Abstract
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.
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Bodlaender, H.L., Grigoriev, A., Grigorieva, N.V., Hendriks, A. (2008). The Valve Location Problem in Simple Network Topologies. In: Broersma, H., Erlebach, T., Friedetzky, T., Paulusma, D. (eds) Graph-Theoretic Concepts in Computer Science. WG 2008. Lecture Notes in Computer Science, vol 5344. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-92248-3_6
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DOI: https://doi.org/10.1007/978-3-540-92248-3_6
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