Results 1  10
of
15
Online bipartite matching with unknown distributions
 In STOC
, 2011
"... We consider the online bipartite matching problem in the unknown distribution input model. We show that the Ranking algorithm of [KVV90] achieves a competitive ratio of at least 0.653. This is the first analysis to show an algorithm which breaks the natural 1 − 1/e ‘barrier ’ in the unknown distribu ..."
Abstract

Cited by 17 (1 self)
 Add to MetaCart
We consider the online bipartite matching problem in the unknown distribution input model. We show that the Ranking algorithm of [KVV90] achieves a competitive ratio of at least 0.653. This is the first analysis to show an algorithm which breaks the natural 1 − 1/e ‘barrier ’ in the unknown distribution model (our analysis in fact works in the stricter, random order model) and answers an open question in [GM08]. We also describe a family of graphs on which Ranking does no better than 0.727 in the random order model. Finally, we show that for graphs which have k> 1 disjoint perfect matchings, Ranking achieves a competitive ratio of at least 1 −
Near Optimal Online Algorithms and Fast Approximation Algorithms for Resource Allocation Problems
, 2011
"... We present algorithms for a class of resource allocation problems both in the online setting with stochastic input and in the offline setting. This class of problems contains many interesting special cases such as the Adwords problem. In the online setting we introduce a new distributional model cal ..."
Abstract

Cited by 12 (3 self)
 Add to MetaCart
We present algorithms for a class of resource allocation problems both in the online setting with stochastic input and in the offline setting. This class of problems contains many interesting special cases such as the Adwords problem. In the online setting we introduce a new distributional model called the adversarial stochastic input model, which is a generalization of the i.i.d model with unknown distributions, where the distributions can change over time. In this model we give a 1 − O(ǫ) approximation algorithm for the resource allocation problem, with almost the weakest possible assumption: the ratio of the maximum amount of resource consumed by any single request to the total capacity of the resource, and the ratio of the profit contributed by any single request to the optimal profit is at most ǫ 2 /log(1/ǫ) 2 where n is the number of resources log n+log(1/ǫ) available. There are instances where this ratio is ǫ 2 /log n such that no randomized algorithm can have a competitive ratio of 1 − o(ǫ) even in the i.i.d model. The upper bound on ratio that we require improves on the previous upperbound for the i.i.d case by a factor of n. Our proof technique also gives a very simple proof that the greedy algorithm has a competitive ratio of 1 −1/e for the Adwords problem in the i.i.d model with unknown distributions, and more generally in the adversarial stochastic input model, when there is no bound on the bid to budget ratio. All the previous proofs assume A full version of this paper, with all the proofs, is available at
When LP is the Cure for Your Matching Woes: Improved Bounds for Stochastic Matchings (Extended Abstract)
"... Abstract. Consider a random graph model where each possible edge e is present independently with some probability pe. We are given these numbers pe, and want to build a large/heavy matching in the randomly generated graph. However, the only way we can find out whether an edge is present or not is to ..."
Abstract

Cited by 10 (3 self)
 Add to MetaCart
Abstract. Consider a random graph model where each possible edge e is present independently with some probability pe. We are given these numbers pe, and want to build a large/heavy matching in the randomly generated graph. However, the only way we can find out whether an edge is present or not is to query it, and if the edge is indeed present in the graph, we are forced to add it to our matching. Further, each vertex i is allowed to be queried at most ti times. How should we adaptively query the edges to maximize the expected weight of the matching? We consider several matching problems in this general framework (some of which arise in kidney exchanges and online dating, and others arise in modeling online advertisements); we give LProunding based constantfactor approximation algorithms for these problems. Our main results are: • We give a 5.75approximation for weighted stochastic matching on general graphs, and a 5approximation on bipartite graphs. This answers an open question from [Chen et al. ICALP 09]. • Combining our LProunding algorithm with the natural greedy algorithm, we give an improved 3.88approximation for unweighted stochastic matching on general graphs and 3.51approximation on bipartite graphs. • We introduce a generalization of the stochastic online matching problem [Feldman et al. FOCS 09] that also models preferenceuncertainty and timeouts of buyers, and give a constant factor approximation algorithm. 1
Simultaneous approximations for adversarial and stochastic online budgeted allocation problems
 In SODA
, 2012
"... Motivated by online ad allocation, we study the problem of simultaneous approximations for the adversarial and stochastic online budgeted allocation problem. This problem consists of a bipartite graph G = (X, Y, E), where the nodes of Y along with their corresponding capacities are known beforehand ..."
Abstract

