133008994
A Randomized Algorithm for Online Unit Clustering
In this paper, we consider the online version of the following problem: partition a set of input points into subsets, each enclosable by a unit ball, so as to minimize the number of subsets used. In the one-dimensional case, we show that surprisingly the naive upper bound of 2 on the competitive ratio can be beaten: we present a new randomized 15/8-competitive online algorithm. We also provide some lower bounds and an extension to higher dimensions.
26929194
Balanced k-colorings
Abstract While discrepancy theory is normally only studied in the context of 2-colorings, we explore the problem of k -coloring, for k ⩾2, a set of vertices to minimize imbalance among a family of subsets of vertices. The imbalance is the maximum, over all subsets in the family, of the largest difference between the size of any two color classes in that subset. The discrepancy is the minimum possible imbalance. We show that the discrepancy is always at most 4 d −3, where d (the “dimension”) is the maximum number of subsets containing a common vertex. For 2-colorings, the bound on the discrepancy is atmost max{2 d −3,2}. Finally, we prove that several restricted versions of computing the discrepancy are NP-complete.
10486597
A fully dynamic algorithm for planar
We show how to maintain the width of a set of $n$ planar points subjec t to insertions and deletions of points in $O(\sqrt{n}\log^3n)$ amortized time per update. Previously, no fully dynamic algorithm with a guaranteed sublinear time bound was known.
10262363
Approximate nearest neighbor queries revisited
This paper proposes new methods to answer approximate nearest neighbor queries on a set of n points in d -dimensional Euclidean space. For any fixed constant d , a data structure with O(\(\varepsilon\) (1-d)/2 n log n) preprocessing time and O(\(\varepsilon\) (1-d)/2 log n) query time achieves an approximation factor 1+\(\varepsilon\) for any given 0 < \(\varepsilon\) < 1; a variant reduces the \(\varepsilon\) -dependence by a factor of \(\varepsilon\) -1/2 . For any arbitrary d , a data structure with O(d 2 n log n) preprocessing time and O(d 2 log n) query time achieves an approximation factor O(d 3/2 ) . Applications to various proximity problems are discussed.
5292943
On enumerating and selecting distances
Given an n-point set, the problems of knumerating the /z closest pairs and selecting the L-th smallest distance ace revisited. l?oc the enumeration problem, we give 8implec randomized and deterministic algorithms with O(n log n-t/~) running time in any fixed-dimensional Euclidean space. l?oc the selection problem, we describe an approach to obtaining b-sensitive time bounds. We also point out output-sensitive results for halfspace range counting that ace of use in more general distance selection problems. None of our algorithms requires pacametric search.
43482019
Three problems about simple polygons
We give three related algorithmic results concerning a simple polygon P: 1. Improving a series of previous work, we show how to find a largest pair of disjoint congruent disks inside P in linear expected time. 2. As a subroutine for the above result, we show how to find the convex hull of any given subset of the vertices of P in linear worst-case time. 3. More generally, we show how to compute a triangulation of any given subset of the vertices or edges of P in almost linear time.
20186109
Balanced information inequalities
In this correspondence, we are interested in linear information inequalities, both discrete and continuous ones. We show that every discrete information inequality is associated with a "balanced" information inequality and a set of "residual weights." To prove the inequality, it is necessary and sufficient to prove that its "balanced" version is valid and all its residual weights are nonnegative. For a continuous information inequality, we prove that it is valid if and only if its discrete counterpart is balanced and valid.
15993467
On a relation between information inequalities and group theory
We establish a one-to-one correspondence between information inequalities and group inequalities. The major implication of our result is that we can prove information inequalities by proving the corresponding group inequalities, and vice versa. By giving a group-theoretic proof for all Shannon-type inequalities, we suggest that new inequalities could be discovered by making use of the rich set of tools in group theory. On the other hand, via a non-Shannon-type information inequality discovered by Zhang and Yeung (1997), we obtain a new inequality in group theory whose meaning is yet to be understood.
15943063
Enterprise Systems Success: A Measurement Model
This paper presents a validated measurement model and instrument for assessing enterprise systems success from multiple perspectives. The final validated study model employs 27 measures of the four dimensions: information quality, system quality, individual impact, and organizational impact. The model is empirically tested with survey data gathered from 27 public sector organizations that implemented SAP R/3 in the late 1990s. The study consists of an exploratory inventory survey (model building) to identify the salient success dimensions and measures, followed by a confirmatory weights survey, for testing model validity (model testing). Test results demonstrate the discriminant validity of the four dimensions, as well as their convergence on a single higher-order phenomenon: enterprise systems success (ESS). Criterion validity testing further demonstrates the additivity of the four dimensions of success, and the completeness of the resultant overarching, second-order measure of ESS.
7832316
Cosine transform based preconditioners for total variation deblurring
In PDE image restoration problems, one has to invert operators which is a sum of a blurring operator and an elliptic operator with highly varying coefficient. We present a preconditioner for such operators, which can be used with the conjugate gradient (CG) method, and compare it with Vogel and Oman's product preconditioner.
18182246
Total variation blind deconvolution
In this paper, we present a blind deconvolution algorithm based on the total variational (TV) minimization method proposed. The motivation for regularizing with the TV norm is that it is extremely effective for recovering edges of images as well as some blurring functions, e.g., motion blur and out-of-focus blur. An alternating minimization (AM)implicit iterative scheme is devised to recover the image and simultaneously identify the point spread function (psf). Numerical results indicate that the iterative scheme is quite robust, converges very fast (especially for discontinuous blur), and both the image and the psf can be recovered under the presence of high noise level. Finally, we remark that psf's without sharp edges, e.g., Gaussian blur, can also be identified through the TV approach.