite matching problem, we are provided with a set of server locations in a metric space. Requests arrive one at a time that have to be immediately and irrevocably matched to a free server. The total cost of matching all the requests to servers, also known as the online matching is the sum of the cost of all the edges in the matching. There are many well-studied models for request generation. We study the problem in the adversarial model where an adversary who knows the decisions made by the algorithm generates a request sequence to maximize ratio of the cost of the online matching and the minimum-cost matching (also called the competitive ratio). An algorithm is a-competitive if the cost of online matching is at most 'a' times the minimum cost. A recently discovered robust and deterministic online algorithm (we refer to this as the robust matching or the RM-Algorithm) was shown to have optimal competitive ratios in the adversarial model and a relatively weaker random arrival model. We extend the analysis of the RM-Algorithm in the adversarial model and show that the competitive ratio of the algorithm is sensitive to the input, i.e., for "nice" input metric spaces or "nice" server placements, the performance guarantees of the RM-Algorithm is significantly better. In fact, we show that the performance is almost optimal for any fixed metric space and server locations. / Master of Science / In various business and military settings, there is an expectation of on-demand delivery of supplies and services. Typically, several delivery vehicles (also called servers) carry these supplies. Requests arrive one at a time and when a request arrives, a server is assigned to this request at a cost that is proportional to the distance between the server and the request. Bad assignments will not only lead to larger costs but will also create bottlenecks by increasing delivery time. There is, therefore, a need to design decision-making algorithms that produce cost-effective assignments of servers to requests in real-time. In this thesis, we consider the online bipartite matching problem where each server can serve exactly one request. In the online minimum metric bipartite matching problem, we are provided with a set of server locations in a metric space. Requests arrive one at a time that have to be immediately and irrevocably matched to a free server. The total cost of matching all the requests to servers, also known as the online matching is the sum of the cost of all the edges in the matching. There are many well-studied models for request generation. We study the problem in the adversarial model where an adversary who knows the decisions made by the algorithm generates a request sequence to maximize ratio of the cost of the online matching and the minimum-cost matching (also called the competitive ratio). An algorithm is α-competitive if the cost of online matching is at most α times the minimum cost. A recently discovered robust and deterministic online algorithm (we refer to this as the robust matching or the RM-Algorithm) was shown to have optimal competitive ratios in the adversarial model and a relatively weaker random arrival model. We extend the analysis of the RM-Algorithm in the adversarial model and show that the competitive ratio of the algorithm is sensitive to the input, i.e., for “nice” input metric spaces or “nice” server placements, the performance guarantees of the RM-Algorithm is significantly better. In fact, we show that the performance is almost optimal for any fixed metric space and server locations.

Emergency Management has received more and more attention in the recent years. Most research in this eld focused on evacuation of victims from dangerous places to safe places, but little on allocation of medical resources to safe places and/or transportation tools to the dangerous places. This thesis studies the problem of delivering medical resources from medical centers to the temporary aid site in a disaster-a ected area to help the wounded victims. In particular, this thesis describes a new algorithm for solving this problem. As requirements of medical resources for a disaster a ected area are not known in advance, the problem is in the so-called on-line environment. The algorithm for such a problem is also called on-line algorithm. The evaluation criterion for such an on-line algorithm is the so-called competitive ratio. This thesis considers four cases of such a problem: (1) the capacity of vehicles for transporting medical resources and the number of vehicles are both in nite, (2) the capacity of vehicles is in nite but the number of vehicles is one, (3) the capacity of vehicles is nite and the number of vehicles is in nite, (4) the capacity of vehicles is nite and the number of vehicles is one. Algorithms for the four cases are called H1, H2, H3, and H4, ii respectively. For all these cases, this thesis presents properties, appropriate on-line algorithms and theoretical analysis of these algorithms. The result of the analysis shows that H1 and H3 are optimal based on the competitive ratio criterion while the other two have a very small gap in terms of the optimum criterion. The thesis also presents a case study for having a sense of the performance of H2 and demonstrating practicality of the developed algorithms. The result of this thesis has contributions to the eld of resource planning and scheduling and has application in not only emergency management but also supply chain management in manufacturing and construction.

With various new alternatives of low-cost sensor devices, there is a strong demand for large scale wireless sensor networks (WSN). Energy efficiency in routing is crucial for achieving the desired levels of longevity in these networks. Existing routing algorithms that do not combine information on transmission energies on links, residual energies at nodes, and the identity of data itself, cannot reach network capacity. A proof-of-concept routing algorithm that combines data aggregation with the minimum-weight path routing is studied in this thesis work. This new algorithm can achieve much larger network lifetime when there is redundancy in messages to be carried by the network, a practical reality in sensor network applications.