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### Network flows : theory, algorithms, and applications

Ahuja, Ravindra K, Magnanti, Thomas L, Orlin, James B
Englewood Cliffs N.J. : Prentice Hall
[1993]
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Titre: Network flows : theory, algorithms, and applications / Ravindra K. Ahuja, Thomas L. Magnanti, James B. Orlin
Auteur: Ahuja, Ravindra K; Magnanti, Thomas L; Orlin, James B
Editeur: Englewood Cliffs N.J. : Prentice Hall
Date: [1993]
Collation: XV, 846 p. : ill. ; 25 cm
Sujet RERO: Communication - Analyse de réseau - Optimisation mathématique
Note: Bibliogr.: p. 821-839. Index
Classification: DIUF 3.7
LC T57.85
Identifiant: 013617549X (ISBN); http://catalogue.bnf.fr/ark:/12148/cb374811664 (URN)
No RERO: 1876470
Permalien:
http://data.rero.ch/01-1876470/html?view=FR_V1
• Plusieurs versions

### On the hardness of finding subsets with equal average

Elkind, Edith, Orlin, James B
Information Processing Letters, 15 July 2013, Vol.113(13), pp.477-480 [Revue évaluée par les pairs]

• Plusieurs versions

### A Simple Approximation Algorithm for Computing Arrow-Debreu Prices

Ghiyasvand, Mehdi, Orlin, James B.
Operations Research, 1 September 2012, Vol.60(5), pp.1245-1248 [Revue évaluée par les pairs]

• Plusieurs versions

### Fast algorithms for convex cost flow problems on circles, lines, and trees

Orlin, James B., Vaidyanathan, Balachandran
Networks, December 2013, Vol.62(4), pp.288-296 [Revue évaluée par les pairs]

• Article
Sélectionner

### Robust optimization with incremental recourse

Cornell University
Disponible
Titre: Robust optimization with incremental recourse
Auteur: Nasrabadi, Ebrahim; Orlin, James B.
Sujet: Computer Science - Computational Complexity ; Mathematics - Optimization And Control
Description: In this paper, we consider an adaptive approach to address optimization problems with uncertain cost parameters. Here, the decision maker selects an initial decision, observes the realization of the uncertain cost parameters, and then is permitted to modify the initial decision. We treat the uncertainty using the framework of robust optimization in which uncertain parameters lie within a given set. The decision maker optimizes so as to develop the best cost guarantee in terms of the worst-case analysis. The recourse decision is incremental"; that is, the decision maker is permitted to change the initial solution by a small fixed amount. We refer to the resulting problem as the robust incremental problem. We study robust incremental variants of several optimization problems. We show that the robust incremental counterpart of a linear program is itself a linear program if the uncertainty set is polyhedral. Hence, it is solvable in polynomial time. We establish the NP-hardness for robust incremental linear programming for the case of a discrete uncertainty set. We show that the robust incremental shortest path problem is NP-complete when costs are chosen from a polyhedral uncertainty set, even in the case that only one new arc may be added to the initial path. We also address the complexity of several special cases of the robust incremental shortest path problem and the robust incremental minimum spanning tree problem.
Identifiant: 1312.4075 (ARXIV ID)
• Article
Sélectionner

### On the power of randomization in network interdiction

Bertsimas, Dimitris, Nasrabadi, Ebrahim, Orlin, James B.
Cornell University
Disponible
Titre: On the power of randomization in network interdiction
Auteur: Bertsimas, Dimitris; Nasrabadi, Ebrahim; Orlin, James B.
Sujet: Computer Science - Computer Science And Game Theory
Description: Network interdiction can be viewed as a game between two players, an "interdictor" and a "flow player". The flow player wishes to send as much material as possible through a network, while the interdictor attempts to minimize the amount of transported material by removing a certain number of arcs, say $\Gamma$ arcs. We introduce the randomized network interdiction problem that allows the interdictor to use randomness to select arcs to be removed. We model the problem in two different ways: arc-based and path-based formulations, depending on whether flows are defined on arcs or paths, respectively. We present insights into the modeling power, complexity, and approximability of both formulations. In particular, we prove that $Z_{\text{NI}}/Z_{\text{RNI}}\leq \Gamma+1$, $Z_{\text{NI}}/Z_{\text{RNI}}^{\text{Path}}\leq \Gamma+1$, $Z_{\text{RNI}}/Z_{\text{RNI}}^{\text{Path}}\leq \Gamma$, where $Z_{\text{NI}}$, $Z_{\text{RNI}}$, and $Z_{\text{RNI}}^{\text{Path}}$ are the optimal values of the network interdiction problem and its randomized versions in arc-based and path-based formulations, respectively. We also show that these bounds are tight. We show that it is NP-hard to compute the values $Z_{\text{RNI}}$ and $Z_{\text{RNI}}^{\text{Path}}$ for a general $\Gamma$, but they are computable in polynomial time when $\Gamma=1$. Further, we provide a $(\Gamma+1)$-approximation for $Z_{\text{NI}}$, a $\Gamma$-approximation for $Z_{\text{RNI}}$, and a $\big(1+\lfloor \Gamma/2\rfloor \cdot \lceil \Gamma/2\rceil/(\Gamma+1)\big)$-approximation for $Z_{\text{RNI}}^{\text{Path}}$.
Identifiant: 1312.3478 (ARXIV ID)
• Plusieurs versions

### A characterization of irreducible infeasible subsystems in flow networks

Joormann, Imke, Orlin, James B., Pfetsch, Marc E.
Networks, September 2016, Vol.68(2), pp.121-129 [Revue évaluée par les pairs]

• Plusieurs versions

### Robust monotone submodular function maximization

Orlin, James, Schulz, Andreas, Udwani, Rajan
Mathematical Programming, 2018, Vol.172(1), pp.505-537 [Revue évaluée par les pairs]

• Plusieurs versions

### Simplifications and speedups of the pseudoflow algorithm

Hochbaum, Dorit S., Orlin, James B.
Networks, January 2013, Vol.61(1), pp.40-57 [Revue évaluée par les pairs]

• Plusieurs versions

### On the power of randomization in network interdiction

Bertsimas, Dimitris, Nasrabadi, Ebrahim, Orlin, James B
Operations Research Letters, January 2016, Vol.44(1), pp.114-120 [Revue évaluée par les pairs]