8,509 research outputs found
Approximation Algorithms for Polynomial-Expansion and Low-Density Graphs
We study the family of intersection graphs of low density objects in low
dimensional Euclidean space. This family is quite general, and includes planar
graphs. We prove that such graphs have small separators. Next, we present
efficient -approximation algorithms for these graphs, for
Independent Set, Set Cover, and Dominating Set problems, among others. We also
prove corresponding hardness of approximation for some of these optimization
problems, providing a characterization of their intractability in terms of
density
Computational Geometry Column 42
A compendium of thirty previously published open problems in computational
geometry is presented.Comment: 7 pages; 72 reference
Finding Pairwise Intersections Inside a Query Range
We study the following problem: preprocess a set O of objects into a data
structure that allows us to efficiently report all pairs of objects from O that
intersect inside an axis-aligned query range Q. We present data structures of
size and with query time
time, where k is the number of reported pairs, for two classes of objects in
the plane: axis-aligned rectangles and objects with small union complexity. For
the 3-dimensional case where the objects and the query range are axis-aligned
boxes in R^3, we present a data structures of size and query time . When the objects and
query are fat, we obtain query time using storage
Efficiently Learning from Revealed Preference
In this paper, we consider the revealed preferences problem from a learning
perspective. Every day, a price vector and a budget is drawn from an unknown
distribution, and a rational agent buys his most preferred bundle according to
some unknown utility function, subject to the given prices and budget
constraint. We wish not only to find a utility function which rationalizes a
finite set of observations, but to produce a hypothesis valuation function
which accurately predicts the behavior of the agent in the future. We give
efficient algorithms with polynomial sample-complexity for agents with linear
valuation functions, as well as for agents with linearly separable, concave
valuation functions with bounded second derivative.Comment: Extended abstract appears in WINE 201
- …