2028079
Strong uniqueness of the restricted Chebyshev center with respect to an RS-set in a Banach space
Let G be a strict RS-set (resp. an RS-set) in X and let F be a bounded (resp. totally bounded) subset of X satisfying rG (F) < rx (F), where rG (F) is the restricted Chebyshev radius of F with respect to G. It is shown that the restricted Chebyshev center of F with respect to G is strongly unique in the case when X is a real Banach space, and that, under some additional convexity assumptions, the restricted Chebyshev center of F with respect to G is strongly unique of order α ≥ 2 in the case when X is a complex Banach space.
10976471
Derivatives of Generalized Distance Functions and Existence of Generalized Nearest Points
The relationship between directional derivatives of generalized distance functions and the existence of generalized nearest points in Banach spaces is investigated. Let G be any nonempty closed subset in a compact locally uniformly convex Banach space. It is proved that if the one-sided directional derivative of the generalized distance function associated to G at x equals to 1 or -1, then the generalized nearest points to x from G exist. We also give a partial answer (Theorem 3.5) to the open problem put forward by S. Fitzpatrick (1989, Bull. Austral. Math. Soc.39, 233-238).
139092767
An Improved Prefix Labeling Scheme: A Binary String Approach for Dynamic Ordered XML
A number of labeling schemes have been designed to facilitate the query of XML, based on which the ancestor-descendant relationship between any two nodes can be determined quickly. Another important feature of XML is that the elements in XML are intrinsically ordered. However the label update cost is high based on the present labeling schemes. They have to re-label the existing nodes or re-calculate some values when inserting an order-sensitive element. Thus it is important to design a scheme that supports order-sensitive queries, yet it has low label update cost. In this paper, we design a binary string prefix scheme which supports order-sensitive update without any re-labeling or re-calculation. Theoretical analysis and experimental results also show that this scheme is compact compared to the existing dynamic labeling schemes, and it provides efficient support to both ordered and un-ordered queries.
2225482
Computing complete answers to queries in the presence of limited access patterns
Abstract.In data applications such as information integration, there can be limited access patterns to relations, i.e., binding patterns require values to be specified for certain attributes in order to retrieve data from a relation. As a consequence, we cannot retrieve all tuples from these relations. In this article we study the problem of computing the complete answer to a query, i.e., the answer that could be computed if all the tuples could be retrieved. A query is stable if for any instance of the relations in the query, its complete answer can be computed using the access patterns permitted by the relations. We study the problem of testing stability of various classes of queries, including conjunctive queries, unions of conjunctive queries, and conjunctive queries with arithmetic comparisons. We give algorithms and complexity results for these classes of queries. We show that stability of datalog programs is undecidable, and give a sufficient condition for stability of datalog queries. Finally, we study data-dependent computability of the complete answer to a nonstable query, and propose a decision tree for guiding the process to compute the complete answer.
4532231
On the Fixed Interval Due-date Scheduling Problem
Abstract We consider the nonpreemptive single machine scheduling problem with multiple due-dates (delivery dates), where the time between two consecutive due-dates is a constant. Given a set of jobs, we are interested in scheduling the jobs such that the sum of the total due-date cost and the total earliness cost is minimized with the constraint that each job must be finished at or before its due-date. We show that this problem is strongly NP-hard in general. We then analyze the problem where the number of due-dates is bounded by a given constant. We describe a pseudo-polynomial dynamic programming algorithm for this restricted problem. A heuristic is also provided and worst-case analysis is performed. An efficient algorithm is developed to solve the special case where all the job processing times are identical.
6907477
Achieving Communication Efficiency through Push-Pull Partitioning of Semantic Spaces to Disseminate Dynamic Information
Many database applications that need to disseminate dynamic information from a server to various clients can suffer from heavy communication costs. Data caching at a client can help mitigate these costs, particularly when individual PUSH-PULL decisions are made for the different semantic regions in the data space. The server is responsible for notifying the client about updates in the PUSH regions. The client needs to contact the server for queries that ask for data in the PULL regions. We call the idea of partitioning the data space into PUSH-PULL regions to minimize communication cost data gerrymandering. In this paper, we present solutions to technical challenges in adopting this simple but powerful idea. We give a provably optimal-cost dynamic programming algorithm for gerrymandering on a single query attribute. We propose a family of efficient heuristics for gerrymandering on multiple query attributes. We handle the dynamic case in which the workloads of queries and updates evolve over time. We validate our methods through extensive experiments on real and synthetic data sets
22347603
Two supervised learning approaches for name disambiguation in author citations