The satissability (SAT) problem is a core problem in mathematical logic and computing theory. In practice, SAT is fundamental in solving many problems in automated reasoning, computer-aided design, computer-aided manufacturing, machine vision, database, robotics, integrated circuit design, computer architecture design, and computer network design.… (More)
A new technique, complement searching, is given for reducing the amount of searching required to solve satisfiability (constraint satisfaction) problems. Search trees for these problems often contain subtrees that have approximately the same shape. When this occurs, knowledge that the first subtree does not have a solution can be used to reduce the… (More)
The Apriori Algorithm examines baskets of items to determine which subsets of the items occur in lots of baskets. Suppose we wish to determine which items sets occur in at least k baskets. The algorithm considers item sets of size l in the order l = 1, 2, : : :. The only way this algorithm can determine that a set occurs at least k times is to count the k… (More)
This paper explores the generation of candidates, which is an important step in frequent itemset mining algorithms, from a theoretical point of view. Important notions in our probabilistic analysis are success (a candidate that is frequent), and failure (a candidate that is infrequent). For a selection of candidate-based frequent itemset mining algorithms,… (More)
Graw and Catherine Rogers for their constructive comments and criticism during the development of this manuscript.
We analyze algorithms that, under the right circumstances, permit efficient mining for frequent itemsets in data with tall peaks (large frequent itemsets). We develop a family of level-by-level peak-jumping algorithms , and study them using a simple probability model. The analysis clarifies why the jumping idea sometimes works well, and which properties the… (More)
Acknowledgments This page is in the very first few pages, but it is the last page I wrote, because I know this page is used to thank people who have helped me and even a few minutes ago, I was getting help from engineers at the NSLS (National Synchrotron Light Source), BNL. this dissertation would simply not exist. I treasure the enjoyable experience of… (More)
Since the introduction of the Frequent Itemset Mining (FIM) problem, several different algorithms for solving it were proposed and experimentally analyzed. Our work focusses on the theoretical analysis of FIM. The aim is to give a detailed probabilistic study of the performance of FIM algorithms for different data distributions. It is joint work with Dirk… (More)