342 research outputs found
Digital Color Imaging
This paper surveys current technology and research in the area of digital
color imaging. In order to establish the background and lay down terminology,
fundamental concepts of color perception and measurement are first presented
us-ing vector-space notation and terminology. Present-day color recording and
reproduction systems are reviewed along with the common mathematical models
used for representing these devices. Algorithms for processing color images for
display and communication are surveyed, and a forecast of research trends is
attempted. An extensive bibliography is provided
Lossy Kernelization
In this paper we propose a new framework for analyzing the performance of
preprocessing algorithms. Our framework builds on the notion of kernelization
from parameterized complexity. However, as opposed to the original notion of
kernelization, our definitions combine well with approximation algorithms and
heuristics. The key new definition is that of a polynomial size
-approximate kernel. Loosely speaking, a polynomial size
-approximate kernel is a polynomial time pre-processing algorithm that
takes as input an instance to a parameterized problem, and outputs
another instance to the same problem, such that . Additionally, for every , a -approximate solution
to the pre-processed instance can be turned in polynomial time into a
-approximate solution to the original instance .
Our main technical contribution are -approximate kernels of
polynomial size for three problems, namely Connected Vertex Cover, Disjoint
Cycle Packing and Disjoint Factors. These problems are known not to admit any
polynomial size kernels unless . Our approximate
kernels simultaneously beat both the lower bounds on the (normal) kernel size,
and the hardness of approximation lower bounds for all three problems. On the
negative side we prove that Longest Path parameterized by the length of the
path and Set Cover parameterized by the universe size do not admit even an
-approximate kernel of polynomial size, for any , unless
. In order to prove this lower bound we need to combine
in a non-trivial way the techniques used for showing kernelization lower bounds
with the methods for showing hardness of approximationComment: 58 pages. Version 2 contain new results: PSAKS for Cycle Packing and
approximate kernel lower bounds for Set Cover and Hitting Set parameterized
by universe siz
Some relations of subsequences in permutations to graph theory with algorithmic applications
A thesis submitted to the Faculty d£ Science of the University
of the Witwatersfand in fulfillment of the requirements for the
degree of Doctor of Philosophy.
Johannesburg, 1977.The representation of some types of graphs as permutations,
is utilized in devising efficient algorithms on those graphs.
Maximum 'cliques in permutation graphs and circle graphs
are found, by searching for a longest ascending or descending
subsequence in their representing permutation.
The correspondence between n-noded binary trees and
the set SSn of stack-sortable permutations, forms the
basis of an algorithm for generating and indexing such trees.
The-relations between a graph and its representing
p ermutation, are also employed in the proof of theorems
concerning properties of subsequences in this permutation.
In particular, expressions for the average lengths of the
longest ascending and descending subsequence a in a random
member of SSn , and the average number of inversions in such
a permutation, are derived using properties of binary trees.
Finally, a correspondence between the set SSn , and the set
of permutations of order n With no descending subsequence of
length 3, is demonstrated
Recommended from our members
Algorithmic Graph Theory
The main focus of this workshop was on mathematical techniques needed for the development of efficient solutions and algorithms for computationally difficult graph problems. The techniques studied at the workshhop included: the probabilistic method and randomized algorithms, approximation and optimization, structured families of graphs and approximation algorithms for large problems. The workshop Algorithmic Graph Theory was attended by 46 participants, many of them being young researchers. In 15 survey talks an overview of recent developments in Algorithmic Graph Theory was given. These talks were supplemented by 10 shorter talks and by two special sessions
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