## Version Description Responsibility Date Comments (2010)

### BibTeX

@MISC{10versiondescription,

author = {},

title = {Version Description Responsibility Date Comments},

year = {2010}

}

### OpenURL

### Abstract

Versioning and contribution history

### Citations

8543 |
Introduction to Algorithms
- Cormen, Leiserson, et al.
- 1990
(Show Context)
Citation Context ... Large Tableau 4.2.3 Two-Phase Simplex with Just One Artificial Variable Note that Program (4.3) has an obvious initial solution x ′ = 0 and y = b ′ , but requires the introduction of m variables. In =-=[23, 5]-=- an auxiliary linear program is introduced that will find either an initial feasible solution, or conclude that there is no solution at all, while introducing only one artificial variable. An initial ... |

636 |
An Introduction to Parallel Algorithms
- JAJA
- 1992
(Show Context)
Citation Context ...om values, pre-computation of all these random values eliminates ⌈log(m)⌉ρ ′ rounds. Protocols that compute the minimum in less steps (and hence less rounds) can be obtained using standard techniques =-=[9]-=-, as shown in [22]. These techniques are rather inefficient for secure computation, because they increase substantially the number of comparisons and the comparison protocols are complex. However, a l... |

347 | Introduction to Linear Optimization. Athena Scientific - Bertsimas, Tsitsiklis - 1997 |

143 | Linear Programming: Foundations and Extensions
- Vanderbei
- 1996
(Show Context)
Citation Context ... Large Tableau 4.2.3 Two-Phase Simplex with Just One Artificial Variable Note that Program (4.3) has an obvious initial solution x ′ = 0 and y = b ′ , but requires the introduction of m variables. In =-=[23, 5]-=- an auxiliary linear program is introduced that will find either an initial feasible solution, or conclude that there is no solution at all, while introducing only one artificial variable. An initial ... |

115 |
Non-Cryptographic Fault-Tolerant Computing
- Bar-Ilan, Beaver
- 1989
(Show Context)
Citation Context ...s then Y ′ has a one in the first entry while the other entries are zero and if y0 is in the basis at position ℓ, then all entries of Y ′ are equal to zero except for Y ′ ℓ+1 = Yℓ =[Sℓ = m + n + 1] = =-=[1]-=-. It follows that R ′ = Y ′ T ′ is equal to row ℓ of T (with a zero appended on the left) if y0 is in the basis of the optimum at position ℓ. And R is equal to the first row of T ′ if y0 is not in the... |

28 |
Numerical Recipes in C (2nd ed.): The art of scientific computing
- Press, Teukolsky, et al.
- 1992
(Show Context)
Citation Context ...iverable secureSCM Cryptographic Aspects D3.2 Protocol Description V2 Project No. FP7-213531 WP No. WP3 Date January 2010 3.2 Implementations of the Simplex Algorithm Recall that simplex-type methods =-=[14]-=- to solve linear programs take as input an LP in canonical form, i.e., programs of the form (3.2): max fx subject to Ax ≤ b x ≥ 0 . Furthermore, like the Basic Simplex Method as described in Section 3... |

20 |
Supply chain modelling using simulation
- Chang, Makatsoris
- 2001
(Show Context)
Citation Context ...echnical term to denote the process of transforming some resource or raw material into a consumer product. Figures 1 and 2 show examples of supply chains. Figure 1: Example of a supply chain, Source: =-=[4]-=- Figure 2: Example of a supply chain, Source: http://www.soc.duke.edu/˜s142tm12/ PUBLIC 1.0 (Jump to Contents Protocols) Page 10/127STREP-Project WPTitle Deliverable secureSCM Cryptographic Aspects D... |

11 | Primitives and Applications for Multi-party Computation
- Toft
- 2007
(Show Context)
Citation Context ...nd no information can be extracted from what a (possible collusion of) participant(s) see. In the literature, there are two solutions present: Li and Atallah’s protocol in [10] and Toft’s protocol in =-=[22]-=-. Both protocols implement an integer variant of classic simplex1 securely in the passive case. The main differences between the protocols are that Li and Atallah’s protocol is designed for two partie... |

10 | Secure computation with fixed-point numbers
- Catrina, Saxena
- 2010
(Show Context)
Citation Context ... algorithm and adequate accuracy of the output. Note that the performance of division protocols can be improved if we drop the requirement to efficiently compute many operations with the same divisor =-=[3]-=-. We first observe that if the divisor is public, division can be immediately computed using fixed-point multiplication, e.g., ˜y =1/ ˜b andthen[z] =TruncPr([a]y, f). We focus on the case when the div... |

10 | Atallah,“Secure and private collaborative linear programming
- Li, J
- 2006
(Show Context)
Citation Context ...ipant follows the protocol and no information can be extracted from what a (possible collusion of) participant(s) see. In the literature, there are two solutions present: Li and Atallah’s protocol in =-=[10]-=- and Toft’s protocol in [22]. Both protocols implement an integer variant of classic simplex1 securely in the passive case. The main differences between the protocols are that Li and Atallah’s protoco... |