Cited by 6 (1 self)
 Add to MetaCart
Motivated by online ad allocation, we study the problem of simultaneous approximations for the adversarial and stochastic online budgeted allocation problem. This problem consists of a bipartite graph G = (X, Y, E), where the nodes of Y along with their corresponding capacities are known beforehand to the algorithm, and the nodes of X arrive online. When a node of X arrives, its incident edges, and their respective weights are revealed, and the algorithm can match it to a neighbor in Y. The objective is to maximize the weight of the final matching, while respecting the capacities. When nodes arrive in an adversarial order, the best competitive ratio is known to be 1 − 1/e, and it can be achieved by the Ranking [18], and its generalizations (Balance [16, 21]). On the other hand, if the nodes arrive through a random permutation, it is possible to achieve a competitive ratio of 1 − ɛ [9]. In this paper we design algorithms that achieve a competitive ratio better than 1 − 1/e on average, while preserving a nearly optimal worst case competitive ratio. Ideally, we want to achieve the best of both worlds, i.e, to design an algorithm with the optimal competitive ratio in both the adversarial and random arrival models. We achieve this for unweighted graphs, but show that it is not possible for weighted graphs. In particular, for unweighted graphs, under some mild assumptions, we show that Balance achieves a competitive ratio of 1 − ɛ in a random permutation model. For weighted graphs, however, we prove this is not possible; we prove that no online algorithm that achieves an approximation factor of 1 − 1 e for the worstcase inputs may achieve an average approximation factor better than 97.6 % for random inputs. In light of this hardness result, we aim to design algorithms with improved approximation ratios in the random arrival in the worst case. To this end, we show the algorithm proposed by [21] achieves a competitive ratio of 0.76 for the random ratio in the worst case. model while preserving the competitive ratio of 1 − 1
Kidney exchange in dynamic sparse heterogenous pools
 In ACM Conference on Electronic Commerce (EC
, 2013
"... Current kidney exchange pools are of moderate size and thin, as they consist of many highly sensitized patients. Creating a thicker pool can be done by waiting for many pairs to arrive. We analyze a simple class of matching algorithms that search periodically for allocations. We find that if only 2 ..."
Abstract

Cited by 3 (0 self)
 Add to MetaCart
Current kidney exchange pools are of moderate size and thin, as they consist of many highly sensitized patients. Creating a thicker pool can be done by waiting for many pairs to arrive. We analyze a simple class of matching algorithms that search periodically for allocations. We find that if only 2way cycles are conducted, in order to gain a significant amount of matches over the online scenario (matching each time a new incompatible pair joins the pool) the waiting period should be “very long”. If 3way cycles are also allowed we find regimes in which waiting for a short period also increases the number of matches considerably. Finally, a significant increase of matches can be obtained by using even one nonsimultaneous chain while still matching in an online fashion. Our theoretical findings and datadriven computational experiments lead to policy recommendations.
Online stochastic matching: New algorithms with better bounds
, 2011
"... We consider variants of the online stochastic bipartite matching problem motivated by Internet advertising display applications, as introduced in Feldman et al. [6]. In this setting, advertisers express specific interests into requests for impressions of different types. Advertisers are fixed and kn ..."
Abstract

