Optimal Search and One-Way Trading Online Algorithms

El‐Yaniv, Ran; Fiat, Amos; Karp, Richard M.; Turpin, G.

doi:10.1007/s00453-001-0003-0

Cited by 173 publications

(273 citation statements)

References 25 publications

(30 reference statements)

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“…After introducing the one-way trading problem, El-Yaniv et al gave in [10] an algorithm for the problem that works under the assumption that there are a lower bound m and an upper bound M on the market prices such that p i ∈ [m, M ] for all p i , and that these bounds m and M are known to the algorithm. They proved that their algorithm has competitive ratio O(log(M/m)), and showed that it is optimal by deriving a matching lower bound.…”

Section: Previous Resultsmentioning

confidence: 99%

“…They showed that if there are n buyers, their algorithm has competitive ratio nαβ−(n−1)(α+β)+(n−2) αβ−1 . In [10], El-Yaniv et al also studied another problem similar to the one-way trading problem, namely the 1-max-search problem, in which there is a sequence of prices coming online, and when a price arrives, we have to decide immediately whether we accept the price or not. The objective is to accept the highest price.…”

Section: Previous Resultsmentioning

confidence: 99%

“…Furthermore, existing algorithms for the problem need to know some information about these constraints, such as the values of m and M , or their ratio, in order to work correctly, (for example, the reservation price policy [10] accepts the first price ≥ √ M m). In this paper, we give a one-way trading algorithm that does not need to impose any constraint on the market prices, and we derive a bound on its competitive ratio that depends directly on the input, or more precisely, depends on r * = p * /p 1 , the ratio of the highest price p * = max i p i and the first price p 1 (in fact, our algorithm will treat p 1 as the lowest price and ignore any prices lower than p 1 ).…”

Section: Our Contributionmentioning

confidence: 99%

“…Here we still assume that the highest market price is unknown; otherwise, the seller would exactly know the highest market price and will wait until the arrival of the buyer with the highest market price and then assign all products to this buyer. For this variant, El-Yaniv et al [10] and Zhang et. al.…”

Section: The Highest Normalized Price R * Is Boundedmentioning

confidence: 99%

“…The one-way trading problem, which was introduced by El-Yaniv et al [9,10], involves selling a fixed amount of a product to a sequence of buyers, with the objective of maximizing the seller's revenue. A major difference between this problem and other general revenue maximization problems commonly studied in economics and computer science is that for the general problems, the seller has some control of the prices; he can determine the amount and the price of product to be sold to each buyer.…”

Section: Introductionmentioning

confidence: 99%

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Competitive Algorithms for Unbounded One-Way Trading

Chin

Fu²,

Jiang

et al. 2014

Algorithmic Aspects in Information and Management

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In the one-way trading problem, a seller has L units of product to be sold to a sequence σ of buyers u 1 , u 2 , . . . , u σ arriving online and he needs to decide, for each u i , the amount of product to be sold to u i at the then-prevailing market price p i . The objective is to maximize the seller's revenue. We note that all previous algorithms for the problem need to impose some artificial upper bound M and lower bound m on the market prices, and the seller needs to know either the values of M and m, or their ratio M/m, at the outset.This paper gives a one-way trading algorithm that does not impose any bounds on market prices and whose performance guarantee depends directly on the input. In particular, we give a class of one-way trading algorithms such that for any positive integer h and any positive number ϵ, we have an algorithm A h,ϵ that has competitive ratio O(log r * (log (2) r * ) . . . (log (h−1) r * )(log (h) r * ) 1+ϵ ) if the value of r * = p * /p 1 , the ratio of the highest market price p * = max i p i and the first price p 1 , is large and satisfies log (h) r * > 1, where log (i) x denotes the application of the logarithm function i times to x ; otherwise, A h,ϵ has a constant competitive ratio Γ h . We also show that our algorithms are near optimal by showing that given any positive integer h and any one-way trading algorithm A, we can construct a sequence of buyers σ with log (h) r * > 1 such that the ratio between the optimal revenue and the revenue obtained by A is Ω(log r * (log (2) r * ) . . . (log (h−1) r * )(log (h) r * )). A special case of the one-way trading is also studied, in which the L units of product is comprised of L items, each of which must be sold atomically (or equivalently, the amount of product sold to each buyer must be an integer).Furthermore, a complementary problem to the one-way trading problem, say, the oneway buying problem, is studied in this paper. In the one-way buying problem, a buyer wants to purchase one unit of product through a sequence of n sellers v 1 , v 2 , . . . , v n arriving online, and she needs to decide the fraction to purchase from each v i at the then-prevailing market price p i . Her objective is to minimize the cost. The optimal competitive algorithms whose performance guarantees depend only on the lowest market price p * = min i p i , and one of M and φ, the price fluctuation ratio, are presented.

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Section: Previous Resultsmentioning

confidence: 99%

Section: Previous Resultsmentioning

confidence: 99%

Section: Our Contributionmentioning

confidence: 99%

Section: The Highest Normalized Price R * Is Boundedmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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