Book ChapterDOI
A Survey of Integer Programming Emphasizing Computation and Relations among Models
R.S. Garfinkel,R.S. Garfinkel,George L. Nemhauser,George L. Nemhauser +3 more
- pp 77-155
TLDR
In this article, the authors discuss integer programming by emphasizing computation and relations among models and present a general enumeration algorithm for the mathematical-programming problem of integer linear program (ILP).Abstract:
Publisher Summary This chapter discusses integer programming by emphasizing computation and relations among models. Integer programming deals with the class of mathematical programming problems in which some or all of the variables are required to be integers. The chapter discusses the case in which both the objective function and constraints are linear. It describes integer linear program (ILP) models and some relationships among integer programming models and presents the classification of them according to computational complexity. A difficulty in reporting computational results is the number of different computers used. There is a problem in reporting results on approximate methods. There is virtually no point in reporting times to find a suboptimal solution without also giving its deviation from optimality. Unfortunately, for the large problems for which approximate methods are designed, optimal solutions are generally unknown. The chapter describes the most widely-used algorithms and presents a general enumeration algorithm for the mathematical-programming problem.read more
Citations
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Journal ArticleDOI
On the facial structure of set packing polyhedra
TL;DR: This paper shows that the cliques of the intersection graph provide a first set of facets for the polyhedron in question, and it is shown that the cycles without chords of odd length of the intersections graph give rise to a further set of facet.
Journal ArticleDOI
Properties of vertex packing and independence system polyhedra
TL;DR: A general class of facets of = convex hull{x∈Rn:Ax≤1m,x binary} is described which subsumes a class examined by Padberg [13].
Journal ArticleDOI
Application of 0-1 integer programming to multitarget tracking problems
TL;DR: This paper presents a new approach to the solution of multi-target tracking problems that is approached as an unsupervised pattern recognition problem and has the computational structure of the set packing and set partitioning problems of 0-1 integer programming.
Book ChapterDOI
Covering, Packing and Knapsack Problems
TL;DR: In this paper, the authors survey some of the recent results that have been obtained in connection with covering, packing, and knapsack problems formulated as linear programming problems in zero-one variables.
Journal ArticleDOI
On the Uncapacitated Plant Location Problem. I: Valid Inequalities and Facets
TL;DR: The uncapacitated plant location problem is considered as a node-packing problem where necessary and sufficient conditions for trivial facets along with necessary conditions for nontrivial facets are derived.
References
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Reducibility Among Combinatorial Problems.
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Book ChapterDOI
An Automatic Method for Solving Discrete Programming Problems
Ailsa H. Land,Alison G. Doig +1 more
TL;DR: In the late 1950s there was a group of teachers and research assistants at the London School of Economics interested in linear programming and its extensions, in particular Helen Makower, George Morton, Ailsa Land and Alison Doig.
Journal ArticleDOI
Theoretical Improvements in Algorithmic Efficiency for Network Flow Problems
Jack Edmonds,Richard M. Karp +1 more
TL;DR: New algorithms for the maximum flow problem, the Hitchcock transportation problem, and the general minimum-cost flow problem are presented, and Dinic shows that, in a network with n nodes and p arcs, a maximum flow can be computed in 0 (n2p) primitive operations by an algorithm which augments along shortest augmenting paths.