Cited by 2 (1 self)
 Add to MetaCart
We consider variants of the online stochastic bipartite matching problem motivated by Internet advertising display applications, as introduced in Feldman et al. [6]. In this setting, advertisers express specific interests into requests for impressions of different types. Advertisers are fixed and known in advance while requests for impressions come online. The task is to assign each request to an interested advertiser (or to discard it) immediately upon its arrival. In the adversarial online model, the ranking algorithm of Karp et al. [11] provides a best possible randomized algorithm with competitive ratio 1−1/e ≈ 0.632. In the stochastic i.i.d. model, when requests are drawn repeatedly and independently from a known probability distribution over the different impression types, Feldman et al. [6] prove that one can do better than 1 − 1/e. Under the restriction that the expected number of request of each impression type is an integer, they provide a 0.670competitive algorithm, later improved by Bahmani and Kapralov [3] to 0.699, and by Manshadi et al. [13] to 0.705. Without this integrality restriction, Manshadi et al. [13] are able to provide a 0.702competitive algorithm. In this paper we consider a general class of online algorithms for the i.i.d. model which improve on all these bounds and which use computationally efficient offline procedures (based on the solution of simple linear programs of maximum flow types). Under the integrality restriction on the expected number of impression types, we get a 1 − 2e−2 ( ≈ 0.729)competitive algorithm. Without this restriction, we get a 0.706competitive algorithm. Our techniques can also be applied to other related problems such as the online stochastic vertexweighted bipartite matching problem as defined in Aggarwal et al. [1]. For this problem, we obtain a 0.725competitive algorithm under the stochastic i.i.d. model with integral arrival rate. Finally we show the validity of all our results under a Poisson arrival model, removing the need to assume that the total number of arrivals is fixed and known in advance, as is required for the analysis of the stochastic i.i.d. models described above. 1
Research Statement
"... My research is primarily focused on the study of allocation problems. A common characteristic of the real world instantiations of these problems is the lack of complete and accurate information about the input. For example, in many practical settings the input may be revealed over time (streaming), ..."
Abstract
 Add to MetaCart
My research is primarily focused on the study of allocation problems. A common characteristic of the real world instantiations of these problems is the lack of complete and accurate information about the input. For example, in many practical settings the input may be revealed over time (streaming), or may be drawn from a distribution that may not even be known in advance. Alternately, the cost of acquiring the entire input may be prohibitively large making it infeasible to use conventional methods that require access to the entire input at once. Modeling and addressing these concerns has been the central theme of my work. Towards this end, I have designed approximation algorithms for several online assignment problems. I have also studied allocation problems in the stochastic paradigm. Another line of my work relates to testing the limits of approximability of various classical allocation problems under general objective functions. Streaming Input Model Online Bipartite Matching: This problem involves a bipartite graph G(L, R, E), with one side L (ads, jobs, or items to sell, in different motivating examples) known beforehand to the algorithm, and vertices from the other side R (adslots, jobcandidates, or buyers) arriving one by one online.
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 ..."
Abstract
 Add to MetaCart
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
[Extended Abstract]
"... We consider a significant generalization of the Adwords problem by allowing arbitrary concave returns, and we characterize the optimal competitive ratio achievable. The problem considers a sequence of items arriving online that have to be allocated to agents, with different agents bidding different ..."
Abstract
 Add to MetaCart
We consider a significant generalization of the Adwords problem by allowing arbitrary concave returns, and we characterize the optimal competitive ratio achievable. The problem considers a sequence of items arriving online that have to be allocated to agents, with different agents bidding different amounts. The objective function is the sum, over each agent i, of a monotonically nondecreasing concave function Mi: R+ → R+ of the total amount allocated to i. All variants of online matching problems (including the Adwords problem) studied in the literature consider the special case of budgeted linear functions, that is, functions of the form Mi(ui) = min{ui, Bi} for some constant Bi. The distinguishing feature of this paper is in allowing arbitrary concave returns. The main result of this paper is that for each concave function M, there exists a constant F (M) ≤ 1 such that • there exists an algorithm with competitive ratio of mini{F (Mi)}, independent of the sequence of items. • No algorithm has a competitive ratio larger than F (M) over all instances with Mi = M for all i. Our algorithm is based on the primaldual paradigm and makes use of convex programming duality. The upper bounds are obtained by formulating the task of finding the right counterexample as an optimization problem. This path takes us through the calculus of variations which deals with optimizing over continuous functions. The algorithm and the upper bound are related to each other via a set of differential equations, which points to a certain kind of duality between them.