Improved Diagnosability Algorithms
The concepts of the PMC and BGM self-diagnosing system models of F. P. Preparata et al. (1967) and F. Barsi et al. (1976), respectively, including the notions of fault sets, consistency, and diagnosability number, are reviewed. Two one-step diagnosability algorithms are applied, one to the PMC model and the other to the BGM model. In both models, one-step diagnosability refers to a system's ability to determine all the faulty units from single collection of test results. Using the letters n, m, and tau to denote the number of units, the number of tests, and the diagnosability number, respectively, it is shown that in the BGM model the algorithm has a complexity of O(n tau /sup 2//log tau ), and, in the PMC model, the algorithm has a complexity of O(n tau /sup 2.5/).

title: On the Limits of Proper Learnability of Subclasses of DNF Formulas
abstract: Bshouty, Goldman, Hancock and Matar have shown that up to log n -term DNF formulas can be properly learned in the exact model with equivalence and membership queries. Given standard complexity-theoretical assumptions, we show that this positive result for proper learning cannot be significantly improved in the exact model or the PAC model extended to allow membership queries. Our negative results are derived from two general techniques for proving such results in the exact model and the extended PAC model. As a further application of these techniques, we consider read-thrice DNF formulas. Here we improve on Aizenstein, Hellerstein, and Pitt's negative result for proper learning in the exact model in two ways. First, we show that their assumption of NP ≠ co-NP can be replaced with the weaker assumption of P ≠ NP. Second, we show that read-thrice DNF formulas are not properly learnable in the extended PAC model, assuming RP ≠ NP.

title: Learning switch configurations

title: Bounded degree graph inference from walks
abstract: Aslam and Rivest considered the problem of inferring the smallest edge-colored graph of degree bound k consistent with the sequence of colors seen in a walk of the graph. Using Church-Rosser properties of certain sets of rewrite rules, they gave a polynomial time algorithm for the case of k = 2. The straightforward implementation of their ideas results in an O(n^5) algorithm, where n is the length of the walk. In this paper, we develop their ideas further and give an O(n log n) algorithm for the same problem. We also show that if the degree bound k is greater than two, then the decision version of the problem is NP-complete, thus settling a conjecture of Aslam and Rivest.

title: Recognition Algorithms for Orders of Small Width and Graphs of Small Dilworth Number
abstract: Partially ordered sets of small width and graphs of small Dilworth number have many interesting properties and have been well studied. Here we show that recognition of such orders and graphs can be done more efficiently than by using the well-known algorithms based on bipartite matching and matrix multiplication. In particular, we show that deciding deciding if an order has width k can be done in O(kn2) time and whether a graph has Dilworth number k can be done in O(k2n2) time.For very small k we have even better results. We show that orders of width at most 3 can be recognized in O(n) time and of width at most 4 in O(nlog n).

title: Read-Twice DNF Formulas are Properly Learnable
abstract: We show that read-twice DNF formulas-Boolean formulas in disjunctive normal form in which each variable appears at most twice-are exactly and properly learnable in polynomial time. Our algorithm uses membership queries and proper equivalence queries and is based on a simple, new characterization of minimal read-twice DNF formulas. The algorithm improves on earlier results of Hancock and Aizenstein and Pitt which showed that read-twice DNF formulas are learnable using more powerful equivalence queries, i.e., where the hypotheses could be arbitrary DNF formulas. We also improve on the time-complexity of these earlier algorithms. Other results which may be of independent interest outside of learning follow directly from this paper. Specifically, we show that read-twice DNF formulas can be tested for equivalence in polynomial time and that the smallest read-twice formula equivalent to a given one can be found in polynomial time.

