Next Article in Journal
Optimization of Setting Take-Profit Levels for Derivative Trading
Previous Article in Journal
Rational Spline Image Upscaling with Constraint Parameters
Article Menu

Export Article

Open AccessArticle
Math. Comput. Appl. 2016, 21(4), 50; doi:10.3390/mca21040050

Reliable Network Interdiction Models with Multiple Unit Costs

School of Computer and Information Engineering, Fuyang Normal University, Fuyang 236037, China
*
Author to whom correspondence should be addressed.
Academic Editor: Fazal M. Mahomed
Received: 1 October 2016 / Revised: 24 November 2016 / Accepted: 29 November 2016 / Published: 14 December 2016
View Full-Text   |   Download PDF [1685 KB, uploaded 14 December 2016]   |  

Abstract

This paper proposes a reliable network interdiction model with multiple unit costs, which maximizes the minimum arrival cost of the invader to the sink by setting obstacles on some arcs with limited resources in the given network. In other words, given a graph with a source and a sink, several arcs will be selected with limited resources such that each path contains as many weights as possible. This model needs to be transferred into a bilevel program because its constraints can hardly be listed explicitly even for a graph with a moderate size, because the number of paths between any two given points increases exponentially according to the size of the graph. This bilevel model is equivalent to an integer model with a low degree number of constraints by converting the inner programming to a shortest path problem. We first prove that this problem is non-deterministic polynomial-time (NP)-hard. Secondly, we reduce the number of constraints to the first power from the exponential degree by using the dual technique. Lastly, the national railway network is used to show the feasibility of our method. View Full-Text
Keywords: bilevel program; dual program; shortest path problems; NP-completeness; knapsack problem bilevel program; dual program; shortest path problems; NP-completeness; knapsack problem
Figures

Figure 1

This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

Scifeed alert for new publications

Never miss any articles matching your research from any publisher
  • Get alerts for new papers matching your research
  • Find out the new papers from selected authors
  • Updated daily for 49'000+ journals and 6000+ publishers
  • Define your Scifeed now

SciFeed Share & Cite This Article

MDPI and ACS Style

Zhao, J.; Sun, G. Reliable Network Interdiction Models with Multiple Unit Costs. Math. Comput. Appl. 2016, 21, 50.

Show more citation formats Show less citations formats

Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Article Metrics

Article Access Statistics

1

Comments

[Return to top]
Math. Comput. Appl. EISSN 2297-8747 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top