2 research outputs found
The Stochastic Bilevel Continuous Knapsack Problem with Uncertain Follower's Objective
We consider a bilevel continuous knapsack problem where the leader controls
the capacity of the knapsack, while the follower chooses a feasible packing
maximizing his own profit. The leader's aim is to optimize a linear objective
function in the capacity and in the follower's solution, but with respect to
different item values. We address a stochastic version of this problem where
the follower's profits are uncertain from the leader's perspective, and only a
probability distribution is known. Assuming that the leader aims at optimizing
the expected value of her objective function, we first observe that the
stochastic problem is tractable as long as the possible scenarios are given
explicitly as part of the input, which also allows to deal with general
distributions using a sample average approximation. For the case of
independently and uniformly distributed item values, we show that the problem
is #P-hard in general, and the same is true even for evaluating the leader's
objective function. Nevertheless, we present pseudo-polynomial time algorithms
for this case, running in time linear in the total size of the items. Based on
this, we derive an additive approximation scheme for the general case of
independently distributed item values, which runs in pseudo-polynomial time.Comment: A preliminary version of parts of this article can be found in
Section 8 of arXiv:1903.02810v
A 4-approximation algorithm for min max correlation clustering
We introduce a lower bounding technique for the min max correlation
clustering problem and, based on this technique, a combinatorial
4-approximation algorithm for complete graphs. This improves upon the previous
best known approximation guarantees of 5, using a linear program formulation
(Kalhan et al., 2019), and 40, for a combinatorial algorithm (Davies et al.,
2023). We extend this algorithm by a greedy joining heuristic and show
empirically that it improves the state of the art in solution quality and
runtime on several benchmark datasets.Comment: 9 page