A separator theorem for graphs with an excluded minor and its applications
STOC '90 Proceedings of the twenty-second annual ACM symposium on Theory of computing
A Linear-Time Algorithm for Finding Tree-Decompositions of Small Treewidth
SIAM Journal on Computing
Measuring the vulnerability for classes of intersection graphs
Discrete Applied Mathematics
A partial k-arboretum of graphs with bounded treewidth
Theoretical Computer Science
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Finding small balanced separators
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Treewidth: characterizations, applications, and computations
WG'06 Proceedings of the 32nd international conference on Graph-Theoretic Concepts in Computer Science
| Hi-index | 0.00 |
To control possible spills in liquid or gas transporting pipe systems, the systems are usually equipped with shutoff valves. In case of an accidental leak these valves separate the system into a number of pieces limiting the spill effect. In this paper, we consider the problem, for a given edge-weighted network representing a pipe system and for a given number of valves, to place the valves in the network in such a way that the maximum possible spill, i.e. the maximum total weight of a piece, is minimized. We show that the problem is NP-hard even if restricted to any of the following settings: (i) for series-parallel graphs and hence for graphs of treewidth two; (ii) if all edge weights equal one. If the network is a simple path, a cycle, or a tree, the problem can be solved in polynomial time. We also give a pseudo-polynomial time algorithm and a fully polynomial approximation scheme for networks of bounded treewidth.