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Papers by Maurice Queyranne
INFORMS Journal on Computing, 1996
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
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 ...
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 ...
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.
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 ...
SIAM Journal on Discrete Mathematics, 2003
SIAM Journal on Computing, 2006
ABSTRACT
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). ...
Operations Research, 1981
Operations Research, 1995
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) ...
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. ...
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.
INFORMS Journal on Computing, 1996
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
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 ...
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 ...
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.
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 ...
SIAM Journal on Discrete Mathematics, 2003
SIAM Journal on Computing, 2006
ABSTRACT
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). ...
Operations Research, 1981
Operations Research, 1995
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) ...
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. ...
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.