Network Interdiction and Stochastic Integer Programming by David L. Woodruff

By David L. Woodruff

The community Interdiction challenge has a wide selection of purposes in parts resembling transportation, yet extra lately and extremely prominently, it has functions within the communications sector. community Interdiction and Stochastic Integer Programming specializes in difficulties linked to maintaining and attacking computing device, transportation, and social networks. those learn components achieve significance because the international turns into extra depending on interconnected platforms. Optimization versions that handle the stochastic nature of the issues are an incredible a part of the booklet and it comprises dialogue of modern efforts to supply tools for addressing stochastic combined integer courses. The booklet is equipped with interdiction papers first and the stochastic programming papers within the moment half. See the foreword through Roger Wets for extra information at the topical assurance. every one bankruptcy represents cutting-edge examine and all chapters were rigorously peer-reviewed.

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A near-minimum minimal cut is a minimal cut whose weight is at most for some and denote the set of minimum and near-minimum (minimal) cuts, respectively. , Ahuja et al. 1993, pp. 184-185), we know that It is also well known that, given any maximum flow we can identify a minimum cut in O(m) time. A rooted tree T is a connected, acyclic, undirected graph in which one node (vertex), called the “root” and denoted by is distinguished from the others. A rooted tree, called an enumeration tree, will describe the enumeration process used for solving AMCP and ANMCP on a graph G.

2. The enumeration algorithm first finds a minimum cut at the root node (level 0), and then recursively partitions the solution space via and Once an edge of a cut at some node has been processed, it will never be processed again at any descendant node of because its status as “included” or “excluded” with Enumerating Near-Min Cuts 29 respect to the current cut has been fixed at node The branches with and correspond to searches for a new min cut by processing the edges as described. If a search is successful, it defines a productive node where a new near-min cut is identified and that cut’s unprocessed edges are recursively processed.

Gupta. The k-most vital arcs in the shortest path problem. Operations Research Letters, 8:223–227, 1989. P. K. Wood. Restricted-recourse bounds for stochastic linear programming. Operations Research, 47:943–956, 1999. K. Reed. Models for proliferation interdiction response analysis. Operations Research Department, Naval Postgraduate School, Monterey, California, 1994. S. Thesis. M. -B. Wets. L-shaped linear programs with applications to optimal control and stochastic programming. SIAM Journal on Applied Mathematics, 17:638–663, 1969.

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