Send-and-split method for minimum-concave-cost network flows
Mathematics of Operations Research
Combinatorial algorithms for integrated circuit layout
Combinatorial algorithms for integrated circuit layout
Faster shortest-path algorithms for planar graphs
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Undirected single source shortest paths in linear time
FOCS '97 Proceedings of the 38th Annual Symposium on Foundations of Computer Science
The equivalence of theorem proving and the interconnection problem
ACM SIGDA Newsletter
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Let G = (V, E) be a plane graph with nonnegative edge lengths, and let N be a family of k vertex sets N1, N2, . . ., Nk ⊆ V, called nets. Then a noncrossing Steiner forest for N in G is a set T of k trees T1; T2; . . .,Tk in G such that each tree Ti ∈ T connects all vertices in Ni, any two trees in T do not cross each other, and the sum of edge lengths of all trees is minimum. In this paper we give an algorithm to find a noncrossing Steiner forest in a plane graph G for the case where all vertices in nets lie on two of the face boundaries of G. The algorithm takes time O(n log n) if G has n vertices.