Results 1  10
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13
Online stochastic packing applied to display ad allocation
 In ESA
, 2010
"... Inspired by online ad allocation, we study online stochastic packing linear programs from theoretical and practical standpoints. We first present a nearoptimal online algorithm for a general class of packing linear programs which model various online resource allocation problems including online va ..."
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Cited by 40 (4 self)
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Inspired by online ad allocation, we study online stochastic packing linear programs from theoretical and practical standpoints. We first present a nearoptimal online algorithm for a general class of packing linear programs which model various online resource allocation problems including online variants of routing, ad allocations, generalized assignment, and combinatorial auctions. As our main theoretical result, we prove that a simple primaldual trainingbased algorithm achieves a (1 − o(1))approximation guarantee in the random order stochastic model. This is a significant improvement over logarithmic or constantfactor approximations for the adversarial variants of the same problems (e.g. factor 1 − 1e for online ad allocation, and log(m) for online routing). We then focus on the online display ad allocation problem and study the efficiency and fairness of various trainingbased and online allocation algorithms on data sets collected from reallife display ad allocation system. Our experimental evaluation confirms the effectiveness of trainingbased primaldual algorithms on real data sets, and also indicate an intrinsic tradeoff between fairness and efficiency. 1
On the approximability of budgeted allocations and improved lower bounds for submodular welfare maximization and GAP
 In Proceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer ScienceVolume 00
, 2008
"... In this paper we consider the following maximum budgeted allocation(MBA) problem: Given a set of m indivisible items and n agents; each agent i willing to pay bij on item j and with a maximum budget of Bi, the goal is to allocate items to agents to maximize revenue. The problem naturally arises as a ..."
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Cited by 36 (3 self)
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In this paper we consider the following maximum budgeted allocation(MBA) problem: Given a set of m indivisible items and n agents; each agent i willing to pay bij on item j and with a maximum budget of Bi, the goal is to allocate items to agents to maximize revenue. The problem naturally arises as auctioneer revenue maximization in budgetconstrained auctions and as winner determination problem in combinatorial auctions when utilities of agents are budgetedadditive. Our main results are: • We give a 3/4approximation algorithm for MBA improving upon the previous best of ≃ 0.632[AM04, FV06]. Our techniques are based on a natural LP relaxation of MBA and our factor is optimal in the sense that it matches the integrality gap of the LP. • We prove it is NPhard to approximate MBA to any factor better than 15/16, previously only NPhardness was known [SS06, LLN01]. Our result also implies NPhardness of approximating maximum submodular welfare with demand oracle to a factor better than 15/16, improving upon the best known hardness of 275/276[FV06]. • Our hardness techniques can be modified to prove that it is NPhard to approximate the Generalized Assignment Problem (GAP) to any factor better than 10/11. This improves upon the 422/423 hardness of [CK00, CC02]. We use iterative rounding on a natural LP relaxation of MBA to obtain the 3/4approximation. We also give a (3/4 − ɛ)factor algorithm based on the primaldual schema which runs in Õ(nm) time, for any constant ɛ> 0. 1
Improved bounds for online stochastic matching
 In Proceedings of the 18th European Symposium on Algorithms, LNCS 6346
, 2010
"... Abstract. We study the online stochastic matching problem in a form motivated by Internet display advertisement. Recently, Feldman et al. gave an algorithm that achieves 0.6702 competitive ratio, thus breaking through the 1−1/e barrier. One of the questions left open in their work is to obtain a bet ..."
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Cited by 18 (1 self)
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Abstract. We study the online stochastic matching problem in a form motivated by Internet display advertisement. Recently, Feldman et al. gave an algorithm that achieves 0.6702 competitive ratio, thus breaking through the 1−1/e barrier. One of the questions left open in their work is to obtain a better competitive ratio by generalizing their two suggested matchings (TSM) algorithm to dsuggested matchings (dSM). We show that the best competitive ratio that can be obtained with the static analysis used in the dSM algorithm is upper bounded by 0.76, even for the special case of dregular graphs, thus suggesting that a dynamic analysis may be needed to improve the competitive ratio significantly. We make the first step in this direction by showing that the RANDOM algorithm, which assigns an impression to a randomly chosen eligible advertiser, achieves 1 − e −d d d /d! = 1 − O(1 / √ d) competitive ratio for dregular graphs, which converges to 1 as d increases. On the hardness side, we improve the upper bound of 0.989 on the competitive ratio of any online algorithm obtained by Feldman et al. to 1 − 1/(e + e 2) ≈ 0.902. Finally, we show how to modify the TSM algorithm to obtain an improved 0.699 approximation for general bipartite graphs. 1
Budgeted allocations in the fullinformation setting
 In: APPROX ’08 (LNCS 5171
, 2008
"... Abstract. We build on the work of Andelman & Mansour and Azar, Birnbaum, Karlin, Mathieu & Thach Nguyen to show that the fullinformation (i.e., offline) budgetedallocation problem can be approximated to within 4/3: we conduct a rounding of the natural LP relaxation, for which our algorithm ..."
