13475547
Towards estimating the number of distinct value combinations for a set of attributes
Accurately and efficiently estimating the number of distinct values for some attribute(s) or sets of attributes in a data set is of critical importance to many database operations, such as query optimization and approximation query answering. Previous work has focused on the estimation of the number of distinct values for a single attribute and most existing work adopts a data sampling approach. This paper addresses the equally important issue of estimating the number of distinct value combinations for multiple attributes which we call COLSCARD (for COLumn Set CARDinality). It also takes a different approach that uses existing statistical information (e.g., histograms) available on the individual attributes to assist estimation. We start with cases where exact frequency information on individual attributes is available, and present a pair of lower and upper bounds on COLSCARD that are consistent with the available information, as well as an estimator of COLSCARD based on probability. We then proceed to study the case where only partial information (in the form of histograms) is available on individual attributes, and show how the proposed estimator can be adapted to this case. We consider two types of widely used histograms and show how they can be constructed in order to obtain optimal approximation. An experimental evaluation of the proposed estimation method on synthetic as well as two real data sets is provided.
1886676
Monitoring k-nearest neighbor queries over moving objects
Many location-based applications require constant monitoring of k-nearest neighbor (k-NN) queries over moving objects within a geographic area. Existing approaches to this problem have focused on predictive queries, and relied on the assumption that the trajectories of the objects are fully predictable at query processing time. We relax this assumption, and propose two efficient and scalable algorithms using grid indices. One is based on indexing objects, and the other on queries. For each approach, a cost model is developed, and a detailed analysis along with the respective applicability is presented. The object-indexing approach is further extended to multi-levels to handle skewed data. We show by experiments that our grid-based algorithms significantly outperform R-tree-based solutions. Extensive experiments are also carried out to study the properties and evaluate the performance of the proposed approaches under a variety of settings.
17384388
Infinite paths in planar graphs IV, dividing cycles
Nash-Williams conjectured that a 4-connected infinite planar graph contains a spanning 2-way infinite path if, and only if, the deletion of any finite set of vertices results in at most two infinite components. In this paper, we prove the Nash-Williams conjecture for graphs with no dividing cycles and for graphs with infinitely many vertex disjoint dividing cycles. A cycle in an infinite plane graph is called dividing if both regions of the plane bounded by this cycle contain infinitely many vertices of the graph. ∗Partially supported by NSF grant DMS-0245530, NSA grant MDA-904-03-1-0052, and RGC grant HKU7056/04P
18410450
Covering planar graphs with forests
We study the problem of covering graphs with trees and a graph of bounded maximum degree. By a classical theorem of Nash-Williams, every planar graph can be covered by three trees. We show that every planar graph can be covered by two trees and a forest, and the maximum degree of the forest is at most 8. Stronger results are obtained for some special classes of planar graphs.
8099466
Nonseparating Planar Chains in 4-Connected Graphs
In this paper, we describe an O(|V(G)||E(G)|) algorithm for finding a nonseparating planar chain in a 4-connected graph G, which will be used to decompose an arbitrary 4-connected graph into planar chains. This work was motivated by the study of a multitree approach to reliability in distributed networks, as well as the study of nonseparating induced paths in highly connected graphs.
2329429
Embodied data objects: tangible interfaces to information appliances
This paper describes the idea of embodied data objects. Using this concept, everyday objects can be used to represent bits and bytes of active information. These data objects can be used to interact with information-appliance-like devices that provide specific services as dictated by the context of interaction. The inherent affordances of physical artifacts are leveraged to make the interaction with these service-oriented devices intuitive and natural. We describe the idea of embodied data objects, followed by the design and implementation of two such service-oriented devices: a presentation projector and a printer.
7732726
Towards a syllabus repository for computer science courses
A syllabus defines the contents of a course, as well as other information such as resources and assignments. In this paper, we report on our work towards creating a syllabus repository of Computer Science courses across universities in the USA. We present some statistics from our initial collection of 8000+ syllabi. We show a syllabus creator that is integrated with Moodle [5] moodle_2006_moodle, an open-source course management system, which allows for the creation of a syllabus for a particular course. Among other information, it includes knowledge units from the Computing Curricula 2001 body of knowledge. The goal of the syllabus repository is to provide added value to the Computer Science Education community, and we present some such offerings. We conclude by presenting our future plans for the syllabus repository. These include using automated techniques to collect and classify syllabi, providing recommendations to instructors when creating a syllabus, and allowing the community to share their syllabi automatically. The syllabus collection will be part of the Computing and Information Technology Interactive Digital Educational Library (CITIDEL), a collection of the National Science Digital Library (NSDL).