8,585 research outputs found
Parameterized Algorithmics for Computational Social Choice: Nine Research Challenges
Computational Social Choice is an interdisciplinary research area involving
Economics, Political Science, and Social Science on the one side, and
Mathematics and Computer Science (including Artificial Intelligence and
Multiagent Systems) on the other side. Typical computational problems studied
in this field include the vulnerability of voting procedures against attacks,
or preference aggregation in multi-agent systems. Parameterized Algorithmics is
a subfield of Theoretical Computer Science seeking to exploit meaningful
problem-specific parameters in order to identify tractable special cases of in
general computationally hard problems. In this paper, we propose nine of our
favorite research challenges concerning the parameterized complexity of
problems appearing in this context
Parameterized Study of the Test Cover Problem
We carry out a systematic study of a natural covering problem, used for
identification across several areas, in the realm of parameterized complexity.
In the {\sc Test Cover} problem we are given a set of items
together with a collection, , of distinct subsets of these items called
tests. We assume that is a test cover, i.e., for each pair of items
there is a test in containing exactly one of these items. The
objective is to find a minimum size subcollection of , which is still a
test cover. The generic parameterized version of {\sc Test Cover} is denoted by
-{\sc Test Cover}. Here, we are given and a
positive integer parameter as input and the objective is to decide whether
there is a test cover of size at most . We study four
parameterizations for {\sc Test Cover} and obtain the following:
(a) -{\sc Test Cover}, and -{\sc Test Cover} are fixed-parameter
tractable (FPT).
(b) -{\sc Test Cover} and -{\sc Test Cover} are
W[1]-hard. Thus, it is unlikely that these problems are FPT
On solving systems of random linear disequations
An important subcase of the hidden subgroup problem is equivalent to the
shift problem over abelian groups. An efficient solution to the latter problem
would serve as a building block of quantum hidden subgroup algorithms over
solvable groups. The main idea of a promising approach to the shift problem is
reduction to solving systems of certain random disequations in finite abelian
groups. The random disequations are actually generalizations of linear
functions distributed nearly uniformly over those not containing a specific
group element in the kernel. In this paper we give an algorithm which finds the
solutions of a system of N random linear disequations in an abelian p-group A
in time polynomial in N, where N=(log|A|)^{O(q)}, and q is the exponent of A.Comment: 13 page
Dagstuhl Reports : Volume 1, Issue 2, February 2011
Online Privacy: Towards Informational Self-Determination on the Internet (Dagstuhl Perspectives Workshop 11061) : Simone Fischer-Hübner, Chris Hoofnagle, Kai Rannenberg, Michael Waidner, Ioannis Krontiris and Michael Marhöfer Self-Repairing Programs (Dagstuhl Seminar 11062) : Mauro Pezzé, Martin C. Rinard, Westley Weimer and Andreas Zeller Theory and Applications of Graph Searching Problems (Dagstuhl Seminar 11071) : Fedor V. Fomin, Pierre Fraigniaud, Stephan Kreutzer and Dimitrios M. Thilikos Combinatorial and Algorithmic Aspects of Sequence Processing (Dagstuhl Seminar 11081) : Maxime Crochemore, Lila Kari, Mehryar Mohri and Dirk Nowotka Packing and Scheduling Algorithms for Information and Communication Services (Dagstuhl Seminar 11091) Klaus Jansen, Claire Mathieu, Hadas Shachnai and Neal E. Youn
Discreteness and rationality of -jumping numbers on singular varieties
We prove that the -jumping numbers of the test ideal \tau(X; \Delta,
\ba^t) are discrete and rational under the assumptions that is a normal
and -finite variety over a field of positive characteristic ,
is \bQ-Cartier of index not divisible , and either is
essentially of finite type over a field or the sheaf of ideals \ba is locally
principal. This is the largest generality for which discreteness and
rationality are known for the jumping numbers of multiplier ideals in
characteristic zero.Comment: 29 pages, minor changes, to appear in Mathematische Annale
Dynamic Complexity Meets Parameterised Algorithms
Dynamic Complexity studies the maintainability of queries with logical formulas in a setting where the underlying structure or database changes over time. Most often, these formulas are from first-order logic, giving rise to the dynamic complexity class DynFO. This paper investigates extensions of DynFO in the spirit of parameterised algorithms. In this setting structures come with a parameter k and the extensions allow additional "space" of size f(k) (in the form of an additional structure of this size) or additional time f(k) (in the form of iterations of formulas) or both. The resulting classes are compared with their non-dynamic counterparts and other classes. The main part of the paper explores the applicability of methods for parameterised algorithms to this setting through case studies for various well-known parameterised problems
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