Maurice Queyranne - Profile on Academia.edu (original) (raw)
Papers by Maurice Queyranne
INFORMS Journal on Computing, 1996
We study the two-level uncapacitated facility location TUFL problem. Given two types of facilitie... more We study the two-level uncapacitated facility location TUFL problem. Given two types of facilities, which w e call y-facilities and z-facilities, the problem is to decide which facilities of both types to open, and to which pair of y-and z-facilities each client should be assigned, in order to satisfy the demand at maximum pro t.
On the structure of all minimum cuts in a network and appli-cations
This paper presents a characterization of all minimum cuts, separating a source from a sink in a ... more This paper presents a characterization of all minimum cuts, separating a source from a sink in a network. A binary relation is associated with any maximum flow in this network, and minimum cuts are identified with closures for this relation. As a consequence, finding all minimum cuts reduces to a straightforward enumeration. Applications of this results arise in sensitivity and
Selected applications of minimum cuts in networks
Scheduling unit jobs with compatible release dates on parallel machines with nonstationary speeds
Lecture Notes in Computer Science, 1995
We consider the problem of nonpreemptively scheduling a set of jobs with identical processing req... more We consider the problem of nonpreemptively scheduling a set of jobs with identical processing requirements (unit jobs) on parallel machines with nonstationary speeds. In addition to the case of uniform machines, this allows for such predictable effects as ...
On the Chvátal Rank of Certain Inequalities
Lecture Notes in Computer Science, 1999
Abstract. The Chvátal rank of an inequality ax ≤ b with integral com-ponents and valid for the in... more Abstract. The Chvátal rank of an inequality ax ≤ b with integral com-ponents and valid for the integral hull of a polyhedron P, is the minimum number of rounds of Gomory-Chvátal cutting planes needed to obtain the given inequality. The Chvátal rank is at most one if b is the integral ...
bimonotone linear inequalities under certain assumptions on the sublattice. We obtain Veinott's p... more bimonotone linear inequalities under certain assumptions on the sublattice. We obtain Veinott's polyhedral representation theorem and a 0-1 version of Birkhoff's Representation Theorem as corollaries. We also point out a few potential pitfalls regarding properties of sublattices of R n .
We consider the min cut problem when capacities depend on a parameter λ. There are some classes o... more We consider the min cut problem when capacities depend on a parameter λ. There are some classes of this parametric min cut problem that are known to have the nice structural property that min cuts are nested in λ, and the nice algorithmic property that all min cuts can be computed in the same asymptotic time as a single min cut computation. We extend these results in several directions: we find three much more general classes of problems for which these two nice properties continue to hold, and we extend other results with the same flavor as well. Structural Property: Min cuts are nested in λ (see Section 1.4 for the technical definition), implying that there are only O(n) pieces to the min cut value function. Gallo, Grigoriadis, and Tarjan [16] (hereafter GGT) then showed that the monotone source-sink class of problems also satisfies an Algorithmic Property: The entire min cut value function can be computed in the same asymptotic time as a single call to an efficient max flow algorithm. GGT proved the Algorithmic Property for the FIFO variant of the Push-Relabel max flow algorithm of Goldberg and Tarjan [18]. Subsequently, Gusfield and Tardos [20] showed the same for the Max Distance variant of Push-Relabel; Babenko et al. [4] noted the same for the King, Rao, and Tarjan [25] version of Granot, McCormick, Queyranne, Tardella: Monotone parametric min cut revisited Mathematics of Operations Research xx(x), pp. xxx-xxx, c 200x INFORMS Push-Relabel; Martel [27] showed the same for Karzanov's [24] and Tarjan's Wave [45] versions of Dinic's Algorithm [9]; and Hochbaum [22]
We study the computational complexity of finding extremal principal minors of a positive definite... more We study the computational complexity of finding extremal principal minors of a positive definite matrix. In particular, we focus on the NP-hard problem of maximizing the determinant over the set of principal submatrices of a given order. This problem arises in the area of statistical design, where one wishes to select a subset of some correlated Gaussian random variables having maximum entropy. In this case, the input matrix is the covariance matrix of the random variables and the entropy is the logarithm of the determinant. \Ale establish an upper bound for the entropy, based on the eigenvalue interlacing property, and we incorporate this bound in a branch-and-bound algorithm for the exact solution for the problem. We present computational results for estimated covariance matrices corresponding to sets of environmental monitoring stations in the United States.
