The design and analysis of approximation algorithms: Facility location as a case study

Shmoys, David B.

doi:10.1090/psapm/061/2104732

Cited by 6 publications

(9 citation statements)

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“…In the first phase we determine the warehouse orders; based on that, we determine the retailer orders in the second phase, and this is done separately for each retailer. Our algorithms are based on new dependent randomized rounding techniques, that are similar in spirit to those used for the metric facility location problem (Shmoys 2004), but are able to exploit the additional special structure of the inventory model. Specifically, we show that the solution produced by the randomized algorithms has expected cost that is guaranteed to be at most 1.8 times the cost of an optimal solution to the OWMR problem.…”

Section: Levi Et Al: a Constant Approximation Algorithm For The One-mentioning

confidence: 99%

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A Constant Approximation Algorithm for the One-Warehouse Multiretailer Problem

et al. 2008

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Deterministic inventory theory provides streamlined optimization models that attempt to capture tradeoffs in managing the flow of goods through a supply chain. We will consider two well-studied deterministic inventory models, called the one-warehouse multi-retailer problem (OWMR) and its special case the joint replenishment problem (JRP), and give approximation algorithms with worst-case performance guarantees.That is, for each instance of the problem, our algorithm produces a solution with cost that is guaranteed to be at most 1.8 times the optimal cost; this is called a 1.8-approximation algorithm. Our results are based on an LP-rounding approach; we provide the first constant approximation algorithm for the OWMR problem and improve the previous results for the JRP problem.

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Section: Levi Et Al: a Constant Approximation Algorithm For The One-mentioning

confidence: 99%

“…It is interesting that the additional structure of these inventory problems is sufficient to extend some of these techniques. (For a survey on the approximation techniques that were applied to the metric facility location problem, see Shmoys (2004). )…”

Section: Levi Et Al: a Constant Approximation Algorithm For The One-mentioning

confidence: 99%

A Constant Approximation Algorithm for the One-Warehouse Multiretailer Problem

et al. 2008

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“…The first algorithm gives an approximation ratio of 4. Our approach generalizes the now classical LP-rounding algorithm for UFL, by Chudak and Shmoys [5,13]. The proof for bounding connection cost is obtained using a natural extension of the argument for UFL.…”

Section: Introductionmentioning

confidence: 98%

Approximation algorithms for the Fault-Tolerant Facility Placement problem

Chrobák

2011

Information Processing Letters

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In the Fault-Tolerant Facility Placement problem (FTFP) we are given a set of customers C, a set of sites F , and distances between customers and sites. We assume that the distances satisfy the triangle inequality. Each customer j has a demand r j and each site may open an unbounded number of facilities. The objective is to minimize the total cost of opening facilities and connecting each customer j to r j different open facilities. We present two LP-rounding algorithms for FTFP. The first algorithm achieves an approximation ratio of 4. The second algorithm uses the method of filtering to improve the ratio to 3.16.Published by Elsevier B.V.

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“…There is a large body of literature that deals with approximation algorithms for (metric) UFL, CFL and its variants; see [14] for a survey on UFL. The first constant approximation guarantee for UFL was obtained by Shmoys et al [15] via an LP-rounding algorithm, and the current state-of-the-art is a 1.488-approximation algorithm due to Li [10].…”

Section: Introductionmentioning

confidence: 99%

Improved Approximation Guarantees for Lower-Bounded Facility Location

Ahmadian

Swamy

2013

Approximation and Online Algorithms

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Abstract. We consider the lower-bounded facility location (LBFL) problem, which is a generalization of uncapacitated facility location (UFL), where each open facility is required to serve a certain minimum amount of demand. The current best approximation ratio for LBFL is 448 [17]. We substantially advance the state-of-the-art for LBFL by improving its approximation ratio from 448 [17] to 82.6. Our improvement comes from a variety of ideas in algorithm design and analysis, which also yield new insights into LBFL. Our chief algorithmic novelty is to present an improved method for solving a more-structured LBFL instance obtained from I via a bicriteria approximation algorithm for LBFL, wherein all clients are aggregated at a subset F ′ of facilities, each having at least αM co-located clients (for some α ∈ [0, 1]). The algorithm in [17] proceeds by reducing I2(α) to CFL. One of our key insights is that one can reduce the resulting LBFL instance, denoted I2(α), to a problem we introduce, called capacity-discounted UFL (CDUFL), which is a structured special case of capacitated facility location (CFL). We give a simple local-search algorithm for CDUFL based on add, delete, and swap moves that achieves a significantly-better approximation ratio than the current-best approximation ratio for CFL, which is one of the reasons behind our algorithm's improved approximation ratio.

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The design and analysis of approximation algorithms: Facility location as a case study

Cited by 6 publications

References 0 publications

A Constant Approximation Algorithm for the One-Warehouse Multiretailer Problem

A Constant Approximation Algorithm for the One-Warehouse Multiretailer Problem

Approximation algorithms for the Fault-Tolerant Facility Placement problem

Improved Approximation Guarantees for Lower-Bounded Facility Location

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