Monotone term decision lists
We introduce a new representation class of Boolean functions ? monotone term decision lists ? which combines compact representation size with tractability of essential operations. We present many properties of the class which make it an attractive alternative to traditional universal representation classes such as DNF formulas or decision trees. We study the learnability of monotone term decision lists in the exact model of equivalence and membership queries. We show that, for any constant k?0, k-term monotone decision lists are exactly and properly learnable with nO(k) membership queries in nO(k3) time. We also show that n?(k) membership queries are necessary for exact learning. In contrast, both k-term monotone decision lists (k?2) and general monotone term decision lists are not learnable with equivalence queries alone. We also show that a subclass of monotone term decision lists (disj-MDL) is learnable with equivalence and membership queries, while neither type of query alone suffices.

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: How many queries are needed to learn?
abstract: We investigate the query complexity of exact learning in the membership and (proper) equivalence query model. We give a complete characterization of concept classes that are learnable with a polynomial number of polynomial sized queries in this model. We give applications of this characterization, including results on learning a natural subclass of DNF formulas, and on learning with membership queries alone. Query complexity has previously been used to prove lower bounds on the time complexity of exact learning. We show a new relationship between query complexity and time complexity in exact learning: If any “honest” class is exactly and properly learnable with polynomial query complexity, but not learnable in polynomial time, then P = NP. In particular, we show that an honest class is exactly polynomial-query learnable if and only if it is learnable using an oracle for Γp4.

title: Learning Monotone Term Decision Lists
abstract: We study the learnability of monotone term decision lists in the exact model of equivalence and membership queries. We show that, for any constant k≥0, k-term monotone decision lists are exactly and properly learnable with nO(k) membership queries in O(nk3) time. We also show nΩ(k) membership queries are necessary for exact learning. In contrast, both k-term monotone decision lists (k≥2) and general monotone decision lists are not learnable with equivalence queries alone.

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: On Single-Fault Set Diagnosability in the PMC Model
abstract: A. Somani et al, (1987) introduced the single-fault set diagnosability measure and gave an O(n/sup 3.5/) algorithm for determining it in the PMC model. The authors present a new algorithm for the same problem with a time complexity of only O(n/sup 2.5/).

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: 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.

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.