Efficient spare allocation in reconfigurable arrays

Kuo, Sy‐Yen; Fuchs, W. Kent

doi:10.1145/318013.318075

Cited by 44 publications

(82 citation statements)

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“…To establish the hardness result, we begin with a lemma, which applies a result obtained by Kuo and Fuchs (1987), where the authors studied the problem of optimally reconfiguring processer arrays with faulty cells.…”

Section: Hardness Resultsmentioning

confidence: 99%

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Worst-Case Analysis of Process Flexibility Designs

Simchi‐Levi

Wei

2015

Operations Research

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Authors are encouraged to submit new papers to INFORMS journals by means of a style file template, which includes the journal title. However, use of a template does not certify that the paper has been accepted for publication in the named journal. INFORMS journal templates are for the exclusive purpose of submitting to an INFORMS journal and should not be used to distribute the papers in print or online or to submit the papers to another publication. Theoretical studies of process flexibility designs have mostly focused on expected sales. In this paper, Worstwe take a different approach by studying process flexibility designs from the worst-case point of view. To study the worst-case performances, we introduce the plant cover indices (PCIs), defined by bottlenecks in flexibility designs containing a fixed number of products. We prove that given a flexibility design, a general class of worst-case performance measures can be expressed as functions of the design's PCIs and the given uncertainty set. This result has several major implications. First, it suggests a method to compare the worstcase performances of different flexibility designs without the need to know the specifics of the uncertainty sets. Second, we prove that under symmetric uncertainty sets and a large class of worst-case performance measures, the long-chain, a celebrated sparse design, is superior to a large class of sparse flexibility designs including any design that has a degree of two on each of its product nodes. Third, we show that under stochastic demand, the classical Jordan and Graves (JG) index can be expressed as a function of the PCIs.Furthermore, the PCIs motivate a modified JG index that is shown to be more effective in our numerical study. Finally, the PCIs lead to a heuristic for finding sparse flexibility designs that perform well under expected sales and have lower risk measures in our computational study.

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Section: Hardness Resultsmentioning

confidence: 99%

“…Consider the case c i = 1 for all 1 ≤ i ≤ m. In this case, note that δ k (A ) ≤ t if and only if there is a vertex cover Kuo and Fuchs (1987) proved that it is NP-hard to determine if there exists such a vertex cover. Thus, we have that determining whether δ k (A ) ≤ t is NP-hard.…”

Section: Lemma 2 Given Non-negative Integers K T and Some Flexibilimentioning

confidence: 99%

Worst-Case Analysis of Process Flexibility Designs

Simchi‐Levi

Wei

2015

Operations Research

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“…We show that if the CNP on the complements of bipartite graphs can be solved in polynomial time, then the constrained vertex cover problem on bipartite graphs (CVCB), which is N P -complete [16], can also be solved in polynomial time. The CVCB is the following problem: given a bipartite graph H = (V 1 , V 2 ; E) and two nonnegative integers k 1 ≤ |V 1 |, k 2 ≤ |V 2 |, determine whether there is a vertex cover of H containing at most (equivalently, exactly) k 1 nodes from V 1 and at most (equivalently, exactly) k 2 nodes from V 2 .…”

Section: Proposition 8 the Cnp Is N P -Hard Even On The Complements Omentioning

confidence: 99%

Identifying critical nodes in undirected graphs: Complexity results and polynomial algorithms for the case of bounded treewidth

Addis

Summa

Grosso

2013

Discrete Applied Mathematics

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“…Note that all intractability results for Basic Homogeneous Team Formation imply intractability results for the more general Homogeneous Team Formation. Membership in NP is easy to see: Guessing a mapping ϕ of the rows from M to pattern vectors from P , it is easy to verify in polynomial time that ϕ is consistent, fulfills the size constraints, and has cost at most s. In the following, we provide a polynomial-time many-one reduction from the NP-complete Constrained Bipartite Vertex Cover problem [19] to show NP-hardness for Basic Homogeneous Team Formation with m = 2.…”

Section: Intractability Resultsmentioning

confidence: 99%

“…Proof We provide a polynomial-time many-to-one reduction from the NPcomplete Constrained Bipartite Vertex Cover [19] problem. A vertex cover of a graph G = (V, E) is a set S ⊆ V of vertices such that for every {u, v} ∈ E it holds that u ∈ S or v ∈ S.…”

Section: Intractability Resultsmentioning

confidence: 99%

Using Patterns to Form Homogeneous Teams

et al. 2013

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Homogeneous team formation is the task of grouping individuals into teams, each of which consists of members who fulfill the same set of prespecified properties. In this theoretical work, we propose, motivate, and analyze a combinatorial model where, given a matrix over a finite alphabet whose rows correspond to individuals and columns correspond to attributes of individuals, the user specifies lower and upper bounds on team sizes as well as combinations of attributes that have to be homogeneous (that is, identical) for all members of the corresponding teams. Furthermore, the user can define a cost for assigning any individual to a certain team. We show that some special cases of our new model lead to NP-hard problems while others allow for (fixed-parameter) tractability results. For example, the problem is already That version concentrates on the anonymization aspects of the model. In our new version we slightly extend our model and show how it applies to (homogeneous) clustering of individuals, that is, to homogeneous team formation. Indeed, we now claim that the models and ideas better fit with these applications than with the previous data anonymization motivation. Apart from full proofs omitted in the extended abstract and also adapting our old ideas to the new extended model, the current article also contains a new and easier proof of NP-hardness, a new proof for showing that polynomial-time data reduction in term of so-called polynomial-size problem kernels is unlikely to exist with respect to certain parameterizations, and a new algorithm for the (still NP-hard) special case ignoring costs. Many of the new findings are part of the diploma thesis [18] NP-hard even if (i) there are no lower and upper bounds on the team sizes, (ii) all costs are zero, and (iii) the matrix has only two columns. In contrast, the problem becomes fixed-parameter tractable for the combined parameter "number of possible teams" and "number of different individuals", the latter being upper-bounded by the number of rows.

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Efficient spare allocation in reconfigurable arrays

Cited by 44 publications

References 0 publications

Worst-Case Analysis of Process Flexibility Designs

Worst-Case Analysis of Process Flexibility Designs

Identifying critical nodes in undirected graphs: Complexity results and polynomial algorithms for the case of bounded treewidth

Using Patterns to Form Homogeneous Teams

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