By Feng Pan, William S. Charlton (auth.), David L. Woodruff (eds.)

On March 15, 2002 we held a workshop on community interdiction and the extra common challenge of stochastic combined integer programming on the college of California, Davis. Jesús De Loera and that i co-chaired the development, which integrated shows of on-going examine and dialogue. on the workshop, we made up our minds to provide a quantity of well timed paintings at the issues. This quantity is the end result. each one bankruptcy represents state of the art study and them all have been refereed through top investigators within the respective fields. difficulties - sociated with holding and attacking desktop, transportation, and social networks achieve value because the global turns into extra dep- dent on interconnected structures. Optimization versions that handle the stochastic nature of those difficulties are a massive a part of the learn schedule. This paintings depends upon contemporary efforts to supply equipment for - dressing stochastic combined integer courses. The booklet is equipped with interdiction papers first and the stochastic programming papers within the moment half. a pleasant assessment of the papers is equipped within the Foreward written via Roger Wets.

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The remainder of this chapter is organized as follows. In section 2 we give a mixed-integer program for network inhibition. In section 3, we describe the pseudo-approximation algorithm in more detail and prove (pseudo)approximation bounds. In section 4 we show how to decompose the solution to the linear-programming relaxation of the mixed-integer program. In section 5 we give a geometric interpretation of the decomposition and the algorithm. Finally, in section 6 we discuss an extension 56 INTERDICTION AND STOCHASTIC PROGRAMS to the multiple-budget case and show how to efficiently find a most costeffective attack.

An undirected graph is defined similarly, except that its edges are unordered pairs from V × V. We typically use e or to denote an edge and we let and We distinguish two vertices and in V as the source and sink, respectively. , breaks all directed paths. If C is a proper superset of some cut, it is a non-minimal cut. ” The value is the weight of cut C. A minimum cut is an cut whose weight, is minimum among all cuts. All minimum cuts are minimal because edge weights are positive. 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.

This paper studies two extensions of MCP, the problem of enumerating all minimum-weight cuts in G (AMCP) and the problem of enumerating all near-minimum (minimal) cuts (ANMCP) whose weight is within a factor of of the minimum for some The main contribution of this paper is an efficient procedure for the latter extension, when is small, or for certain graph topologies. Even when not provably efficient, the algorithm shows good empirical efficiency on our test problems. A cut-enumeration algorithm is “efficient” if the amount of work per cut enumerated is polynomial in the size of G.

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