5 research outputs found
Improved Approximation Algorithms for the Min-Max Selecting Items Problem
We give a simple deterministic approximation
algorithm for the Min-Max Selecting Items problem, where is the number of
scenarios. While our main goal is simplicity, this result also improves over
the previous best approximation ratio of due to Kasperski, Kurpisz,
and Zieli\'nski (Information Processing Letters (2013)). Despite using the
method of pessimistic estimators, the algorithm has a polynomial runtime also
in the RAM model of computation. We also show that the LP formulation for this
problem by Kasperski and Zieli\'nski (Annals of Operations Research (2009)),
which is the basis for the previous work and ours, has an integrality gap of at
least
On the approximability of robust spanning tree problems
In this paper the minimum spanning tree problem with uncertain edge costs is
discussed. In order to model the uncertainty a discrete scenario set is
specified and a robust framework is adopted to choose a solution. The min-max,
min-max regret and 2-stage min-max versions of the problem are discussed. The
complexity and approximability of all these problems are explored. It is proved
that the min-max and min-max regret versions with nonnegative edge costs are
hard to approximate within for any unless
the problems in NP have quasi-polynomial time algorithms. Similarly, the
2-stage min-max problem cannot be approximated within unless the
problems in NP have quasi-polynomial time algorithms. In this paper randomized
LP-based approximation algorithms with performance ratio of for
min-max and 2-stage min-max problems are also proposed
A parameterized view to the robust recoverable base problem of matroids under structural uncertainty
We study a robust recoverable version of the matroid base problem where the uncertainty is imposed on combinatorial structures rather than on weights as studied in the literature. We prove that the problem is NP-hard even when a given matroid is uniform or graphic. On the other hand, we prove that the problem is fixed-parameter tractable with respect to the number of scenarios