- Max Bannach, Christoph Stockhusen, Till Tantau:
Fast Parallel Fixed-Parameter Algorithms via Color Coding.
In Proceedings of the 10th International Symposium on Parameterized and Exact Computation (IPEC 2015), LIPIcs,
2015.
Go to website | Show PDF | Show abstract
Fixed-parameter algorithms have been successfully applied to solve numerous difficult problems within acceptable time bounds on large inputs. However, most fixed-parameter algorithms are inherently \emph{sequential} and, thus, make no use of the parallel hardware present in modern computers. We show that parallel fixed-parameter algorithms do not only exist for numerous parameterized problems from the literature -- including vertex cover, packing problems, cluster editing, cutting vertices, finding embeddings, or finding matchings -- but that there are parallel algorithms working in \emph{constant} time or at least in time \emph{depending only on the parameter} (and not on the size of the input) for these problems. Phrased in terms of complexity classes, we place numerous natural parameterized problems in parameterized versions of AC$^0$. On a more technical level, we show how the \emph{color coding} method can be implemented in constant time and apply it to embedding problems for graphs of bounded tree-width or tree-depth and to model checking first-order formulas in graphs of bounded degree.
- Sebastian Berndt, Klaus Jansen, Kim-Manuel Klein:
Fully Dynamic Bin Packing Revisited.
In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2015), Volume 40 of Leibniz International Proceedings in Informatics (LIPIcs), pp. 135-151.
Schloss Dagstuhl-Leibniz-Zentrum für Informatik,
2015.
Go to website | Show abstract
We consider the fully dynamic bin packing problem, where items arrive and depart in an online fashion and repacking of previously packed items is allowed. The goal is, of course, to minimize both the number of bins used as well as the amount of repacking. A recently introduced way of measuring the repacking costs at each timestep is the migration factor, defined as the total size of repacked items divided by the size of an arriving or departing item. Concerning the trade-off between number of bins and migration factor, if we wish to achieve an asymptotic competitive ratio of 1 + epsilon for the number of bins, a relatively simple argument proves a lower bound of Omega(1/epsilon) of the migration factor. We establish a fairly close upper bound of O(1/epsilon^4 log(1/epsilon)) using a new dynamic rounding technique and new ideas to handle small items in a dynamic setting such that no amortization is needed. The running time of our algorithm is polynomial in the number of items n and in 1/epsilon. The previous best trade-off was for an asymptotic competitive ratio of 5/4 for the bins (rather than 1+epsilon) and needed an amortized number of O(log n) repackings (while in our scheme the number of repackings is independent of n and non-amortized).
- Matthias Ernst, Maciej Liskiewicz, Rüdiger Reischuk:
Algorithmic Learning for Steganography: Proper Learning of k-term DNF Formulas from Positive Samples.
In Proc. International Symposium on Algorithms and Computation (ISAAC 2015), Volume 9472 of Lecture Notes in Computer Science, pp. 151-162.
Springer,
2015.
Go to website | Show abstract
Proper learning from positive samples is a basic ingredient for designing secure steganographic systems for unknown covertext channels. In addition, security requirements imply that the hypothesis should not contain false positives. We present such a learner for k-term DNF formulas for the uniform distribution and a generalization to q-bounded distributions. We briefly also describe how these results can be used to design a secure stegosystem.
- Till Tantau:
Existential Second-order Logic over Graphs: A Complete Complexity-theoretic Classification.
In 32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015), Volume 30 of Leibniz International Proceedings in Informatics (LIPIcs), pp. 703-715.
Schloss Dagstuhl-Leibniz-Zentrum für Informatik,
2015.
Go to website | Show abstract
Descriptive complexity theory aims at inferring a problem's computational complexity from the syntactic complexity of its description. A cornerstone of this theory is Fagin's Theorem, by which a property is expressible in existential second-order logic (ESO logic) if, and only if, it is in NP. A natural question, from the theory's point of view, is which syntactic fragments of ESO logic also still characterize NP. Research on this question has culminated in a dichotomy result by Gottlob, Kolaitis, and Schwentick: for each possible quantifier prefix of an ESO formula, the resulting prefix class over graphs either contains an NP-complete problem or is contained in P. However, the exact complexity of the prefix classes inside P remained elusive. In the present paper, we clear up the picture by showing that for each prefix class of ESO logic, its reduction closure under first-order reductions is either FO, L, NL, or NP. For undirected self-loop-free graphs two containment results are especially challenging to prove: containment in L for the prefix \exists R_1\cdots \exists R_n \forall x \exists y and containment in FO for the prefix \exists M \forall x \exists y for monadic M. The complex argument by Gottlob et al. concerning polynomial time needs to be carefully reexamined and either combined with the logspace version of Courcelle's Theorem or directly improved to first-order computations. A different challenge is posed by formulas with the prefix \exists M \forall x\forall y, which we show to express special constraint satisfaction problems that lie in L.
- Johannes Textor, Alexander Idelberger, Maciej Liskiewicz:
On the Faithful DAGs of a Dependency Graph.
In Proceedings of the 31st Conference on Uncertainty in Artificial Intelligence (UAI'15), pp. 882-891.
AUAI Press,
2015.
Show PDF - Benito van der Zander, Johannes Textor, Maciej Liskiewicz:
Efficiently Finding Conditional Instruments for Causal Inference.
In IJCAI 2015, Proceedings of the 24th International Joint Conference on Artificial Intelligence, Buenos Aires, Argentina, July 25-31, 2015, pp. 3243-3249.
AAAI Press / International Joint Conferences on Artificial Intelligence,
2015.
Show PDF