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Cited by 12 (1 self)
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Abstract. We build on the work of Andelman & Mansour and Azar, Birnbaum, Karlin, Mathieu & Thach Nguyen to show that the fullinformation (i.e., offline) budgetedallocation problem can be approximated to within 4/3: we conduct a rounding of the natural LP relaxation, for which our algorithm matches the known lowerbound on the integrality gap. 1
Online Matching with Stochastic Rewards
"... The online matching problem has received significant attention in recent years because of its connections to allocation problems in Internet advertising, crowdsourcing, etc. In these realworld applications, the typical goal is not to maximize the number of allocations; rather it is to maximize th ..."
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Cited by 5 (1 self)
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The online matching problem has received significant attention in recent years because of its connections to allocation problems in Internet advertising, crowdsourcing, etc. In these realworld applications, the typical goal is not to maximize the number of allocations; rather it is to maximize the number of “successful ” allocations, where success of an allocation is governed by a stochastic process which follows the allocation. To address such applications, we propose and study the online matching problem with stochastic rewards (called the ONLINE STOCHASTIC MATCHING problem) in this paper. Our problem also has close connections to the existing literature on stochastic packing problems; in fact, our work initiates the study of online stochastic packing problems. We give a deterministic algorithm for the ONLINE STOCHASTIC MATCHING problem whose competitive ratio converges to (approximately) 0.567 for uniform and vanishing probabilities. We also give a randomized algorithm which outperforms the deterministic algorithm for higher probabilities. Finally, we complement our algorithms by giving an upper bound on the competitive ratio of any algorithm for this problem. This result shows that the best achievable competitive ratio for the ONLINE STOCHASTIC MATCHING problem is provably worse than that for the (nonstochastic) online matching problem.
On Revenue Maximization in Secondprice Ad Auctions
"... Most recent papers addressing the algorithmic problem of allocating advertisement space for keywords in sponsored search auctions assume that pricing is done via a firstprice auction, which does not realistically model the Generalized Second Price (GSP) auction used in practice. Towards the goal of ..."
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Cited by 4 (0 self)
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Most recent papers addressing the algorithmic problem of allocating advertisement space for keywords in sponsored search auctions assume that pricing is done via a firstprice auction, which does not realistically model the Generalized Second Price (GSP) auction used in practice. Towards the goal of more realistically modeling these auctions, we introduce the SecondPrice Ad Auctions problem, in which bidders’ payments are determined by the GSP mechanism. We show that the complexity of the SecondPrice Ad Auctions problem is quite different than that of the more studied FirstPrice Ad Auctions problem. First, unlike the firstprice variant, for which small constantfactor approximations are known, it is NPhard to approximate the SecondPrice Ad Auctions problem to any nontrivial factor. Second, this discrepancy extends even to the 01 special case that we call the SecondPrice Matching problem (2PM). In particular, offline 2PM is APXhard, and for online 2PM there is no deterministic algorithm achieving a nontrivial competitive ratio and no randomized algorithm achieving a competitive ratio better than 2. This stands in contrast to the results for the analogous special case in the firstprice model, the standard bipartite matching problem, which is solvable in polynomial time and which has deterministic and randomized online algorithms achieving better competitive ratios. On the positive side, we provide a 2approximation for offline 2PM and a 5.083competitive randomized algorithm for online 2PM. The latter result makes use of a new generalization of a classic result on the performance of the “Ranking” algorithm for online bipartite matching.
AdCell: Ad Allocation in Cellular Networks
"... Abstract. With more than four billion usage of cellular phones worldwide, mobile advertising has become an attractive alternative to online advertisements. In this paper, we propose a new targeted advertising policy for Wireless Service Providers (WSPs) via SMS or MMS namely AdCell. In our model, a ..."
