Analysis of algorithms for online routing and scheduling in networks

We study situations in which an algorithm must make decisions about how to best route and schedule data transfer requests in a communication network before each transfer leaves its source. For some situations, such as those requiring quality of service guarantees, this is essential. For other situations, doing work in advance can simplify decisions in transit and increase the speed of the network. In order to reflect realistic scenarios, we require that our algorithms be online, or make their decisions without knowing future requests. We measure the efficiency of an online algorithm by its competitive ratio, which is the maximum ratio, over all request sequences, of the cost of the online algorithm\u27s solution to that of an optimal solution constructed by knowing all the requests in advance.;We identify and study two distinct variations of this general problem. In the first, data transfer requests are permanent virtual circuit requests in a circuit-switched network and the goal is to minimize the network congestion caused by the route assignment. In the second variation, data transfer requests are packets in a packet-switched network and the goal is to minimize the makespan of the schedule, or the time that the last packet reaches its destination. We present new lower bounds on the competitive ratio of any online algorithm with respect to both network congestion and makespan.;We consider two greedy online algorithms for permanent virtual circuit routing on arbitrary networks with unit capacity links, and prove both lower and upper bounds on their competitive ratios. While these greedy algorithms are not optimal, they can be expected to perform well in many circumstances and require less time to make a decision, when compared to a previously discovered asymptotically optimal online algorithm. For the online packet routing and scheduling problem, we consider an algorithm which simply assigns to each packet a priority based upon its arrival time. No packet is delayed by another packet with a lower priority. We analyze the competitive ratio of this algorithm on linear array, tree, and ring networks

Dynamic Multiple Pattern Matching

This work was also published as a Rice University thesis/dissertation: http://hdl.handle.net/1911/16740Pattern matching algorithms are among the most important and practical contributions of theoretical computer science. Pattern matching is used in a wide variety of applications such as text editing, information retrieval, DNA sequencing, and computer vision. Several combinatorial problems arise in pattern matching such as matching in the presence of local errors, scaling, rotation, compression, and multiple patterns. A common feature shared by many solutions to these problems is the notion of preprocessing the patterns and/or texts prior to the actual matching. We study the problem of pattern matching with multiple patterns. The set of patterns is called a "dictionary." Furthermore, the dictionary can be dynamic in the sense that it can change overtime by insertion or deletion of individual patterns. We need to preprocess the dictionary so as to provide efficient searching as well as efficient updates. We first present a solution to the one dimensional version of the problem where the patterns are strings. A salient feature of our solution is a DFA-based searching mechanism similar to the Knuth-Morris-Pratt algorithm. We then use this solution to solve the two dimensional version of the problem where the patterns are restricted to have square shapes. Finally, we solve the general case, where the patterns can have any rectangular shape, by reducing this problem to a range searching problem in computational geometry