139 research outputs found
05201 Abstracts Collection -- Design and Analysis of Randomized and Approximation Algorithms
From 15.05.05 to 20.05.05, the Dagstuhl Seminar 05201 ``Design and Analysis of Randomized and Approximation Algorithms\u27\u27 was held
in the International Conference and Research Center (IBFI),
Schloss Dagstuhl.
During the seminar, several participants presented their current
research, and ongoing work and open problems were discussed. Abstracts of
the presentations given during the seminar as well as abstracts of
seminar results and ideas are put together in this paper. The first section
describes the seminar topics and goals in general.
Links to extended abstracts or full papers are provided, if available
Robust optimization with incremental recourse
In this paper, we consider an adaptive approach to address optimization
problems with uncertain cost parameters. Here, the decision maker selects an
initial decision, observes the realization of the uncertain cost parameters,
and then is permitted to modify the initial decision. We treat the uncertainty
using the framework of robust optimization in which uncertain parameters lie
within a given set. The decision maker optimizes so as to develop the best cost
guarantee in terms of the worst-case analysis. The recourse decision is
``incremental"; that is, the decision maker is permitted to change the initial
solution by a small fixed amount. We refer to the resulting problem as the
robust incremental problem. We study robust incremental variants of several
optimization problems. We show that the robust incremental counterpart of a
linear program is itself a linear program if the uncertainty set is polyhedral.
Hence, it is solvable in polynomial time. We establish the NP-hardness for
robust incremental linear programming for the case of a discrete uncertainty
set. We show that the robust incremental shortest path problem is NP-complete
when costs are chosen from a polyhedral uncertainty set, even in the case that
only one new arc may be added to the initial path. We also address the
complexity of several special cases of the robust incremental shortest path
problem and the robust incremental minimum spanning tree problem
The Rabin index of parity games
We study the descriptive complexity of parity games by taking into account
the coloring of their game graphs whilst ignoring their ownership structure.
Colored game graphs are identified if they determine the same winning regions
and strategies, for all ownership structures of nodes. The Rabin index of a
parity game is the minimum of the maximal color taken over all equivalent
coloring functions. We show that deciding whether the Rabin index is at least k
is in PTIME for k=1 but NP-hard for all fixed k > 1. We present an EXPTIME
algorithm that computes the Rabin index by simplifying its input coloring
function. When replacing simple cycle with cycle detection in that algorithm,
its output over-approximates the Rabin index in polynomial time. Experimental
results show that this approximation yields good values in practice.Comment: In Proceedings GandALF 2013, arXiv:1307.416
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