18966889
On Levels in Arrangements of Curves 


Abstract. Analyzing the worst-case complexity of the k -level in a planar arrangement of n curves is a fundamental problem in combinatorial geometry. We give the first subquadratic upper bound (roughly O( nk^ 1-1/(9· 2s-3) ) ) for curves that are graphs of polynomial functions of an arbitrary fixed degree s . Previously, nontrivial results were known only for the case s=1 and s=2 . We also improve the earlier bound for pseudo-parabolas (curves that pairwise intersect at most twice) to O( nk7/9 log2/3k) . The proofs are simple and rely on a theorem of Tamaki and Tokuyama on cutting pseudo-parabolas into pseudo-segments, as well as a new observation for cutting pseudo-segments into pieces that can be extended to pseudo-lines. We mention applications to parametric and kinetic minimum spanning trees.

15654193
A dynamic data structure for 3-d convex hulls and 2-d nearest neighbor queries
We present a fully dynamic randomized data structure that can answer queries about the convex hull of a set of <i>n</i> points in three dimensions, where insertions take <i>O</i>(log<sup>3</sup> <i>n</i>) expected amortized time, deletions take <i>O</i>(log<sup>6</sup> <i>n</i>) expected amortized time, and extreme-point queries take <i>O</i>(log<sup>2</sup> <i>n</i>) worst-case time. This is the first method that guarantees polylogarithmic update and query cost for arbitrary sequences of insertions and deletions, and improves the previous <i>O</i>(<i>n</i><sup>ε</sup>)-time method by Agarwal and Matoušek a decade ago. As a consequence, we obtain similar results for nearest neighbor queries in two dimensions and improved results for numerous fundamental geometric problems (such as levels in three dimensions and dynamic Euclidean minimum spanning trees in the plane).
18265362
Approximation Algorithms for Maximum Cliques in 3D Unit-Disk Graphs
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.
15785799
Semi-online maintenance of geometric optima and measures
We give the first nontrivial worst-case results for dynamic versions of various basic geometric optimization and measure problems under the semi-online model, where during the insertion of an object we are told when the object is to be deleted. Problems that we can solve with sublinear update time include the Hausdorff distance of two point sets, discrete 1-center, largest empty circle, convex hull volume in three dimensions, volume of the union of axis-parallel cubes, and minimum enclosing rectangle. The decision versions of the Hausdorff distance and discrete 1-center problems can be solved fully dynamically. Some applications are mentioned.
15997426
On levels in arrangements of curves
Analyzing the worst-case complexity of the k-level in a planar arrangement of n curves is a fundamental problem in combinatorial geometry. We give the first subquadratic upper bound (roughly O(nk/sup 1-2/3/*)) for curves that are graphs of polynomial functions of an arbitrary fixed degree s. Previously, nontrivial results were known only for the case s=1 and s=2. We also improve the earlier bound for pseudo-parabolas (curves that pairwise intersect at most twice) to O(nk/sup 7/9/log/sup 2/3/ k). The proofs are simple and rely on a theorem of Tamaki and Tokuyama on cutting pseudo-parabolas into pseudo-segments, as well as a new observation for cutting pseudo-segments into pieces that can be extended to pseudo-lines. We mention applications to parametric and kinetic minimum spanning trees.
15821497
An Examination Of Barriers To Benefits-realisation From Enterprise Systems In The Public Service
Examination of barriers to benefits-realisation from Enterprise Systems (ES) has potential to provide an innovative perspective on strategic management of large-scale packaged software, and on the extended virtual enterprise explicitly or implicitly deployed across the ES life-cycle. Private sector experience has revealed distinctive conditions applying to ES that create barriers to benefit-realisation. For public service organisations, ES have the potential to enable the provision of end-to-end integrated services, consistent with the demands of public accountability, but are encumbered by a poor track record in large systems implementation and associated process-reengineering. This research analyses the Australian Public Service ES experience, with the aim of dismantling barriers to public sector exploitation of ES. Early results reflect conventional perceptions of implementation issues, but application of the distinctive Dephi-based methodology designed for this study is expected to yield a basis for shared action on the part of government administration, vendors and consultants.
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.
45840953
Dynamic Cluster Formation Using Level Set Methods
Density-based clustering has the advantages for (i) allowing arbitrary shape of cluster and (ii) not requiring the number of clusters as input. However, when clusters touch each other, both the cluster centers and cluster boundaries (as the peaks and valleys of the density distribution) become fuzzy and difficult to determine. In higher dimension, the boundaries become wiggly and over-fitting often occurs. We introduce the notion of cluster intensity function (CIF) which captures the important characteristics of clusters. When clusters are well-separated, CIFs are similar to density functions. But as clusters touch each other, CIFs still clearly reveal cluster centers, cluster boundaries, and, degree of membership of each data point to the cluster that it belongs. Clustering through bump hunting and valley seeking based on these functions are more robust than that based on kernel density functions which are often oscillatory or over-smoothed. These problems of kernel density estimation are resolved using Level Set Methods and related techniques. Comparisons with two existing density-based methods, valley seeking and DBSCAN, are presented to illustrate the advantages of our approach.
32811638
Timing of Software Replacement
Analogous to the replacement of an old machine, such as a car, replacing an aged softwitre may contain its escalating cost of maintenance. Prior research has assumed that increasing maintenance cost is due to the deterioration of the system maintainability. However, cost of maintenance depends also on the number of incoming maintenance requests. While software maintainability is determined by its complexity and development environment, number of maintenance requests is affected by the business environment. This distinction is significant in analyzing economic tradeoffs in software maintenance because replacement improves system maintainability but will not affect the number of maintenance requests. Unlike replacement of hardware, rewriting software takes an extended length of time, Thus, the old software must still be maintained before the new software is ready. We develop an economic model that considers the number of maintenance requests and the rewriting period explicitly. The model is an extension of Gode, Barua, and Mukhopadhyay (1990), which assumes a constant number of maintenance requests and instantaneous replacement. Our model allows us to draw some additional policy implications about software inaintenatice aild replacement. For instance, we show that in certain situations delaying a system replacement can be inore cost effective when the user environment changes more rapidly, contrary to our intuition. Moreover, it is shown that rewriting should begin earlier when the instantane(,us replacement assumption is relaxed.
2980605
A Simplified Approach to the Order Conditions of Integration Methods
We present an approach to the numerical integration of ordinary differential equations based on the algebraic theory of Butcher (Math. Comp. 26, 79–106, 1972) and the -series theory of Hairer and Wanner (Computing 13, 1–15, 1974). We clarify the differences of these two approaches by equating the elementary weight functions and showing the differences of the composition rules. By interpreting the elementary weight function as a mapping from input values to output values and introducing some special mappings, we are able to derive the order conditions of several types of integration methods in a straight-forward way. The simplicity of the derivation is illustrated by linear multistep methods that use the second derivative as an input value, Runge-Kutta type methods that use the second as well as first derivatives, and general two-step Runge-Kutta methods. We derive new high stage-order methods in each example. In particular, we found a symmetric and stiffly-accurate method of order eight in the second example.