Semiamarts and finite values

Krengel, Ulrich; Sucheston, Louis

doi:10.1090/s0002-9904-1977-14378-4

Cited by 187 publications

(142 citation statements)

References 2 publications

(6 reference statements)

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“…Starting with the works of Krengel-Sucheston [36,37] and Dynkin [14], there has been a long line of research on both prophet inequalities and secretary problems. One of the first generalizations is the multiple-choice prophet inequalities [28,29,30] in which we are allowed to pick k items and the goal is to maximize their sum.…”

Section: Related Workmentioning

confidence: 99%

Prophet Secretary for Combinatorial Auctions and Matroids

Ehsani¹,

Hajiaghayi²,

Keßelheim³

et al. 2018

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

108

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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). and Feldman et al. [17] show that for adversarial arrival order of random variables the optimal prophet inequalities give a 1/2-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 1/2-approximation and obtain (1 − 1/e)-approximation prophet inequalities for both matroids and combinatorial auctions. This also gives improvements to the results of Yan [45] and Esfandiari et al. [15] 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.

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Section: Related Workmentioning

confidence: 99%

Prophet Secretary for Combinatorial Auctions and Matroids

Ehsani¹,

Hajiaghayi²,

Keßelheim³

et al. 2018

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

108

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“…We note that since the distributions are not necessary i.i.d., this model generalizes the well-known prophet inequalities. 5 Even with stochastic information about the arriving queries, no online algorithm can achieve a competitive ratio better than 1 2 [1,14,17,18]. Consider the simple example from before where the value of the first item is 1 with probability one and the value of the second item is 1 with probability , and 0 with probability 1 − .…”

Section: Introductionmentioning

confidence: 99%

The Online Stochastic Generalized Assignment Problem

Alaei

Hajiaghayi

Liaghat

2013

Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques

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Abstract. We present a 1 − 1 √ k -competitive algorithm for the online stochastic generalized assignment problem under the assumption that no item takes up more than 1 k fraction of the capacity of any bin. Items arrive online; each item has a value and a size; upon arrival, an item can be placed in a bin or discarded; the objective is to maximize the total value of the placement. Both value and size of an item may depend on the bin in which the item is placed; the size of an item is revealed only after it has been placed in a bin; distribution information is available about the value and size of each item in advance (not necessarily i.i.d), however items arrive in adversarial order (non-adaptive adversary). We also present an application of our result to subscription-based advertising where each advertiser, if served, requires a given minimum number of impressions (i.e., the "all or nothing" model).

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“…Although there have been many comparisons of M and V for fixed distri butions X, apparently the first universal inequality for a large natural class of random variables is the following now-classical result of Krengel, Sucheston and Garling [49,50] which has directly or indirectly inspired most of the results rnentioned in this paper.…”

Section: Introductionmentioning

confidence: 94%

“…There are other classes of distributions which give SOllle prophet inequalities with universal constants which are close to those of the independent case. These include a class of discountecl independent r. v. 's [7]; classes of averages and weighted Sluns of independent r. v. 1 S [11,27,49, 50]; a class of finite sequences of exchangeable r.v. 's [21,22]~ a class of negatively dependent r.v.…”

Section: Introductionmentioning

confidence: 99%