title: Visualizing association mining results through hierarchical clusters
abstract: We propose a new methodology for visualizing association mining results. Inter-item distances are computed from combinations of itemset supports. The new distances retain a simple pairwise structure, and are consistent with important frequently occurring itemsets. Thus standard tools of visualization, e.g. hierarchical clustering dendrograms can still be applied, while the distance information upon which they are based is richer. Our approach is applicable to general association mining applications, as well as applications involving information spaces modeled by directed graphs, e.g. the Web. In the context of collections of hypertext documents, the inter-document distances capture the information inherent in a collection's link structure, a form of link mining. We demonstrate our methodology with document sets extracted from the Science Citation Index, applying a metric that measures consistency between clusters and frequent itemsets.

title: A Theoretical Framework for Association Mining Based on the Boolean Retrieval Model
abstract: Data mining has been defined as the non-trivial extraction of implicit, previously unknown and potentially useful information from data. Association mining is one of the important sub-fields in data mining, where rules that imply certain association relationships among a set of items in a transaction database are discovered. 
 
The efforts of most researchers focus on discovering rules in the form of implications between itemsets, which are subsets of items that have adequate supports. Having itemsets as both antecedent and precedent parts was motivated by the original application pertaining to market baskets and they represent only the simplest form of predicates. This simplicity is also due in part to the lack of a theoretical framework that includes more expressive predicates. 
 
The framework we develop derives from the observation that information retrieval and association mining are two complementary processes on the same data records or transactions. In information retrieval, given a query, we need to find the subset of records that matches the query. In contrast, in data mining, we need to find the queries (rules) having adequate number of records that support them. 
 
In this paper we introduce the theory of association mining that is based on a model of retrieval known as the Boolean Retrieval Model. The potential implications of the proposed theory are presented.

title: Concept Based Retrieval Using Generalized Retrieval Functions
abstract: One of the essential goals in information retrieval is to bridge the gap between the way users would prefer to specify their information needs and the way queries are required to be expressed. Rule Based Information Retrieval by Computer (RUBRIC) is one of the approaches proposed to achieve this goal. This approach involves the use of production rules to capture user-query concepts (or topics). In RUBRIC, a set of related production rules is represented as an AND/OR tree, or alternatively by a disjunction of Minimal Term Sets (MTSs). The retrieval output is determined by the evaluation of the weighted Boolean expressions of the AND/OR tree, and processing efficiency can be enhanced by employing MTSs. However, since the weighted Boolean expression ignores the term-term association unless it is explicitly represented in the tree, the terminological gap between users' queries and their information needs may still remain. To solve this problem, we adopt the generalized vector space model (GVSM) and the p-norm based extended Boolean model. Experiments are performed for two variations of the RUBRIC model, extended with GVSM, as well as for the integrated use of RUBRIC with the p-norm based extended Boolean model. The results are compared to the original RUBRIC model based on recall-precision.

title: Dynamic Data Mining
abstract: Business information received from advanced data analysis and data mining is a critical success factor for companies wishing to maximize competitive advantage. The use of traditional tools and techniques to discover knowledge is ruthless and does not give the right information at the right time. Data mining should provide tactical insights to support the strategic directions. In this paper, we introduce a dynamic approach that uses knowledge discovered in previous episodes. The proposed approach is shown to be effective for solving problems related to the efficiency of handling database updates, accuracy of data mining results, gaining more knowledge and interpretation of the results, and performance. Our results do not depend on the approach used to generate itemsets. In our analysis, we have used an Apriori-like approach as a local procedure to generate large itemsets. We prove that the Dynamic Data Mining algorithm is correct and complete.

title: The Item-Set Tree: A Data Structure for Data Mining
abstract: Enhancements in data capturing technology have lead to exponential growth in amounts of data being stored in information systems. This growth in turn has motivated researchers to seek new techniques for extraction of knowledge implicit or hidden in the data. In this paper, we motivate the need for an incremental data mining approach based on data structure called the item-set tree. The motivated approach is shown to be effective for solving problems related to efficiency of handling data updates, accuracy of data mining results, processing input transactions, and answering user queries. We present efficient algorithms to insert transactions into the item-set tree and to count frequencies of itemsets for queries about strength of association among items. We prove that the expected complexity of inserting a transaction is ≅ O(1), and that of frequency counting is O(n), where n is the cardinality of the domain of items.