A Monge property for the d-dimensional transportation problem

Bein, Wolfgang; Brucker, Peter; Park, James K.; Pathak, Pramod K.

doi:10.1016/0166-218x(93)e0121-e

Cited by 39 publications

(29 citation statements)

References 7 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…It may be possible to maximize the expectation of at least some overlap functions through a greedy algorithm. Optimality proofs would depend on higher-dimensional analogs of Monge matrices (Bein, Brucker, Park, and Pathak 1995). The d > 2 case is the subject of ongoing work.…”

Section: More Than Two Surveysmentioning

confidence: 99%

Optimizing the Expected Overlap of Survey Samples via the Northwest Corner Rule

Mach

Reiss

Şchiopu-Kratina

2006

Journal of the American Statistical Association

View full text Add to dashboard Cite

Section: More Than Two Surveysmentioning

confidence: 99%

Optimizing the Expected Overlap of Survey Samples via the Northwest Corner Rule

Mach

Reiss

Şchiopu-Kratina

2006

Journal of the American Statistical Association

View full text Add to dashboard Cite

“…Further details on the computational complexity and connections to assignment problems can be found in [30] and [17], respectively. For additional results on variants of 3D-Matching with different cost functions see [10,22,23,39,52]; for a polynomial-time solvable variant, where the cost function has the so-called Monge property, see [11] (for applications, see [19]). Now, suppose we are given such a (restricted) instance (n; X, Y, Z; W ) of 3D-Matching.…”

Section: 4mentioning

confidence: 99%

Dynamic discrete tomography

Alpers¹,

Gritzmann²

2018

Inverse Problems

View full text Add to dashboard Cite

Abstract. We consider the problem of reconstructing the paths of a set of points over time, where, at each of a finite set of moments in time the current positions of points in space are only accessible through some small number of their X-rays. This particular particle tracking problem, with applications, e.g., in plasma physics, is the basic problem in dynamic discrete tomography. We introduce and analyze various different algorithmic models. In particular, we determine the computational complexity of the problem (and various of its relatives) and derive algorithms that can be used in practice. As a byproduct we provide new results on constrained variants of min-cost flow and matching problems.

show abstract

“…Matrices with this property arise quite often in practical applications, especially in geometric settings. Note that the north-west corner rule produces an optimal solution of Hitchcock transportation problems if the cost matrix is a Monge matrix, so we can obtain an optimal solution of HTP(x p , x q ,Ĉ) by north-west corner rule [6].…”

Section: Monge Propertymentioning

confidence: 99%

Approximation Algorithm for Cycle-Star Hub Network Design Problems and Cycle-Metric Labeling Problems

Kuroki

Matsui

2017

WALCOM: Algorithms and Computation

View full text Add to dashboard Cite

Abstract. We consider a single allocation hub-and-spoke network design problem which allocates each non-hub node to exactly one of given hub nodes so as to minimize the total transportation cost. This paper deals with a case in which the hubs are located in a cycle, which is called a cycle-star hub network design problem. The problem is essentially equivalent to a cycle-metric labeling problem. The problem is useful in the design of networks in telecommunications and airline transportation systems. We propose a 2(1 − 1/h)-approximation algorithm where h denotes the number of hub nodes. Our algorithm solves a linear relaxation problem and employs a dependent rounding procedure. We analyze our algorithm by approximating a given cycle-metric matrix by a convex combination of Monge matrices.

show abstract

A Monge property for the d-dimensional transportation problem

Cited by 39 publications

References 7 publications

Optimizing the Expected Overlap of Survey Samples via the Northwest Corner Rule

Optimizing the Expected Overlap of Survey Samples via the Northwest Corner Rule

Dynamic discrete tomography

Approximation Algorithm for Cycle-Star Hub Network Design Problems and Cycle-Metric Labeling Problems

Contact Info

Product

Resources

About