17566608
Porosity of mutually nearest and mutually furthest points in Banach spaces
Let X be a real strictly convex and Kadec Banach space and G a nonempty closed relatively boundedly weakly compact subset of X. Let B(X) (resp. K(X)) be the family of nonempty bounded closed (resp. compact) subsets of X endowed with the Hausdorff distance and let BG(X) denote the closure of the set {A ∈ B(X) : A ∩ G = φ} and KG(X) = BG(X)∩K(X). We introduce the admissible family A of B(X) and prove that EAo(G) (resp. EoA(G)), the set of all subsets F ∈ A ⊆ BG(X) (resp. F ∈ A ⊆ BG(X)) such that the minimization problem min(F, G) (resp. the maximization problem max(F, G)) is well-posed, is a dense Gδ-subset of A. Furthermore, when X is uniformly convex, we prove that A\EAo(G) and A\EoA(G) are σ-porous in A.
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).
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.
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.
206571122
On Half-Transitive Metacirculant Graphs of Prime-Power Order
In this paper, infinitely many graphs of large valency which are half-transitive (that is vertex- and edge-transitive but not arc-transitive) are constructed, and a complete classification is given of half-transitive metacirculant graphs of order a p-power and valency less than 2p, where p is a prime. In particular, it is shown that, for any odd prime p, integers n?3 and k?2 such that k divides p?1, there are exactly (pn?2?1)/2+pn?3?1 nonisomorphic connected half-transitive metacirculants of order pn and valency 2k.
3194322
Efficient record linkage in large data sets
This paper describes an efficient approach to record linkage. Given two lists of records, the record-linkage problem consists of determining all pairs that are similar to each other where the overall similarity between two records is defined based on domain-specific similarities over individual attributes constituting the record. The record-linkage problem arises naturally in the context of data cleansing that usually precedes data analysis and mining. We explore a novel approach to this problem. For each attribute of records, we first map values to a multidimensional Euclidean space that preserves domain-specific similarity. Many mapping algorithms can be applied, and we use the FastMap approach as an example. Given the merging rule that defines when two records are Similar a set of attributes are chosen along which the merge will proceed A multidimensional similarity join over the chosen attributes is used to determine similar pairs of records. Our extensive experiments using real data sets show that our solution has very good efficiency and accuracy.
11931665
Clustering for Approximate Similarity Search in High-Dimensional Spaces
We present a clustering and indexing paradigm (called Clindex) for high-dimensional search spaces. The scheme is designed for approximate similarity searches, where one would like to find many of the data points near a target point, but where one can tolerate missing a few near points. For such searches, our scheme can find near points with high recall in very few IOs and perform significantly better than other approaches. Our scheme is based on finding clusters and, then, building a simple but efficient index for them. We analyze the trade-offs involved in clustering and building such an index structure, and present extensive experimental results.
17330404
A supervised visual wrapper generator for Web-data extraction
Extracting data from Web pages using wrappers is a fundamental problem arising in a large variety of applications of vast practical interest. In this paper, we propose a novel schema-guided approach to wrapper generation. We provide a user-friendly interface that allows users to define the schema of the data to be extracted, and specifies mappings from a HTML page to the target schema. Based on the mappings, the system can automatically generate an extraction rule to extract data from the page. Our approach to wrapper generation can significantly reduce the work of human beings in this process. And the user never has to deal with the internal extraction rule, or even familiarity with the details of HTML.