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Abstract. With more than four billion usage of cellular phones worldwide, mobile advertising has become an attractive alternative to online advertisements. In this paper, we propose a new targeted advertising policy for Wireless Service Providers (WSPs) via SMS or MMS namely AdCell. In our model, a WSP charges the advertisers for showing their ads. Each advertiser has a valuation for specific types of customers in various times and locations and has a limit on the maximum available budget. Each query is in the form of time and location and is associated with one individual customer. In order to achieve a nonintrusive delivery, only a limited number of ads can be sent to each customer. Recently, new services have been introduced that offer locationbased advertising over cellular network that fit in our model (e.g., ShopAlerts by AT&T). We consider both online and offline version of the AdCell problem and develop approximation algorithms with constant competitive ratio. For the online version, we assume that the appearances of the queries follow a stochastic distribution and thus consider a Bayesian setting. Furthermore, queries may come from different
Offline Optimization for Online Ad Allocation (Extended Abstract)
, 2009
"... We consider online ad allocation from the perspective of optimizing delivery of a given set of ad reservations. Ad allocation naturally fits into the class of online bipartite matching problems: ad nodes are fixed, and impression (ad slot) nodes arrive one at a time, and must be assigned a qualified ..."
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We consider online ad allocation from the perspective of optimizing delivery of a given set of ad reservations. Ad allocation naturally fits into the class of online bipartite matching problems: ad nodes are fixed, and impression (ad slot) nodes arrive one at a time, and must be assigned a qualified ad upon arrival. However most previous work on online matching does not model an important aspect of ad allocation: since past site traffic is known to the the ad serving system, it can make useful forecasts about impression supply, and use those forecasts to make better serving decisions. We model these forecasts as a known distribution over ad slot types. Inspired by the “optimizeanddispatch ” architecture for expressive ad auctions (Parkes & Sandholm, 2005), we explore the use of offline optimization as way to “guide ” online decisions about ad allocation. This general approach not only leads to better allocations, it has the advantage that it can incorporate complex constraints on ad targeting or serving (e.g., fairness, scheduling, budgets) while still maintaining the robustness of an online, dynamic allocation rule. Our technical contribution focuses on maximizing a simple efficiency metric (the number of ads served). We give an algorithm that employs a novel application of the idea of the power of two choices from load balancing (Azar et al, 1999; Mitzenmacher, 2001): we compute two disjoint solutions to the expected instance, and use both of them in the online algorithm in a prescribed preference order. We prove that our algorithm achieves an approximation ratio of 0.67 when compared to the optimal “in hindsight”
Online Stochastic Matching: Beating 1 − 1 e
, 905
"... We study the online stochastic bipartite matching problem, in a form motivated by display ad allocation on the Internet. In the online, but adversarial case, the celebrated result of Karp, Vazirani and Vazirani gives an approximation ratio of 1 − 1 e ≃ 0.632, a very familiar bound that holds for man ..."
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We study the online stochastic bipartite matching problem, in a form motivated by display ad allocation on the Internet. In the online, but adversarial case, the celebrated result of Karp, Vazirani and Vazirani gives an approximation ratio of 1 − 1 e ≃ 0.632, a very familiar bound that holds for many online problems; further, the bound is tight in this case. In the online, stochastic case when nodes are drawn repeatedly from a known distribution, the greedy algorithm matches this approximation ratio, but still, no algorithm is known that beats the 1 − 1 e bound. Our main result is a 0.67approximation online algorithm for stochastic bipartite matching, breaking this 1 − 1 e barrier. Furthermore, we show that no online algorithm can produce a 1−ǫ approximation for an arbitrarily small ǫ for this problem. Our algorithms are based on computing an optimal offline solution to the expected instance, and using this solution as a guideline in the process of online allocation. We employ a novel application of the idea of the power of two choices from load balancing: we compute two disjoint solutions to the expected instance, and use both of them in the online algorithm in a prescribed preference order. To identify these two disjoint solutions, we solve a max flow problem in a boosted flow graph, and then carefully decompose this maximum flow to two edgedisjoint (near)matchings. In addition to guiding the online decision making, these two offline solutions are used to characterize an upper bound for the optimum in any scenario. This is done by identifying a cut whose value we can bound under the arrival distribution. At the end, we discuss extensions of our results to more general bipartite allocations that are important in a display ad application.