New PDF release: Integer Programming and Combinatorial Optimization: 7th

By Karen Aardal, Robert E. Bixby (auth.), Gérard Cornuéjols, Rainer E. Burkard, Gerhard J. Woeginger (eds.)

ISBN-10: 3540487778

ISBN-13: 9783540487777

ISBN-10: 3540660194

ISBN-13: 9783540660194

This ebook constitutes the refereed complaints of the seventh overseas convention on Integer Programming and Combinatorial Optimization, IPCO'99, held in Graz, Austria, in June 1999.
The 33 revised complete papers provided have been conscientiously reviewed and chosen from a complete of ninety nine submissions. one of the subject matters addressed are theoretical, computational, and application-oriented features of approximation algorithms, department and sure algorithms, computational biology, computational complexity, computational geometry, slicing aircraft algorithms, diaphantine equations, geometry of numbers, graph and community algorithms, on-line algorithms, polyhedral combinatorics, scheduling, and semidefinite courses.

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Additional resources for Integer Programming and Combinatorial Optimization: 7th International IPCO Conference Graz, Austria, June 9–11, 1999 Proceedings

Sample text

He showed that the Lagrangian multiplier problem is a minimum convex cost network flow problem. We use his transformation as our starting point for our approach. We solve the Lagrangian multiplier problem by Solving the Convex Cost Integer Dual Network Flow Problem 33 using an adaptation of the preflow-push cost-scaling algorithm for the minimum cost flow problem due to Goldberg and Tarjan [1987] and show that a solution to the Lagrangian multiplier can be used to solve the dual network flow problem.

Wiley, New York. Bertsekas, D. P. 1979. A distributed algorithm for the assignment problem. Working Paper, Laboratory for Information and Decision Sciences, MIT, Cambridge, MA. , and R. Shamir. 1991. Convex separable minimization over partial order constraints. Report No. RRR 27-91, RUTCOR, Rutgers University, New Brunswick, NJ. 44 Ravindra K. Ahuja, Dorit S. Hochbaum, and James B. Orlin Elmaghraby, S. E. 1978. Activity Networks: Project Planning and Control by Network Models. Wiley-Interscience, New York.

T. j ∈ J, (32) i∈Sj n ci xi ≤ B, (33) i=1 0 ≤ xi , zj ≤ 1, xi ∈ {0, 1}, i ∈ I, j ∈ J i ∈ I. (34) (35) Note that one can exclude variables zj by rewriting (31)–(35) as the following equivalent nonlinear program: m max wj 1 − F (x) = j=1 (1 − xi ) (36) i∈Sj subject to (33)–(35). Set k = max{|Sj | : j ∈ J}. Denote by IP [I0 , I1 ] and LP [I0 , I1 ] the integer program (31)–(35) and its linear relaxation (31)–(34) respectively, subject to the additional constraints: xi = 0 for i ∈ I0 and xi = 1 for i ∈ I1 where I0 and I1 are disjoint subsets of I.

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Integer Programming and Combinatorial Optimization: 7th International IPCO Conference Graz, Austria, June 9–11, 1999 Proceedings by Karen Aardal, Robert E. Bixby (auth.), Gérard Cornuéjols, Rainer E. Burkard, Gerhard J. Woeginger (eds.)


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