Finding all optimal solutions for submodular function minimization
Single Machine Scheduling with Release Dates
SIAM Journal on Discrete Mathematics, 2002
Abstract. We consider the scheduling problem of minimizing the average weighted completion time o... more Abstract. We consider the scheduling problem of minimizing the average weighted completion time of n jobs with release dates on a single machine. We first study two linear programming relaxations of the problem, one based on a time-indexed formulation, the other on a ...
Minimizing a Convex Cost Closure Set
SIAM Journal on Discrete Mathematics, 2003
Approximation Bounds for a General Class of Precedence Constrained Parallel Machine Scheduling Problems
SIAM Journal on Computing, 2006
ABSTRACT
Decompositions, Network Flows, and a Precedence Constrained Single-Machine Scheduling Problem
Operations Research, 2003
... We assume throughout that G = (N, s) does not contain a directed Hamiltonian path and that wj... more ... We assume throughout that G = (N, s) does not contain a directed Hamiltonian path and that wj > 0 for some j EN, for otherwise the scheduling problem would be trivial. ... Recall that the set Part(N) of all partitions of a set N is a lattice (Gratzer 1978). ...
On the One-Dimensional Space Allocation Problem
Operations Research, 1981
Operations Research, 1995
The Time-Dependent Traveling Salesman Problem and Its Application to the Tardiness Problem in One-Machine Scheduling
Operations Research, 1978
The time-dependent traveling salesman problem may be stated as a scheduling problem in which n jo... more The time-dependent traveling salesman problem may be stated as a scheduling problem in which n jobs have to be processed at minimum cost on a single machine. The set-up cost associated with each job depends not only on the job that precedes it, but also on its position (time) ...
Letter to the Editor—On “A ‘Hard’ Assignment Problem” by Machol and Wien
Operations Research, 1978
Operations Research, 1996
... Thus every order, say order k for item i, with size qik units of item i received at time tik,... more ... Thus every order, say order k for item i, with size qik units of item i received at time tik, must satisfy the "precise timing" conditions tik = T + yiqik where T = maxj {1tjG: t < tikI is the latest replenishment instant of any item be-fore time tik. ...
Disconnecting sets in single and two-terminal-pair networks
Networks, 1996
ABSTRACT We consider mixed networks, which may include both directed and undirected edges. For a ... more ABSTRACT We consider mixed networks, which may include both directed and undirected edges. For a nontrivial vertex subset S, an S-disconnecting set is a set of edges and vertices which intersects every path from any vertex in S to any vertex not in S. Given nonnegative edge and vertex costs, we show that the minimum cost of an S-disconnecting set defines a submodular function. This implies that the set of all S inducing minimum-cost disconnecting sets is the set of closures of a binary relation, thus extending Picard-Queyranne's (1980) result on ordinary minimum cuts. We apply this result to two-pair multicommodity problems in undirected networks, extending Hu's (1963) result to disconnecting sets that may include vertices as well as edges. These results and a result of Provan and Shier (1994) may be used for generating all sets S that induce such minimum-cost disconnecting sets and ranking such sets in order of corresponding costs, for both one-pair problems in mixed networks and two-pair problems in undirected networks. © 1996 John Wiley & Sons, Inc.
