Results 1  10
of
24
Fast greedy algorithms in mapreduce and streaming
 In SPAA
, 2013
"... Greedy algorithms are practitioners ’ best friends—they are intuitive, simple to implement, and often lead to very good solutions. However, implementing greedy algorithms in a distributed setting is challenging since the greedy choice is inherently sequential, and it is not clear how to take advant ..."
Abstract

Cited by 22 (1 self)
 Add to MetaCart
(Show Context)
Greedy algorithms are practitioners ’ best friends—they are intuitive, simple to implement, and often lead to very good solutions. However, implementing greedy algorithms in a distributed setting is challenging since the greedy choice is inherently sequential, and it is not clear how to take advantage of the extra processing power. Our main result is a powerful sampling technique that aids in parallelization of sequential algorithms. We then show how to use this primitive to adapt a broad class of greedy algorithms to the MapReduce paradigm; this class includes maximum cover and submodular maximization subject to psystem constraints. Our method yields efficient algorithms that run in a logarithmic number of rounds, while obtaining solutions that are arbitrarily close to those produced by the standard sequential greedy algorithm. We begin with algorithms for modular maximization subject to a matroid constraint, and then extend this approach to obtain approximation algorithms for submodular maximization subject to knapsack or psystem constraints. Finally, we empirically validate our algorithms, and show that they achieve the same quality of the solution as standard greedy algorithms but run in a substantially fewer number of rounds. Categories and Subject Descriptors
Dynamic resource allocation in conservation planning
 In AAAI Conference on Artificial Intelligence (AAAI
, 2011
"... Consider the problem of protecting endangered species by selecting patches of land to be used for conservation purposes. Typically, the availability of patches changes over time, and recommendations must be made dynamically. This is a challenging prototypical example of a sequential optimization pr ..."
Abstract

Cited by 14 (2 self)
 Add to MetaCart
Consider the problem of protecting endangered species by selecting patches of land to be used for conservation purposes. Typically, the availability of patches changes over time, and recommendations must be made dynamically. This is a challenging prototypical example of a sequential optimization problem under uncertainty in computational sustainability. Existing techniques do not scale to problems of realistic size. In this paper, we develop an efficient algorithm for adaptively making recommendations for dynamic conservation planning, and prove that it obtains nearoptimal performance. We further evaluate our approach on a detailed reserve design case study of conservation planning for three rare species in the Pacific Northwest of the United States. 1
Matroid Secretary Problem in the Random Assignment Model
, 2011
"... In the Matroid Secretary Problem, introduced by Babaioff et al. [5], the elements of a given matroid are presented to an online algorithm in random order. When an element is revealed, the algorithm learns its weight and decides whether or not to select it. The objective is to return a maximum weight ..."
Abstract

Cited by 11 (1 self)
 Add to MetaCart
In the Matroid Secretary Problem, introduced by Babaioff et al. [5], the elements of a given matroid are presented to an online algorithm in random order. When an element is revealed, the algorithm learns its weight and decides whether or not to select it. The objective is to return a maximum weight independent set of the matroid. There are different variants for this problem depending on the information known about the weights beforehand. In the random assignment model, a hidden list of weights is randomly assigned to the matroid ground set, independently from the random order they are revealed to the algorithm. Our main result is the first constant competitive algorithm for this version of the problem, solving an open question of Babaioff et al. Our algorithm achieves
Improved Competitive Ratios for Submodular Secretary Problems (Extended Abstract)
, 2011
"... The Classical Secretary Problem was introduced during the 60’s of the 20 th century, nobody is sure exactly when. Since its introduction, many variants of the problem have been proposed and researched. In the classical secretary problem, and many of its variant, the input (which is a set of secret ..."
Abstract

