Hyperbolic 0–1 programming and query optimization in information retrieval

Hansen, Pierre; Aragão, Marcus V. Poggi De; Ribeiro, Celso C.

doi:10.1007/bf01582890

Cited by 43 publications

(30 citation statements)

References 3 publications

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“…On the other extreme, when the segments are disjoint, recall that we know from van Ryzin and Liu [16,Section 6.3] that problem (6) is polynomial (e.g. see also Hammer and Rudeanu [8], and Hansen et al [9]). The following theorem establishes that the NP-Hard problem minimum vertex cover (see Garey and Johnson [7, problem GT1]) can be reduced to (6), so that our problem (6) is also NP-Hard.…”

Section: Complexity Of the Column Generation Subproblemmentioning

confidence: 99%

A Column Generation Algorithm for Choice-Based Network Revenue Management

Miranda-Bront

Méndez-Díaz

Vulcano

2009

Operations Research

275

222

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In the last few years, there has been a trend to enrich traditional revenue management models built upon the independent demand paradigm by accounting for customer choice behavior. This extension involves both modeling and computational challenges.One way to describe choice behavior is to assume that each customer belongs to a segment, which is characterized by a consideration set, i.e., a subset of the products provided by the firm that a customer views as options. Customers choose a particular product according to a multinomial-logit criterion, a model widely used in the marketing literature.In this paper, we consider the choice-based, deterministic, linear programming model (CDLP) of Gallego et al. [6], and the follow-up dynamic programming (DP) decomposition heuristic of van Ryzin and Liu [16], and focus on the more general version of these models, where customers belong to overlapping segments. To solve the CDLP for real-size networks, we need to develop a column generation algorithm. We prove that the associated column generation subproblem is indeed NP-Complete, and propose a simple, greedy heuristic to overcome the complexity of an exact algorithm. Our computational results show that the heuristic is quite effective, and that the overall approach has good practical potential and leads to high quality solutions.

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Section: Complexity Of the Column Generation Subproblemmentioning

confidence: 99%

A Column Generation Algorithm for Choice-Based Network Revenue Management

Miranda-Bront

Méndez-Díaz

Vulcano

2009

Operations Research

275

222

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“…Our new algorithm is based on the known fact that we can compute the median of a set of n elements in linear time (see, e.g., [4]); our use of median is similar to the one from [3,9]. Let us first describe the algorithm itself.…”

Section: Comment Some Preliminary Results Have Previously Appeared Imentioning

confidence: 99%

“…The only difference is in the replacement part. Namely, once we computed m, P − , P + , e − , and e + , we do the following.• If e − + e + > 1, then we replace I − with I − ∪ P − , E − with e − , and I with P + .• If e − + e + + 2∆ m < 1, then we replace I + with I + ∪ P + , E + with e + , and I with P − .• For this problem, linear-time algorithms are known; see, e.g., [3,9]. Let us show that this problem can be also solved by a simple modification of the above algorithm.…”

mentioning

confidence: 99%

Computing Population Variance and Entropy under Interval Uncertainty: Linear-Time Algorithms

2007

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“…It is possible to avoid sorting when estimating variance under interval uncertainty (see, e.g., [6], [15]), and use instead the known fact that we can compute the median of a set of n elements in linear time (see, e.g., [3]). (This use of median is similar to the one from [2], [7]. )…”

Section: Comment About the Possibility Of Linear-time Algorithmsmentioning

confidence: 94%