1,220 research outputs found
Computational Geometry Column 42
A compendium of thirty previously published open problems in computational
geometry is presented.Comment: 7 pages; 72 reference
Maximizing Maximal Angles for Plane Straight-Line Graphs
Let be a plane straight-line graph on a finite point set
in general position. The incident angles of a vertex
of are the angles between any two edges of that appear consecutively in
the circular order of the edges incident to .
A plane straight-line graph is called -open if each vertex has an
incident angle of size at least . In this paper we study the following
type of question: What is the maximum angle such that for any finite set
of points in general position we can find a graph from a certain
class of graphs on that is -open? In particular, we consider the
classes of triangulations, spanning trees, and paths on and give tight
bounds in most cases.Comment: 15 pages, 14 figures. Apart of minor corrections, some proofs that
were omitted in the previous version are now include
A Message Passing Algorithm for the Minimum Cost Multicut Problem
We propose a dual decomposition and linear program relaxation of the NP -hard
minimum cost multicut problem. Unlike other polyhedral relaxations of the
multicut polytope, it is amenable to efficient optimization by message passing.
Like other polyhedral elaxations, it can be tightened efficiently by cutting
planes. We define an algorithm that alternates between message passing and
efficient separation of cycle- and odd-wheel inequalities. This algorithm is
more efficient than state-of-the-art algorithms based on linear programming,
including algorithms written in the framework of leading commercial software,
as we show in experiments with large instances of the problem from applications
in computer vision, biomedical image analysis and data mining.Comment: Added acknowledgment
Subclass Discriminant Analysis of Morphological and Textural Features for HEp-2 Staining Pattern Classification
Classifying HEp-2 fluorescence patterns in Indirect Immunofluorescence (IIF) HEp-2 cell imaging is important for the differential diagnosis of autoimmune diseases. The current technique, based on human visual inspection, is time-consuming, subjective and dependent on the operator's experience. Automating this process may be a solution to these limitations, making IIF faster and more reliable. This work proposes a classification approach based on Subclass Discriminant Analysis (SDA), a dimensionality reduction technique that provides an effective representation of the cells in the feature space, suitably coping with the high within-class variance typical of HEp-2 cell patterns. In order to generate an adequate characterization of the fluorescence patterns, we investigate the individual and combined contributions of several image attributes, showing that the integration of morphological, global and local textural features is the most suited for this purpose. The proposed approach provides an accuracy of the staining pattern classification of about 90%
Heuristics for optimum binary search trees and minimum weight triangulation problems
AbstractIn this paper we establish new bounds on the problem of constructing optimum binary search trees with zero-key access probabilities (with applications e.g. to point location problems). We present a linear-time heuristic for constructing such search trees so that their cost is within a factor of 1 + Δ from the optimum cost, where Δ is an arbitrary small positive constant. Furthermore, by using an interesting amortization argument, we give a simple and practical, linear-time implementation of a known greedy heuristics for such trees.The above results are obtained in a more general setting, namely in the context of minimum length triangulations of so-called semi-circular polygons. They are carried over to binary search trees by proving a duality between optimum (m â 1)-way search trees and minimum weight partitions of infinitely-flat semi-circular polygons into m-gons. With this duality we can also obtain better heuristics for minimum length partitions of polygons by using known algorithms for optimum search trees
Happy endings for flip graphs
We show that the triangulations of a finite point set form a flip graph that
can be embedded isometrically into a hypercube, if and only if the point set
has no empty convex pentagon. Point sets of this type include convex subsets of
lattices, points on two lines, and several other infinite families. As a
consequence, flip distance in such point sets can be computed efficiently.Comment: 26 pages, 15 figures. Revised and expanded for journal publicatio
The Traveling Salesman Problem
This paper presents a self-contained introduction into algorithmic and computational aspects of the traveling salesman problem and of related problems, along with their theoretical prerequisites as seen from the point of view of an operations researcher who wants to solve practical problem instances. Extensive computational results are reported on most of the algorithms described. Optimal solutions are reported for instances with sizes up to several thousand nodes as well as heuristic solutions with provably very high quality for larger instances
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