Cited by 10 (2 self)
 Add to MetaCart
(Show Context)
The Classical Secretary Problem was introduced during the 60’s of the 20 th century, nobody is sure exactly when. Since its introduction, many variants of the problem have been proposed and researched. In the classical secretary problem, and many of its variant, the input (which is a set of secretaries, or elements) arrives in a random order. In this paper we apply to the secretary problem a simple observation which states that the random order of the input can be generated by independently choosing a random continuous arrival time for each secretary. Surprisingly, this simple observation enables us to improve the competitive ratio of several known and studied variants of the secretary problem. In addition, in some cases the proofs we provide assuming random arrival times are shorter and simpler in comparison to existing proofs. In this work we consider three variants of the secretary problem, all of which have the same objective of maximizing the value of the chosen set of secretaries given a monotone submodular function f. In the first variant we are allowed to hire a set of secretaries only if it is an independent set of a given partition matroid. The second variant allows us to choose any set of up to k secretaries. In the last and third variant, we can hire any set of secretaries satisfying a given knapsack constraint.
How to crowdsource tasks truthfully without sacrificing utility: online incentive mechanisms with budget constraint
 in Proc. of IEEE INFOCOM
, 2014
"... Abstract—Mobile crowdsourced sensing (MCS) is a new paradigm which takes advantage of the pervasive smartphones to efficiently collect data, enabling numerous novel applications. To achieve good service quality for a MCS application, incentive mechanisms are necessary to attract more user participat ..."
Abstract

Cited by 10 (2 self)
 Add to MetaCart
(Show Context)
Abstract—Mobile crowdsourced sensing (MCS) is a new paradigm which takes advantage of the pervasive smartphones to efficiently collect data, enabling numerous novel applications. To achieve good service quality for a MCS application, incentive mechanisms are necessary to attract more user participation. Most of existing mechanisms apply only for the offline scenario where all users ’ information are known a priori. On the contrary, we focus on a more realistic scenario where users arrive one by one online in a random order. Based on the online auction model, we investigate the problem that users submit their private types to the crowdsourcer when arrive, and the crowdsourcer aims at selecting a subset of users before a specified deadline for maximizing the value of the services (assumed to be a nonnegative monotone submodular function) provided by selected users under a budget constraint. We design two online mechanisms, OMZ and OMG, satisfying the computational efficiency, individual rationality, budget feasibility, truthfulness, consumer sovereignty and constant competitiveness under the zero arrivaldeparture interval case and a more general case, respectively. Through extensive simulations, we evaluate the performance and validate the theoretical properties of our online mechanisms. I.
Geometry of online packing linear programs
"... Abstract. We consider packing LP’s with m rows where all constraint coefficients are normalized to be in the unit interval. The n columns arrive in random order and the goal is to set the corresponding decision variables irrevocably when they arrive to obtain a feasible solution maximizing the expe ..."
Abstract

Cited by 10 (1 self)
 Add to MetaCart
(Show Context)
Abstract. We consider packing LP’s with m rows where all constraint coefficients are normalized to be in the unit interval. The n columns arrive in random order and the goal is to set the corresponding decision variables irrevocably when they arrive to obtain a feasible solution maximizing the expected reward. Previous (1 − )competitive algorithms require the righthand side of the LP to be
Advances on Matroid Secretary Problems: Free Order Model and Laminar Case
, 2012
"... The most wellknown conjecture in the context of matroid secretary problems claims the existence of a constantfactor approximation applicable to any matroid. Whereas this conjecture remains open, modified forms of it were shown to be true, when assuming that the assignment of weights to the secreta ..."
Abstract

