Algorithms for computing sparsest shifts of polynomials in power, Chebyshev, and Pochhammer bases
We give a new class of algorithms for computing sparsest shifts of a given polynomial. Our algorithms are based on the early termination version of sparse interpolation algorithms: for a symbolic set of interpolation points, a sparsest shift must be a root of the first possible zero discrepancy that can be used as the early termination test. Through reformulating as multivariate shifts in a designated set, our algorithms can compute the sparsest shifts that simultaneously minimize the terms of a given set of polynomials. Our algorithms can also be applied to the Pochhammer and Chebyshev bases for the polynomials, and potentially to other bases as well. For a given univariate polynomial, we give a lower bound for the optimal sparsity. The efficiency of our algorithms can be further improved by imposing such a bound and pruning the highest degree terms.

title: Symbolic-numeric sparse interpolation of multivariate polynomials
abstract: We consider the problem of sparse interpolation of an approximate multivariate black-box polynomial in floating-point arithmetic. That is, both the inputs and outputs of the black-box polynomial have some error, and all numbers are represented in standard, fixed-precision, floating point arithmetic. By interpolating the black box evaluated at random primitive roots of unity, we give efficient and numerically robust solutions. We note the similarity between the exact Ben-Or/Tiwari sparse interpolation algorithm and the classical Prony's method for interpolating a sum of exponential functions, and exploit the generalized eigenvalue reformulation of Prony's method. We analyze the numerical stability of our algorithms and the sensitivity of the solutions, as well as the expected conditioning achieved through randomization. Finally, we demonstrate the effectiveness of our techniques in practice through numerical experiments and applications.

title: Spatial Queries in Wireless Broadcast Systems
abstract: Owing to the advent of wireless networking and personal digital devices, information systems in the era of mobile computing are expected to be able to handle a tremendous amount of traffic and service requests from the users. Wireless data broadcast, thanks to its high scalability, is particularly suitable for meeting such a challenge. Indexing techniques have been developed for wireless data broadcast systems in order to conserve the scarce power resources in mobile clients. However, most of the previous studies do not take into account the impact of location information of users. In this paper, we address the issues of supporting spatial queries (including window queries and kNN queries) of location-dependent information via wireless data broadcast. A linear index structure based on the Hilbert curve and corresponding search algorithms are proposed to answer spatial queries on air. Experiments are conducted to evaluate the performance of the proposed indexing technique. Results show that the proposed index and its enhancement outperform existing algorithms significantly.

title: Approaching the Skyline in Z Order
abstract: Given a set of multidimensional data points, skyline query retrieves a set of data points that are not dominated by any other points. This query is useful for multi-preference analysis and decision making. By analyzing the skyline query, we observe a close connection between Z-order curve and skyline processing strategies and propose to use a new index structure called ZBtree, to index and store data points based on Z-order curve. We develop a suite of novel and efficient skyline algorithms, which scale very well to data dimensionality and cardinality, including (1) ZSearch, which processes skyline queries and supports progressive result delivery; (2) ZUpdate, which facilitates incremental skyline result maintenance; and (3) k-ZSearch, which answers k-dominant skyline query (a skyline variant that retrieves a representative subset of skyline results). Extensive experiments have been conducted to evaluate our proposed algorithms and compare them against the best available algorithms designed for skyline search, skyline result update, and k-dominant skyline search, respectively. The result shows that our algorithms, developed coherently based on the same ideas and concepts, soundly outperforms the state-of-the-art skyline algorithms in their specialized domains.

title: Distributed caching of multi-dimensional data in mobile environments
abstract: Caching has been an important technique for saving network traffic and reducing response time, especially in mobile environments where bandwidth is often a scarce resource. In this paper, we propose a novel approach for caching multidimensional data in a cluster of mobile devices. In particular, we focus on the most common types of multi-dimensional queries, namely range and k-nearest neighbor queries, by computing a cacheable region for every query, caching the result at the client, and indexing it in an R*-tree at the cluster gateway. Subsequent queries are first issued to the R*-tree and only remainder queries or queries that cannot be guaranteed exact answers are sent to the remote data server. To the best of our knowledge, our work is the first to study caching results from complex multi-dimensional queries (e.g., kNN query) and propose to build an R*-tree on previously fetched query results in a cluster of mobile devices. Rigorous experiments show that our approach significantly reduces network traffic and response time.

title: Channel allocation methods for data dissemination in mobile computing environments
abstract: We discuss several channel allocation methods for data dissemination in mobile computing systems. We suggest that the broadcast and on-demand channels have different access performance under different system parameters and that a mobile cell should use a combination of both to obtain optimal access time for a given workload and system parameters. We study the data access efficiency of three channel configurations: all channels are used as on-demand channels (exclusive on-demand); all channels are used for broadcast (exclusive broadcast); and some channels are on-demand channels and some are broadcast channels (hybrid). Simulations on obtaining the optimal channel allocation for lightly-loaded, medium-loaded, and heavy-loaded conditions is conducted and the result shows that an optimal channel allocation significantly improves the system performance.

title: Supporting XML Security Models Using Relational Databases: A Vision
abstract: As the secure distribution and sharing of information over the World Wide Web becomes increasingly important, the needs for flexible and efficient support of access control systems naturally arise. Since the eXtensible Markup Language (XML) is emerging as the format of the Internet era for storing and exchanging information, there have been, recently, many proposals to extend the XML model to incorporate security aspects. To the lesser or greater extent, however, such proposals neglect the fact that the data for XML documents will most likely reside in relational databases, and consequently do not utilize various security models proposed for and implemented in relational databases.