The grammar problem, a generalization of the single-source shortest-path problem introduced by Knuth, is to compute the minimum-cost derivation of a terminal string from each non-terminal of a given context-free grammar, with the cost of a derivation being suitably defined. This problem also subsumes the problem of finding optimal hyperpaths in directed hypergraphs (under varying optimization criteria) that has received attention recently. In this paper we present an incremental algorithm for a version of the grammar problem. As a special case of this algorithm we obtain an efficient incremental algorithm for the single-source shortest-path problem with positive edge lengths. The aspect of our work that distinguishes it from other work on the dynamic shortest-path problem is its ability to handle "multiple heterogeneous modifications": between updates, the input graph is allowed to be restructured by an arbitrary mixture of edge insertions, edge deletions, and edge-length changes.

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Optimizing Incremental View Maintenance Expressions in Relational Databases Dimitra Vista Doctor of Philosophy Graduate Department of Computer Science University of Toronto 1996 In the last few years, there has been significant interest in the design of incremental methods to improve the performance of view maintenance. Despite that, very little analysis or experimentation supports the predominant view that incremental methods are more efficient than their non-incremental counterparts. We argue that the performance of incremental view maintenance depends on system aspects of the database, such as the availability of indices, the sizes of the relations involved, and the sizes of the database updates. We also argue that the database query optimizer is a reasonable component of the database system to decide, at the time of view maintenance, whether a view is to be maintained incrementally or not, because the query optimizer has knowledge of, and access to, all of the parameters that...

An incremental algorithm (also called a dynamic update algorithm) updates the answer to some problem after an incremental change is made in the input. We examine methods for bounding the performance of such algorithms. First, quite general but relatively weak bounds are considered, along with a careful examination of the conditions under which they hold. Next, a more powerful proof method, the Incremental Relative Lower Bound is presented, along with its application to a number of important problems. We then examine an alternative approach, delta-analysis, which had been proposed previously, apply it to several new problems and show how it can be extended. For the specific problem of updating the transitive closure of an acyclic digraph, we present the first known incremental algorithm that is efficient in the delta-analysis sense. Finally, we criti...

This thesis is concerned with graph theory-based algorithms to handle the genetic map assembly problem. These algorithms are designed to build the genetic maps using only graph theoretical properties so as to better understand how much information can be obtained from the graph structure. In particular, several algorithms are developed using ideas from interval graphs and the asteroidal triple-free graphs. The core of the problem is dealing with the noise present in the data. This noise can be split into two different categories: false negatives (edges removed from a graph), and false positives (edges added to a graph). For the case of noise introduced as a result of false negatives, lexicographic breadth-first search is used to produce useful orderings even under heavy noise conditions. Three different algorithms are developed for dealing with false positives. The algorithms can detect the effects of false positives, but none are effective in removing this type of noise. ii Acknowle...