Cited by 7 (1 self)
 Add to MetaCart
(Show Context)
The most wellknown conjecture in the context of matroid secretary problems claims the existence of a constantfactor approximation applicable to any matroid. Whereas this conjecture remains open, modified forms of it were shown to be true, when assuming that the assignment of weights to the secretaries is not adversarial but uniformly random [19, 17]. However, so far, there was no variant of the matroid secretary problem with adversarial weight assignment for which a constantfactor approximation was found. We address this point by presenting a 9approximation for the free order model, a model suggested shortly after the introduction of the matroid secretary problem, and for which no constantfactor approximation was known so far. The free order model is a relaxed version of the original matroid secretary problem, with the only difference that one can choose the order in which secretaries are interviewed. Furthermore, we consider the classical matroid secretary problem for the special case of laminar matroids. Only recently, a constantfactor approximation has been found for this case, using a clever but rather involved method and analysis [12] that leads to a 16000/3approximation. This is arguably the most involved special case of the matroid secretary problem for which a constantfactor approximation is known. We present a considerably simpler and stronger 3 √ 3e ≈ 14.12approximation, based on reducing the problem to a matroid secretary problem on a partition matroid.
Streaming Submodular Maximization: Massive Data Summarization on the Fly
, 2014
"... How can one summarize a massive data set “on the fly”, i.e., without even having seen it in its entirety? In this paper, we address the problem of extracting representative elements from a large stream of data. I.e., we would like to select a subset of say k data points from the stream that are most ..."
Abstract

Cited by 7 (3 self)
 Add to MetaCart
How can one summarize a massive data set “on the fly”, i.e., without even having seen it in its entirety? In this paper, we address the problem of extracting representative elements from a large stream of data. I.e., we would like to select a subset of say k data points from the stream that are most representative according to some objective function. Many natural notions of “representativeness ” satisfy submodularity, an intuitive notion of diminishing returns. Thus, such problems can be reduced to maximizing a submodular set function subject to a cardinality constraint. Classical approaches to submodular maximization require full access to the data set. We develop the first efficient streaming algorithm with constant factor 1/2 − ε approximation guarantee to the optimum solution, requiring only a single pass through the data, and memory independent of data size. In our experiments, we extensively evaluate the effectiveness of our approach on several applications, including training largescale kernel methods and exemplarbased clustering, on millions of data points. We observe that our streaming method, while achieving practically the same utility value, runs about 100 times faster than previous work.
Optimal online selection of an alternating subsequence: a central limit theorem’, Adv
 in Appl. Probab
, 2014
"... Abstract. We analyze the optimal policy for the sequential selection of an alternating subsequence from a sequence of n independent observations from a continuous distribution F , and we prove a central limit theorem for the number of selections made by that policy. The proof exploits the backward ..."
Abstract

Cited by 5 (5 self)
 Add to MetaCart
Abstract. We analyze the optimal policy for the sequential selection of an alternating subsequence from a sequence of n independent observations from a continuous distribution F , and we prove a central limit theorem for the number of selections made by that policy. The proof exploits the backward recursion of dynamic programming and assembles a detailed understanding of the associated value functions and selection rules.
Secretary Problems with Convex Costs
"... We consider online resource allocation problems where given a set of requests our goal is to select a subset that maximizes a value minus cost type of objective function. Requests are presented online in random order, and each request possesses an adversarial value and an adversarial size. The onlin ..."
Abstract

Cited by 4 (1 self)
 Add to MetaCart
(Show Context)
We consider online resource allocation problems where given a set of requests our goal is to select a subset that maximizes a value minus cost type of objective function. Requests are presented online in random order, and each request possesses an adversarial value and an adversarial size. The online algorithm must make an irrevocable accept/reject decision as soon as it sees each request. The “profit ” of a set of accepted requests is its total value minus a convex cost function of its total size. This problem generalizes the socalled knapsack secretary problem and is closely related to the submodular secretary problem. Unlike previous work on secretary problems, one of the main challenges we face is that the objective function can be positive or negative and we must guard against accepting requests that look good early on but cause the solution to have an arbitrarily large cost as more requests are accepted. We study this problem under various feasibility constraints and present online algorithms with competitive ratios only a constant factor worse than those known in the absence of costs for the same feasibility constraints. We also consider a multidimensional version of the problem that generalizes multidimensional knapsack within a secretary framework. In the absence of