44 research outputs found
Buyback Problem - Approximate matroid intersection with cancellation costs
In the buyback problem, an algorithm observes a sequence of bids and must
decide whether to accept each bid at the moment it arrives, subject to some
constraints on the set of accepted bids. Decisions to reject bids are
irrevocable, whereas decisions to accept bids may be canceled at a cost that is
a fixed fraction of the bid value. Previous to our work, deterministic and
randomized algorithms were known when the constraint is a matroid constraint.
We extend this and give a deterministic algorithm for the case when the
constraint is an intersection of matroid constraints. We further prove a
matching lower bound on the competitive ratio for this problem and extend our
results to arbitrary downward closed set systems. This problem has applications
to banner advertisement, semi-streaming, routing, load balancing and other
problems where preemption or cancellation of previous allocations is allowed
Prophet Secretary for Combinatorial Auctions and Matroids
The secretary and the prophet inequality problems are central to the field of
Stopping Theory. Recently, there has been a lot of work in generalizing these
models to multiple items because of their applications in mechanism design. The
most important of these generalizations are to matroids and to combinatorial
auctions (extends bipartite matching). Kleinberg-Weinberg \cite{KW-STOC12} and
Feldman et al. \cite{feldman2015combinatorial} show that for adversarial
arrival order of random variables the optimal prophet inequalities give a
-approximation. For many settings, however, it's conceivable that the
arrival order is chosen uniformly at random, akin to the secretary problem. For
such a random arrival model, we improve upon the -approximation and obtain
-approximation prophet inequalities for both matroids and
combinatorial auctions. This also gives improvements to the results of Yan
\cite{yan2011mechanism} and Esfandiari et al. \cite{esfandiari2015prophet} who
worked in the special cases where we can fully control the arrival order or
when there is only a single item.
Our techniques are threshold based. We convert our discrete problem into a
continuous setting and then give a generic template on how to dynamically
adjust these thresholds to lower bound the expected total welfare.Comment: Preliminary version appeared in SODA 2018. This version improves the
writeup on Fixed-Threshold algorithm
Online Auctions with Dual-Threshold Algorithms: An Experimental Study and Practical Evaluation
Online auctions are a viable alternative to conventional posted price mechanisms. Agrawal, Wang, and Ye [1] have proposed two primal-dual algorithms for revenue-maximizing multi-item allocation tasks. Although promising in terms of theoretical properties and competitive ratios, there is alack of evidence regarding the real-world practicability of these mechanisms, for instance referring to online auction-based tickets sales. In this paper, we conduct an experimental study on both the One-Time Learning Algorithm(OLA) and the Dynamic Learning Algorithm (DLA) based on synthetic data, revealing the remarkable aptitude of the latter for non-trivial online auctions. Being robust to most input variations, the inherent dynamic update of dual thresholds achieves a superior balance with respect to the trade-off between objective function values and runtimes. We address critical sensitivities quantitatively and draft several small extensions by incorporating input distribution knowledge