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Abstract Dynamic HamSandwich Cuts of Convex Polygons in the Plane
"... We provide an efficient data structure for dynamically maintaining a hamsandwich cut of two nonoverlapping convex polygons in the plane. Given two nonoverlapping convex polygons P1 and P2 in the plane, the hamsandwich cut of P1 and P2 is a line that simultaneously bisects the area (or perimeter o ..."
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We provide an efficient data structure for dynamically maintaining a hamsandwich cut of two nonoverlapping convex polygons in the plane. Given two nonoverlapping convex polygons P1 and P2 in the plane, the hamsandwich cut of P1 and P2 is a line that simultaneously bisects the area (or perimeter
Dynamic HamSandwich Cuts in the Plane
, 2005
"... We design efficient data structures for dynamically maintaining a hamsandwich cut of two point sets in the plane subject to insertions and deletions of points in either set. A hamsandwich cut is a line that simultaneously bisects the cardinality of both point sets. For general point sets, our first ..."
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Cited by 1 (1 self)
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We design efficient data structures for dynamically maintaining a hamsandwich cut of two point sets in the plane subject to insertions and deletions of points in either set. A hamsandwich cut is a line that simultaneously bisects the cardinality of both point sets. For general point sets, our
Dynamic HamSandwich Cuts for Two Overlapping Point Sets
"... We provide an efficient data structure for dynamically maintaining a hamsandwich cut of two overlapping point sets in convex position in the plane. The hamsandwich cut of S1 and S2 is a line that simultaneously bisects the area, perimeter or vertex count of both point sets. Our algorithm supports ..."
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(c log n) time for insertions and deletions and O(log 3 n) query time. Our algorithm improves previous results [15, 1]. The static method of Stojmenović [15] and the dynamic algorithm of Abbott et al. [1] maintain a hamsandwich cut of two disjoint convex polygons in the plane. Our dynamic algorithm
Dynamic HamSandwich Cuts for Two Point Sets with Bounded ConvexHullPeeling Depth
"... We provide an efficient data structure for dynamically maintaining a hamsandwich cut of two (possibly overlapping) point sets in the plane, with a bounded number of convexhull peeling layers. The hamsandwich cut of S1 and S2 is a line that simultaneously bisects the area, perimeter or vertex coun ..."
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layers. Our algorithm considerably improves previous results [15, 1]. Stojmenović’s [15] static method finds a hamsandwich cut for two separated point sets. The dynamic algorithm of Abbott et al. [1] maintains a hamsandwich cut of two disjoint convex polygons in the plane. Our dynamic algorithm removes
HamSandwich Cuts and Other Tasks in Arrangements
"... Given a set L = {# 1 ,...,# n } of n lines in general position in the plane and subsets A and B of vertices in the arrangement A(L), the goal is to find a line that simultaneously bisects both A and B.WegiveanO(n(logn) 2 ) algorithm for this task, in the special case where A and B are the v ..."
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Cited by 1 (0 self)
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are the vertices in di#erent halfspaces, and an O(n(log n) 3 ) algorithm for nonseparated cases. These statements should be compared to an# (n log n) lower bound, and to the O(n 2 ) complexity of the known hamsandwich algorithm that is optimal for arbitrary sets of size O(n 2 ) but which does
Convex Analysis
, 1970
"... In this book we aim to present, in a unified framework, a broad spectrum of mathematical theory that has grown in connection with the study of problems of optimization, equilibrium, control, and stability of linear and nonlinear systems. The title Variational Analysis reflects this breadth. For a lo ..."
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Cited by 5350 (67 self)
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In this book we aim to present, in a unified framework, a broad spectrum of mathematical theory that has grown in connection with the study of problems of optimization, equilibrium, control, and stability of linear and nonlinear systems. The title Variational Analysis reflects this breadth. For a long time, ‘variational ’ problems have been identified mostly with the ‘calculus of variations’. In that venerable subject, built around the minimization of integral functionals, constraints were relatively simple and much of the focus was on infinitedimensional function spaces. A major theme was the exploration of variations around a point, within the bounds imposed by the constraints, in order to help characterize solutions and portray them in terms of ‘variational principles’. Notions of perturbation, approximation and even generalized differentiability were extensively investigated. Variational theory progressed also to the study of socalled stationary points, critical points, and other indications of singularity that a point might have relative to its neighbors, especially in association with existence theorems for differential equations.
Improved Approximation Algorithms for Maximum Cut and Satisfiability Problems Using Semidefinite Programming
 Journal of the ACM
, 1995
"... We present randomized approximation algorithms for the maximum cut (MAX CUT) and maximum 2satisfiability (MAX 2SAT) problems that always deliver solutions of expected value at least .87856 times the optimal value. These algorithms use a simple and elegant technique that randomly rounds the solution ..."
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Cited by 1231 (13 self)
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We present randomized approximation algorithms for the maximum cut (MAX CUT) and maximum 2satisfiability (MAX 2SAT) problems that always deliver solutions of expected value at least .87856 times the optimal value. These algorithms use a simple and elegant technique that randomly rounds
A Framework for Dynamic Graph Drawing
 CONGRESSUS NUMERANTIUM
, 1992
"... Drawing graphs is an important problem that combines flavors of computational geometry and graph theory. Applications can be found in a variety of areas including circuit layout, network management, software engineering, and graphics. The main contributions of this paper can be summarized as follows ..."
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Cited by 627 (44 self)
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as follows: ffl We devise a model for dynamic graph algorithms, based on performing queries and updates on an implicit representation of the drawing, and we show its applications. ffl We present several efficient dynamic drawing algorithms for trees, seriesparallel digraphs, planar stdigraphs, and planar
Results 1  10
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54,259