Incremental Network Optimization: Theory and Algorithms

Authors:
Onur Şeref;Ravindra K. Ahuja;James B. Orlin
Affiliations:
Department of Business Information Technology, Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24061;Department of Industrial and Systems Engineering, University of Florida, Gainesville, Florida 32611;Sloan School of Management, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
Venue:
Operations Research
Year:
2009

Citing 13
Cited 0

Matching is as easy as matrix inversion

Combinatorica
A study of user interface aids for model-oriented decision support systems

Management Science
Network flows: theory, algorithms, and applications

Network flows: theory, algorithms, and applications
Toward a Theory of Continuous Improvement and the Learning Curve

Management Science
Process Improvement, Quality, and Learning Effects

Management Science
A minimum spanning tree algorithm with inverse-Ackermann type complexity

Journal of the ACM (JACM)
Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control and Artificial Intelligence

Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control and Artificial Intelligence
Local Search in Combinatorial Optimization

Local Search in Combinatorial Optimization
A survey of very large-scale neighborhood search techniques

Discrete Applied Mathematics
Toward Comprehensive Real-Time Bidder Support in Iterative Combinatorial Auctions

Information Systems Research
Professional Decision Modeling: Practitioner as Professor

Interfaces
Multicommodity network flow approach to the railroad crew-scheduling problem

IBM Journal of Research and Development - Business optimization
Solving Real-Life Railroad Blocking Problems

Interfaces

Quantified Score

Hi-index	0.00

Visualization

Abstract

In an incremental optimization problem, we are given a feasible solution x0 of an optimization problem P, and we want to make an incremental change in x0 that will result in the greatest improvement in the objective function. In this paper, we study the incremental optimization versions of six well-known network problems. We present a strongly polynomial algorithm for the incremental minimum spanning tree problem. We show that the incremental minimum cost flow problem and the incremental maximum flow problem can be solved in polynomial time using Lagrangian relaxation. We consider two versions of the incremental minimum shortest path problem, where increments are measured via arc inclusions and arc exclusions. We present a strongly polynomial time solution for the arc inclusion version and show that the arc exclusion version is NP-complete. We show that the incremental minimum cut problem is NP-complete and that the incremental minimum assignment problem reduces to the minimum exact matching problem, for which a randomized polynomial time algorithm is known.