Dynamic programming: Models and applications, by Eric V. Denardo, Prentice-Hall, Englewood Cliffs, NJ, 1932, 227 pp. Price: $26.95
Networks, 1984
INFORMS Journal on Computing, 1996
We study the two-level uncapacitated facility location TUFL problem. Given two types of facilitie... more We study the two-level uncapacitated facility location TUFL problem. Given two types of facilities, which w e call y-facilities and z-facilities, the problem is to decide which facilities of both types to open, and to which pair of y-and z-facilities each client should be assigned, in order to satisfy the demand at maximum pro t.
On the structure of all minimum cuts in a network and appli-cations
This paper presents a characterization of all minimum cuts, separating a source from a sink in a ... more This paper presents a characterization of all minimum cuts, separating a source from a sink in a network. A binary relation is associated with any maximum flow in this network, and minimum cuts are identified with closures for this relation. As a consequence, finding all minimum cuts reduces to a straightforward enumeration. Applications of this results arise in sensitivity and
Selected applications of minimum cuts in networks
Scheduling unit jobs with compatible release dates on parallel machines with nonstationary speeds
Lecture Notes in Computer Science, 1995
We consider the problem of nonpreemptively scheduling a set of jobs with identical processing req... more We consider the problem of nonpreemptively scheduling a set of jobs with identical processing requirements (unit jobs) on parallel machines with nonstationary speeds. In addition to the case of uniform machines, this allows for such predictable effects as ...
On the Chvátal Rank of Certain Inequalities
Lecture Notes in Computer Science, 1999
Abstract. The Chvátal rank of an inequality ax ≤ b with integral com-ponents and valid for the in... more Abstract. The Chvátal rank of an inequality ax ≤ b with integral com-ponents and valid for the integral hull of a polyhedron P, is the minimum number of rounds of Gomory-Chvátal cutting planes needed to obtain the given inequality. The Chvátal rank is at most one if b is the integral ...
bimonotone linear inequalities under certain assumptions on the sublattice. We obtain Veinott's p... more bimonotone linear inequalities under certain assumptions on the sublattice. We obtain Veinott's polyhedral representation theorem and a 0-1 version of Birkhoff's Representation Theorem as corollaries. We also point out a few potential pitfalls regarding properties of sublattices of R n .
We consider the min cut problem when capacities depend on a parameter λ. There are some classes o... more We consider the min cut problem when capacities depend on a parameter λ. There are some classes of this parametric min cut problem that are known to have the nice structural property that min cuts are nested in λ, and the nice algorithmic property that all min cuts can be computed in the same asymptotic time as a single min cut computation. We extend these results in several directions: we find three much more general classes of problems for which these two nice properties continue to hold, and we extend other results with the same flavor as well. Structural Property: Min cuts are nested in λ (see Section 1.4 for the technical definition), implying that there are only O(n) pieces to the min cut value function. Gallo, Grigoriadis, and Tarjan [16] (hereafter GGT) then showed that the monotone source-sink class of problems also satisfies an Algorithmic Property: The entire min cut value function can be computed in the same asymptotic time as a single call to an efficient max flow algorithm. GGT proved the Algorithmic Property for the FIFO variant of the Push-Relabel max flow algorithm of Goldberg and Tarjan [18]. Subsequently, Gusfield and Tardos [20] showed the same for the Max Distance variant of Push-Relabel; Babenko et al. [4] noted the same for the King, Rao, and Tarjan [25] version of Granot, McCormick, Queyranne, Tardella: Monotone parametric min cut revisited Mathematics of Operations Research xx(x), pp. xxx-xxx, c 200x INFORMS Push-Relabel; Martel [27] showed the same for Karzanov's [24] and Tarjan's Wave [45] versions of Dinic's Algorithm [9]; and Hochbaum [22]
We study the computational complexity of finding extremal principal minors of a positive definite... more We study the computational complexity of finding extremal principal minors of a positive definite matrix. In particular, we focus on the NP-hard problem of maximizing the determinant over the set of principal submatrices of a given order. This problem arises in the area of statistical design, where one wishes to select a subset of some correlated Gaussian random variables having maximum entropy. In this case, the input matrix is the covariance matrix of the random variables and the entropy is the logarithm of the determinant. \Ale establish an upper bound for the entropy, based on the eigenvalue interlacing property, and we incorporate this bound in a branch-and-bound algorithm for the exact solution for the problem. We present computational results for estimated covariance matrices corresponding to sets of environmental monitoring stations in the United States.
