Abstract
Let G be an undirected graph and \(\mathcal{T}=\{T_{1},\ldots,T_{k}\}\) be a collection of disjoint subsets of nodes. Nodes in T 1∪⋅⋅⋅∪T k are called terminals, other nodes are called inner. By a \(\mathcal{T}\) -path we mean a path P such that P connects terminals from distinct sets in \(\mathcal{T}\) and all internal nodes of P are inner. We study the problem of finding a maximum cardinality collection ℘ of \(\mathcal{T}\) -paths such that at most two paths in ℘ pass through any node. Our algorithm is purely combinatorial and has the time complexity O(mn 2), where n and m denote the numbers of nodes and edges in G, respectively.
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Supported by RFBR grants 03-01-00475, 05-01-02803, and 06-01-00122.
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Babenko, M.A. A Fast Algorithm for the Path 2-Packing Problem. Theory Comput Syst 46, 59–79 (2010). https://doi.org/10.1007/s00224-008-9141-y
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DOI: https://doi.org/10.1007/s00224-008-9141-y