192 research outputs found
The PACE 2017 Parameterized Algorithms and Computational Experiments Challenge: The Second Iteration
In this article, the Program Committee of the Second Parameterized Algorithms and Computational Experiments challenge (PACE 2017) reports on the second iteration of the PACE challenge. Track A featured the Treewidth problem and Track B the Minimum Fill-In problem. Over 44 participants on 17 teams from 11 countries submitted their implementations to the competition
The Power and Limitations of Uniform Samples in Testing Properties of Figures
We investigate testing of properties of 2-dimensional figures that consist of a black object on a white background. Given a parameter epsilon in (0,1/2), a tester for a specified property has to accept with probability at least 2/3 if the input figure satisfies the property and reject with probability at least 2/3 if it does not. In general, property testers can query the color of any point in the input figure.
We study the power of testers that get access only to uniform samples from the input figure. We show that for the property of being a half-plane, the uniform testers are as powerful as general testers: they require only O(1/epsilon) samples. In contrast, we prove that convexity can be tested with O(1/epsilon) queries by testers that can make queries of their choice while uniform testers for this property require Omega(1/epsilon^{5/4}) samples. Previously, the fastest known tester for convexity needed Theta(1/epsilon^{4/3}) queries
Interim research assessment 2003-2005 - Computer Science
This report primarily serves as a source of information for the 2007 Interim Research Assessment Committee for Computer Science at the three technical universities in the Netherlands. The report also provides information for others interested in our research activities
Recent Advances in Fully Dynamic Graph Algorithms
In recent years, significant advances have been made in the design and
analysis of fully dynamic algorithms. However, these theoretical results have
received very little attention from the practical perspective. Few of the
algorithms are implemented and tested on real datasets, and their practical
potential is far from understood. Here, we present a quick reference guide to
recent engineering and theory results in the area of fully dynamic graph
algorithms
Distance Estimation Between Unknown Matrices Using Sublinear Projections on Hamming Cube
Using geometric techniques like projection and dimensionality reduction, we
show that there exists a randomized sub-linear time algorithm that can estimate
the Hamming distance between two matrices. Consider two matrices and
of size whose dimensions are known to the algorithm but
the entries are not. The entries of the matrix are real numbers. The access to
any matrix is through an oracle that computes the projection of a row (or a
column) of the matrix on a vector in . We call this query oracle to
be an {\sc Inner Product} oracle (shortened as {\sc IP}). We show that our
algorithm returns a approximation to with high probability by making {\cal
O}\left(\frac{n}{\sqrt{{{\bf D}}_{\bf M} ({\bf A},{\bf
B})}}\mbox{poly}\left(\log n, \frac{1}{\epsilon}\right)\right) oracle queries,
where denotes the Hamming distance (the
number of corresponding entries in which and differ)
between two matrices and of size . We also show
a matching lower bound on the number of such {\sc IP} queries needed. Though
our main result is on estimating using
{\sc IP}, we also compare our results with other query models.Comment: 30 pages. Accepted in RANDOM'2
Towards Exact Structural Thresholds for Parameterized Complexity
Parameterized complexity seeks to optimally use input structure to obtain faster algorithms for NP-hard problems. This has been most successful for graphs of low treewidth, i.e., graphs decomposable by small separators: Many problems admit fast algorithms relative to treewidth and many of them are optimal under the Strong Exponential-Time Hypothesis (SETH). Fewer such results are known for more general structure such as low clique-width (decomposition by large and dense but structured separators) and more restrictive structure such as low deletion distance to some sparse graph class.
Despite these successes, such results remain "islands" within the realm of possible structure. Rather than adding more islands, we seek to determine the transitions between them, that is, we aim for structural thresholds where the complexity increases as input structure becomes more general. Going from deletion distance to treewidth, is a single deletion set to a graph with simple components enough to yield the same lower bound as for treewidth or does it take many disjoint separators? Going from treewidth to clique-width, how much more density entails the same complexity as clique-width? Conversely, what is the most restrictive structure that yields the same lower bound?
For treewidth, we obtain both refined and new lower bounds that apply already to graphs with a single separator X such that G-X has treewidth at most r = ?(1), while G has treewidth |X|+?(1). We rule out algorithms running in time ?^*((r+1-?)^k) for Deletion to r-Colorable parameterized by k = |X|; this implies the same lower bound relative to treedepth and (hence) also to treewidth. It specializes to ?^*((3-?)^k) for Odd Cycle Transversal where tw(G-X) ? r = 2 is best possible. For clique-width, an extended version of the above reduction rules out time ?^*((4-?)^k), where X is allowed to be a possibly large separator consisting of k (true) twinclasses, while the treewidth of G - X remains r; this is proved also for the more general Deletion to r-Colorable and it implies the same lower bound relative to clique-width. Further results complement what is known for Vertex Cover, Dominating Set and Maximum Cut. All lower bounds are matched by existing and newly designed algorithms
- …