Approximation algorithms
The Combinatorics of Network Reliability
The Combinatorics of Network Reliability
An efficient network flow code for finding all minimum cost s-t cutsets
Computers and Operations Research
An Algorithm for Enumerating all Directed Spanning Trees in a Directed Graph
ISAAC '96 Proceedings of the 7th International Symposium on Algorithms and Computation
Scientific contributions of Leo Khachiyan (a short overview)
Discrete Applied Mathematics
Proceedings of the 3rd ACM workshop on Assurable and usable security configuration
Automating security mediation placement
ESOP'10 Proceedings of the 19th European conference on Programming Languages and Systems
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Let G=(V,E) be a (directed) graph with vertex set V and edge (arc) set E. Given a set P of source-sink pairs of vertices of G, an important problem that arises in the computation of network reliability is the enumeration of minimal subsets of edges (arcs) that connect/disconnect all/at least one of the given source-sink pairs of P. For undirected graphs, we show that the enumeration problems for conjunctions of paths and disjunctions of cuts can be solved in incremental polynomial time. Furthermore, under the assumption that P consists of all pairs within a given vertex set, we also give incremental polynomial time algorithm for enumerating all minimal path disjunctions and cut conjunctions. For directed graphs, the enumeration problem for cut disjunction is known to be NP-complete. We extend this result to path conjunctions and path disjunctions, leaving open the complexity of the enumeration of cut conjunctions. Finally, we give a polynomial delay algorithm for enumerating all minimal sets of arcs connecting two given nodes s"1 and s"2 to, respectively, a given vertex t"1, and each vertex of a given subset of vertices T"2.