Algebraic algorithms for linear matroid parity problems
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
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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.