9 | Pivot Rules for Linear Programming - Terlaky, Zhang - 1993 |

6 | Enumeration of all extreme equilibria of bimatrix games with integer pivoting and improved degeneracy check
- Rosenberg
- 2005
(Show Context)
Citation Context ...tion. This is, however, very time consuming. Much more efficient approaches are known in the literature. We will describe them briefly in the Section 3.2. For a detailed description we refer to [2] or=-=[16]-=-. Basically, the intuition is as follows. Given Program (3.3) and a basic feasible solution x with associated basis matrix B and basis index set S, one can easily check that by construction the column... |

4 |
Multiparty comparison – An improved multiparty protocol for comparison of secret-shared values
- Reistad
- 2009
(Show Context)
Citation Context ...y of all these protocols is summarized in Section 5.5.4. The constant-round variant of BitLT is called BitLTC, a protocol for bitwise integer comparison. The protocol is based on an idea presented in =-=[15]-=-. BitLTC has lower round complexity than BitLT. The communication complexity is higher, but 75% of it is due to operations that can be precomputed (33% of the rounds). Constant-rounds secure compariso... |

4 |
Secure Computation Models and Frameworks. Deliverable D9.1, SecureSCM project
- SecureSCM
- 2008
(Show Context)
Citation Context ...the black box in addition to the information implied by the output one gets from the black box. Our goal is to implement this black box by means of Secure multiparty Computation (see Deliverable D9.1 =-=[18]-=-). More precisely, suppose n companies C1,...,Cn, having private data x1,...,xn respectively, wish to evaluate fi(x1,...,xn) fori =1,...,n, then by means of Secure multiparty Computation every company... |

3 |
Hazards in full-disclosure supply chains
- Frati, Damiani, et al.
- 2008
(Show Context)
Citation Context ...obfuscate the shared parameters, the risk must be correlated to the range obtainable from the leakages exploitation. A comprehensive discussion on the relation between risk and payoff can be found in =-=[8]-=- and[19] underline that managing a supply chain implies the resolution of a social dilemma [11]. Actually, each partner participates in the coalition with their own objectives, which need to be concil... |

3 |
Happy together?: Insights and implications of viewing managed supply chains as a social dilemma
- McCarter, Northcraft
- 2007
(Show Context)
Citation Context ...leakages exploitation. A comprehensive discussion on the relation between risk and payoff can be found in [8] and[19] underline that managing a supply chain implies the resolution of a social dilemma =-=[11]-=-. Actually, each partner participates in the coalition with their own objectives, which need to be conciliated with the common good of the coalition. We can assume that individual partners will be wil... |

3 |
Coordinating supply chain decisions: an optimization model, volume 24
- Lanzenauer, Pilz-Glombik
(Show Context)
Citation Context ...tion can induce an assessment on the part of each partner, for their own profitability. In other words, if revealed, this information can lead to non-cooperative behavior on the part of some partners =-=[24]-=-. The outcome of the analysis in [8] is that it is convenient to misrepresent things, when the probability is localized otherwise, misrepresentation, on average, makes things worse. For our case, this... |

2 |
Parallelizing secure linear programming
- Deitos, Kerschbaum
(Show Context)
Citation Context ...c result it followed that with respect to the round and communication complexity, both parallelization techniques are almost equivalent. We will not repeat this discussion in this report but refer to =-=[6]-=- instead. PUBLIC 1.0 (Jump to Contents Protocols) Page 8/127STREP-Project WPTitle Deliverable secureSCM Cryptographic Aspects D3.2 Protocol Description V2 Project No. FP7-213531 WP No. WP3 Date Janua... |

2 |
An overview on the simplex algorithm
- Nabli
- 2009
(Show Context)
Citation Context ...roject WPTitle Deliverable secureSCM Cryptographic Aspects D3.2 Protocol Description V2 Project No. FP7-213531 WP No. WP3 Date January 2010 Figure 7: Experimental comparison between variants, source: =-=[12]-=- (4.7) in its first phase: max −y0 subject to ⎡ ⎢ ⎣ A Im ⎤ ⎡ −1 x ⎥ . ⎦ ⎣ x −1 s ⎤ ⎦ = b y0 x, xs ,y0 ≥ 0 . Recall furthermore that by Remark 8 this variant of the Two-Phase Simplex performs the follo... |

2 |
Centralised and decentralised supply chain planning
- Pibernik, Sucky
(Show Context)
Citation Context ...e Deliverable secureSCM Cryptographic Aspects D3.2 Protocol Description V2 Project No. FP7-213531 WP No. WP3 Date January 2010 2.1 Mathematical Representation of a Supply Chain We use the notation of =-=[13]-=-. A supply chain is represented with a restricted acyclic directed graph of ℓ levels. Each level i ∈ [1..ℓ] denotes a process and contains ni nodes with ni ≥ 1. Nodes at level ℓ represent customers. O... |

2 |
Aerospace Scenario Requirements. Deliverable D1.1, SecureSCM project
- SecureSCM
- 2008
(Show Context)
Citation Context ...companies in the chain acts with respect to their local data only. Areas in which collaborative supply chain management will lead to improved performance of the supply chain are (see Deliverable D1.1 =-=[17]-=-) product development and supply and demand management. Inorder to enable collaborative supply chain management, the companies in the supply chain need to provide their private data. Unfortunately, th... |