A Unified Approach to a Class of Best Choice Problems with an Unknown Number of Options

Bruss, F. Thomas

doi:10.1214/aop/1176993237

Cited by 75 publications

(54 citation statements)

References 6 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…For example, for semi-arbitrary-arrival model, our protocol gets a total profit that is almost 20-30 percent of the optimum, while it has been proven in [6] that no mechanism can achieve social efficiency ratio better than 1=e in the worst case. The spectrum utilization is also around 20-40 percent for this model.…”

Section: Introductionmentioning

confidence: 92%

SALSA: Strategyproof Online Spectrum Admissions for Wireless Networks

Wang

2010

IEEE Trans. Comput.

View full text Add to dashboard Cite

Abstract-It is imperative to design efficient and effective online spectrum allocation methods since requests for spectrums often come in an online fashion. In this paper, we propose SALSA, strategyproof online spectrum admission for wireless networks. We assume that the requests arrival follows the Poisson distribution. Upon receiving an online spectrum request, our protocol will decide immediately whether to grant its exclusive usage or not, and how much the request should pay. Preempting existing spectrum usage is not allowed. We proposed two protocols that have guaranteed performances for two different scenarios: 1) random-arrival case: the bid values and requested time durations follow some distributions that can be learned, or 2) semi-arbitrary-arrival case: the bid values could be arbitrary, but the request arrival sequence is random. We analytically prove that our protocols are strategyproof, and are both approximately social efficient and revenue efficient. Our extensive simulation results show that they perform almost optimum. Our method for semi-arbitrary-arrival model achieves social efficiency and revenue efficiency almost 20-30 percent of the optimum, while it has been proven that no mechanism can achieve social efficiency ratio better than 1=e ' 37 percent. Our protocol for the randomarrival case even achieves social efficiency and revenue efficiency two-six times the expected performances by the celebrated VCG mechanism.

show abstract

Section: Introductionmentioning

confidence: 92%

SALSA: Strategyproof Online Spectrum Admissions for Wireless Networks

Wang

2010

IEEE Trans. Comput.

View full text Add to dashboard Cite

show abstract

“…It is well known that the asymptotic value, as n → ∞, of the optimal rule is e −1 = 0.3678 · · · , and that the optimal rule is easily described. Moreover, as the e −1 -law (Bruss (1984)) shows, e −1 is the precise lower bound for the value even in the continuous-time model for unknown n, if all n objects have independent, identically distributed arrival times. In contrast to the above no-information version of the problem, the informed version is the problem in which the observations are the true values of the objects, assumed to be independent, identically distributed random variables from a known continuous distribution that is taken, without loss of generality, to be the uniform distribution on the interval [0,1].…”

Section: Introductionmentioning

confidence: 99%

An Explicit Formula for the Optimal Gain in the Full-Information Problem of Owning a Relatively Best Object

Mazalov

Tamaki

2006

J. Appl. Probab.

View full text Add to dashboard Cite

A full-information version of the secretary problem in which the objective is to maximize the time of possession of a relatively best object is considered both in the case in which only the most recently observed object may be chosen and in the case in which any of the previously observed objects may be chosen. The main purpose of this paper is to obtain, under an optimal rule, both the asymptotic proportional durations when the number of objects tends to infinity, and the expected durations when the number of objects remains finite. The integral expressions for these asymptotic values are derived in both cases: the approximate numerical values are 0.435 in the former (no-recall) case and 0.449 in the latter (recall) case, indicating a surprisingly small difference. The expected values of the optimal stopping times are also obtained from the planar Poisson process analysis.

show abstract

“…Continuous Model. Bruss introduced the continuous model [3], in which there is still a totally ordered set of n items, but each item picks an arrival time independently and uniformly at random from [0,1]. Any algorithm in the previous step model can still work in the continuous model by simply ignoring the arrival times, whereas any algorithm in the continuous model can be implemented as a randomized algorithm in the finite step model by first artificially generating n independent time-stamps uniformly at random from [0,1], and giving the i-th arriving item the i-th smallest time-stamp.…”

Section: Introductionmentioning

confidence: 99%

Revealing Optimal Thresholds for Generalized Secretary Problem via Continuous LP: Impacts on Online K-Item Auction and Bipartite K-Matching with Random Arrival Order

Chan¹,

Chen²,

Jiang³

2014

Proceedings of the Twenty-Sixth Annual ACM-SIAM Symposium on Discrete Algorithms

View full text Add to dashboard Cite

We consider the general (J, K)-secretary problem, where n totally ordered items arrive in a random order. An algorithm observes the relative merits of arriving items and is allowed to make J selections. The objective is to maximize the expected number of items selected among the K best items.Buchbinder, Jain and Singh proposed a finite linear program (LP) that completely characterizes the problem, but it is difficult to analyze the asymptotic behavior of its optimal solution as n tends to infinity. Instead, we prove a formal connection between the finite model and an infinite model, where there are a countably infinite number of items, each of which has arrival time drawn independently and uniformly from [0, 1].The finite LP extends to a continuous LP, whose complementary slackness conditions reveal an optimal algorithm which involves JK thresholds that play a similar role as the 1 e -threshold in the optimal classical secretary algorithm. In particular, for the case K = 1, the J optimal thresholds have a nice "rational description". Our continuous LP analysis gives a very clear perspective on the problem, and the new insights inspire us to solve two related problems.1. We settle the open problem whether algorithms based only on relative merits can achieve optimal ratio for matroid secretary problems. We show that, for online 2-item auction with random arriving bids (the K-uniform matroid problem with K = 2), an algorithm making decisions based only on relative merits cannot achieve the optimal ratio. This is in contrast with the folklore that, for online 1-item auction, no algorithm can have performance ratio strictly larger than 1 e , which is achievable by an algorithm that considers only relative merits. 2. We give a general transformation technique that takes any monotone algorithm (such as threshold

show abstract

A Unified Approach to a Class of Best Choice Problems with an Unknown Number of Options

Cited by 75 publications

References 6 publications

SALSA: Strategyproof Online Spectrum Admissions for Wireless Networks

SALSA: Strategyproof Online Spectrum Admissions for Wireless Networks

An Explicit Formula for the Optimal Gain in the Full-Information Problem of Owning a Relatively Best Object

Revealing Optimal Thresholds for Generalized Secretary Problem via Continuous LP: Impacts on Online K-Item Auction and Bipartite K-Matching with Random Arrival Order

Contact Info

Product

Resources

About