Finding all optimal solutions for submodular function minimization
Single Machine Scheduling with Release Dates
SIAM Journal on Discrete Mathematics, 2002
Abstract. We consider the scheduling problem of minimizing the average weighted completion time o... more Abstract. We consider the scheduling problem of minimizing the average weighted completion time of n jobs with release dates on a single machine. We first study two linear programming relaxations of the problem, one based on a time-indexed formulation, the other on a ...
Minimizing a Convex Cost Closure Set
SIAM Journal on Discrete Mathematics, 2003
Approximation Bounds for a General Class of Precedence Constrained Parallel Machine Scheduling Problems
SIAM Journal on Computing, 2006
ABSTRACT
Decompositions, Network Flows, and a Precedence Constrained Single-Machine Scheduling Problem
Operations Research, 2003
... We assume throughout that G = (N, s) does not contain a directed Hamiltonian path and that wj... more ... We assume throughout that G = (N, s) does not contain a directed Hamiltonian path and that wj > 0 for some j EN, for otherwise the scheduling problem would be trivial. ... Recall that the set Part(N) of all partitions of a set N is a lattice (Gratzer 1978). ...
On the One-Dimensional Space Allocation Problem
Operations Research, 1981
Operations Research, 1995
The Time-Dependent Traveling Salesman Problem and Its Application to the Tardiness Problem in One-Machine Scheduling
Operations Research, 1978
The time-dependent traveling salesman problem may be stated as a scheduling problem in which n jo... more The time-dependent traveling salesman problem may be stated as a scheduling problem in which n jobs have to be processed at minimum cost on a single machine. The set-up cost associated with each job depends not only on the job that precedes it, but also on its position (time) ...
Letter to the Editor—On “A ‘Hard’ Assignment Problem” by Machol and Wien
Operations Research, 1978
Operations Research, 1996
... Thus every order, say order k for item i, with size qik units of item i received at time tik,... more ... Thus every order, say order k for item i, with size qik units of item i received at time tik, must satisfy the "precise timing" conditions tik = T + yiqik where T = maxj {1tjG: t < tikI is the latest replenishment instant of any item be-fore time tik. ...
Disconnecting sets in single and two-terminal-pair networks
Networks, 1996
ABSTRACT We consider mixed networks, which may include both directed and undirected edges. For a ... more ABSTRACT We consider mixed networks, which may include both directed and undirected edges. For a nontrivial vertex subset S, an S-disconnecting set is a set of edges and vertices which intersects every path from any vertex in S to any vertex not in S. Given nonnegative edge and vertex costs, we show that the minimum cost of an S-disconnecting set defines a submodular function. This implies that the set of all S inducing minimum-cost disconnecting sets is the set of closures of a binary relation, thus extending Picard-Queyranne's (1980) result on ordinary minimum cuts. We apply this result to two-pair multicommodity problems in undirected networks, extending Hu's (1963) result to disconnecting sets that may include vertices as well as edges. These results and a result of Provan and Shier (1994) may be used for generating all sets S that induce such minimum-cost disconnecting sets and ranking such sets in order of corresponding costs, for both one-pair problems in mixed networks and two-pair problems in undirected networks. © 1996 John Wiley & Sons, Inc.
Dynamic programming: Models and applications, by Eric V. Denardo, Prentice-Hall, Englewood Cliffs, NJ, 1932, 227 pp. Price: $26.95
Networks, 1984