Linear-time computation of optimal subgraphs of decomposable graphs
Journal of Algorithms
Send-and-split method for minimum-concave-cost network flows
Mathematics of Operations Research
Complexity of finding embeddings in a k-tree
SIAM Journal on Algebraic and Discrete Methods
The steiner problem with edge lengths 1 and 2,
Information Processing Letters
A Linear-Time Algorithm for Finding Tree-Decompositions of Small Treewidth
SIAM Journal on Computing
SODA '94 Proceedings of the fifth annual ACM-SIAM symposium on Discrete algorithms
Fourier meets möbius: fast subset convolution
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
A polynomial-time approximation scheme for Steiner tree in planar graphs
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
An O(n log n) approximation scheme for Steiner tree in planar graphs
ACM Transactions on Algorithms (TALG)
The Steiner Forest Problem revisited
Journal of Discrete Algorithms
Treewidth: structure and algorithms
SIROCCO'07 Proceedings of the 14th international conference on Structural information and communication complexity
Approximation schemes for steiner forest on planar graphs and graphs of bounded treewidth
Proceedings of the forty-second ACM symposium on Theory of computing
Solving Connectivity Problems Parameterized by Treewidth in Single Exponential Time
FOCS '11 Proceedings of the 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science
Practical partitioning-based methods for the steiner problem
WEA'06 Proceedings of the 5th international conference on Experimental Algorithms
Prize-collecting Steiner problems on planar graphs
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Parameterized Complexity
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We propose a new algorithm that solves the Steiner tree problem on graphs with vertex set V to optimality in O(B"t"w"+"2^2@?tw@?|V|) time, where tw is the graph@?s treewidth and the Bell numberB"k is the number of partitions of a k-element set. This is a linear-time algorithm for graphs with fixed treewidth and a polynomial algorithm for tw@?O(log|V|/loglog|V|). While being faster than the previously known algorithms, the coloring scheme used in our algorithm can be extended to give new, improved algorithms for the prize-collecting Steiner tree as well as the k-cardinality tree problems with similar runtime bounds.