Abstract
Networks form the backbone of many familiar, and economically critical, activities in our modern life, as exemplified by electrical grid systems, computer systems, telecommunication systems, and transportation systems. Network models, and associated optimization algorithms, are important in ensuring the smooth and efficient operation of such systems. In this chapter, we wish to introduce the reader to a variety of less apparent network models. Such models are drawn from application areas such as genomics, sports, artificial intelligence, and decision analysis as well as transportation and communication. Our objective is to illustrate how network modelling can be useful in formulating problems occurring in these diverse areas — problems that at first blush seem quite remote from the standard applications of networks.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
R. K. Ahuja, T. L. Magnanti, and J. B. Orlin, Network Flows: Theory, Algorithms, and Applications, Prentice-Hall, Englewood Cliffs, NJ, 1993.
R. K. Ahuja, T. L. Magnanti, J. B. Orlin, and M. R. Reddy, Applications of network optimization, in Handbooks in Operations Research and Management Science, Vol. 7, M. O. Ball et al. (eds.), Elsevier, Amsterdam, 1995, pp. 1–83.
A. Arbel, Approximate articulation of preference and priority derivation, European Journal of Operational Research 43 (1989), 317–326.
M. L. Balinksi, On a selection problem, Management Science 17 (1970), 230–231.
L. A. Belady, A study of replacement algorithms for virtual storage computers, IBM Systems Journal 5 (1966), 78–101.
R. E. Bellman and S. E. Dreyfus, Applied Dynamic Programming, Princeton University Press, Princeton, NJ, 1962.
A. Cohen and W. A. Burkhard, A proof of the optimality of the MIN paging algorithm using linear programming duality, Operations Research Letters 18 (1995), 7–13.
R. Dechter, I. Meiri, and J. Pearl, Temporal constraint networks, Artificial Intelligence 49 (1991), 61–95.
L. R. Ford, Jr. and D. R. Fulkerson, Flows in Networks, Princeton University Press, Princeton, NJ, 1962.
J. F. Gilsinn, P. B. Saunders, and M. H. Pearl, Path finding algorithms and data structures for point-to-point trip management, NBSIR 75-676, National Bureau of Standards, Washington, DC, 1975.
D. Gusfield, R. Karp, L. Wang, and P. Stelling, Graph traversals, genes and matroids: an efficient case of the travelling salesman problem, Discrete Applied Mathematics 88 (1998), 167–180.
D. S. Hochbaum, A new-old algorithm for minimum-cut and maximum-flow in closure graphs, Networks 37 (2001), 171–193.
A. J. Hoffman and T. J. Rivlin, When is a team “mathematically” eliminated?, in Princeton Symposium on Mathematical Programming, 1967, H. W. Kuhn (ed.), Princeton University Press, Princeton, NJ, 1970, pp. 391–401.
J. C. Picard, Maximal closure of a graph and applications to combinatorial problems, Management Science 22 (1976), 1268–1272.
J. M. W. Rhys, A selection problem of shared fixed costs and network flows, Management Science 17 (1970), 200–207.
L. W. Robinson, Baseball playoff eliminations: an application of linear programming, Operations Research Letters 10 (1991), 67–74.
A. A. Salo and R. P. Hämäläinen, Preference programming through approximate ratio comparisons, European Journal of Operational Research 82 (1995), 458–475.
B. L. Schwartz, Possible winners in partially completed tournaments, SIAM Review 8 (1966), 302–308.
R. E. Tarjan, Data Structures and Network Flows, SIAM, Philadelphia, 1983.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer Science+Business Media, Inc.
About this chapter
Cite this chapter
Shier, D.R. (2006). Network Modelling. In: Appa, G., Pitsoulis, L., Williams, H.P. (eds) Handbook on Modelling for Discrete Optimization. International Series in Operations Research & Management Science, vol 88. Springer, Boston, MA. https://doi.org/10.1007/0-387-32942-0_5
Download citation
DOI: https://doi.org/10.1007/0-387-32942-0_5
Publisher Name: Springer, Boston, MA
Print ISBN: 978-0-387-32941-3
Online ISBN: 978-0-387-32942-0
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)