25 research outputs found
Reading Articles Online
We study the online problem of reading articles that are listed in an
aggregated form in a dynamic stream, e.g., in news feeds, as abbreviated social
media posts, or in the daily update of new articles on arXiv. In such a
context, the brief information on an article in the listing only hints at its
content. We consider readers who want to maximize their information gain within
a limited time budget, hence either discarding an article right away based on
the hint or accessing it for reading. The reader can decide at any point
whether to continue with the current article or skip the remaining part
irrevocably. In this regard, Reading Articles Online, RAO, does differ
substantially from the Online Knapsack Problem, but also has its similarities.
Under mild assumptions, we show that any -competitive algorithm for the
Online Knapsack Problem in the random order model can be used as a black box to
obtain an -competitive algorithm for RAO, where
measures the accuracy of the hints with respect to the information profiles of
the articles. Specifically, with the current best algorithm for Online
Knapsack, which is -competitive, we obtain an upper bound
of on the competitive ratio of RAO. Furthermore, we study a
natural algorithm that decides whether or not to read an article based on a
single threshold value, which can serve as a model of human readers. We show
that this algorithmic technique is -competitive. Hence, our algorithms
are constant-competitive whenever the accuracy is a constant.Comment: Manuscript of COCOA 2020 pape
Packing Returning Secretaries
We study online secretary problems with returns in combinatorial packing
domains with candidates that arrive sequentially over time in random order.
The goal is to accept a feasible packing of candidates of maximum total value.
In the first variant, each candidate arrives exactly twice. All arrivals
occur in random order. We propose a simple 0.5-competitive algorithm that can
be combined with arbitrary approximation algorithms for the packing domain,
even when the total value of candidates is a subadditive function. For
bipartite matching, we obtain an algorithm with competitive ratio at least
for growing , and an algorithm with ratio at least
for all . We extend all algorithms and ratios to arrivals
per candidate.
In the second variant, there is a pool of undecided candidates. In each
round, a random candidate from the pool arrives. Upon arrival a candidate can
be either decided (accept/reject) or postponed (returned into the pool). We
mainly focus on minimizing the expected number of postponements when computing
an optimal solution. An expected number of is always
sufficient. For matroids, we show that the expected number can be reduced to
, where is the minimum of the ranks of matroid and
dual matroid. For bipartite matching, we show a bound of , where
is the size of the optimum matching. For general packing, we show a lower
bound of , even when the size of the optimum is .Comment: 23 pages, 5 figure
Think Eternally: Improved Algorithms for the Temp Secretary Problem and Extensions
The Temp Secretary Problem was recently introduced by [Fiat et al., ESA 2015]. It is a generalization of the Secretary Problem, in which commitments are temporary for a fixed duration. We present a simple online algorithm with improved performance guarantees for cases already considered by [Fiat et al., ESA 2015] and give competitive ratios for new generalizations of the problem. In the classical setting, where candidates have identical contract durations gamma << 1 and we are allowed to hire up to B candidates simultaneously, our algorithm is (1/2) - O(sqrt{gamma})-competitive. For large B, the bound improves to 1 - O(1/sqrt{B}) - O(sqrt{gamma}).
Furthermore we generalize the problem from cardinality constraints towards general packing constraints. We achieve a competitive ratio of 1 - O(sqrt{(1+log(d) + log(B))/B}) - O(sqrt{gamma}), where d is the sparsity of the constraint matrix and B is generalized to the capacity ratio of linear constraints. Additionally we extend the problem towards arbitrary hiring durations.
Our algorithmic approach is a relaxation that aggregates all temporal constraints into a non-temporal constraint. Then we apply a linear scaling algorithm that, on every arrival, computes a tentative solution on the input that is known up to this point. This tentative solution uses the non-temporal, relaxed constraints scaled down linearly by the amount of time that has already passed
Exponentiated Subgradient Algorithm for Online Optimization under the Random Permutation Model
Online optimization problems arise in many resource allocation tasks, where
the future demands for each resource and the associated utility functions
change over time and are not known apriori, yet resources need to be allocated
at every point in time despite the future uncertainty. In this paper, we
consider online optimization problems with general concave utilities. We modify
and extend an online optimization algorithm proposed by Devanur et al. for
linear programming to this general setting. The model we use for the arrival of
the utilities and demands is known as the random permutation model, where a
fixed collection of utilities and demands are presented to the algorithm in
random order. We prove that under this model the algorithm achieves a
competitive ratio of under a near-optimal assumption that the
bid to budget ratio is , where
is the number of resources, while enjoying a significantly lower computational
cost than the optimal algorithm proposed by Kesselheim et al. We draw a
connection between the proposed algorithm and subgradient methods used in
convex optimization. In addition, we present numerical experiments that
demonstrate the performance and speed of this algorithm in comparison to
existing algorithms