186,965 research outputs found
Fixed-Parameter Algorithms for Computing Kemeny Scores - Theory and Practice
The central problem in this work is to compute a ranking of a set of elements
which is "closest to" a given set of input rankings of the elements. We define
"closest to" in an established way as having the minimum sum of Kendall-Tau
distances to each input ranking. Unfortunately, the resulting problem Kemeny
consensus is NP-hard for instances with n input rankings, n being an even
integer greater than three. Nevertheless this problem plays a central role in
many rank aggregation problems. It was shown that one can compute the
corresponding Kemeny consensus list in f(k) + poly(n) time, being f(k) a
computable function in one of the parameters "score of the consensus", "maximum
distance between two input rankings", "number of candidates" and "average
pairwise Kendall-Tau distance" and poly(n) a polynomial in the input size. This
work will demonstrate the practical usefulness of the corresponding algorithms
by applying them to randomly generated and several real-world data. Thus, we
show that these fixed-parameter algorithms are not only of theoretical
interest. In a more theoretical part of this work we will develop an improved
fixed-parameter algorithm for the parameter "score of the consensus" having a
better upper bound for the running time than previous algorithms.Comment: Studienarbei
Finitely fibered Rosenthal compacta and trees
We study some topological properties of trees with the interval topology. In
particular, we characterize trees which admit a 2-fibered compactification and
we present two examples of trees whose one-point compactifications are
Rosenthal compact with certain renorming properties of their spaces of
continuous functions.Comment: Small changes, mainly in the introduction and in final remark
Finiteness theorems in stochastic integer programming
We study Graver test sets for families of linear multi-stage stochastic
integer programs with varying number of scenarios. We show that these test sets
can be decomposed into finitely many ``building blocks'', independent of the
number of scenarios, and we give an effective procedure to compute these
building blocks. The paper includes an introduction to Nash-Williams' theory of
better-quasi-orderings, which is used to show termination of our algorithm. We
also apply this theory to finiteness results for Hilbert functions.Comment: 36 p
Learning by stochastic serializations
Complex structures are typical in machine learning. Tailoring learning
algorithms for every structure requires an effort that may be saved by defining
a generic learning procedure adaptive to any complex structure. In this paper,
we propose to map any complex structure onto a generic form, called
serialization, over which we can apply any sequence-based density estimator. We
then show how to transfer the learned density back onto the space of original
structures. To expose the learning procedure to the structural particularities
of the original structures, we take care that the serializations reflect
accurately the structures' properties. Enumerating all serializations is
infeasible. We propose an effective way to sample representative serializations
from the complete set of serializations which preserves the statistics of the
complete set. Our method is competitive or better than state of the art
learning algorithms that have been specifically designed for given structures.
In addition, since the serialization involves sampling from a combinatorial
process it provides considerable protection from overfitting, which we clearly
demonstrate on a number of experiments.Comment: Submission to NeurIPS 201
Order Invariance on Decomposable Structures
Order-invariant formulas access an ordering on a structure's universe, but
the model relation is independent of the used ordering. Order invariance is
frequently used for logic-based approaches in computer science. Order-invariant
formulas capture unordered problems of complexity classes and they model the
independence of the answer to a database query from low-level aspects of
databases. We study the expressive power of order-invariant monadic
second-order (MSO) and first-order (FO) logic on restricted classes of
structures that admit certain forms of tree decompositions (not necessarily of
bounded width).
While order-invariant MSO is more expressive than MSO and, even, CMSO (MSO
with modulo-counting predicates), we show that order-invariant MSO and CMSO are
equally expressive on graphs of bounded tree width and on planar graphs. This
extends an earlier result for trees due to Courcelle. Moreover, we show that
all properties definable in order-invariant FO are also definable in MSO on
these classes. These results are applications of a theorem that shows how to
lift up definability results for order-invariant logics from the bags of a
graph's tree decomposition to the graph itself.Comment: Accepted for LICS 201
The number of weakly compact convex subsets of the Hilbert space
We prove that for k an uncountable cardinal, there exist 2^k many non
homeomorphic weakly compact convex subsets of weight k in the Hilbert space of
density k
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