论文信息 - Polynomially solvable special cases of the Steiner problem in planar networks

Polynomially solvable special cases of the Steiner problem in planar networks

We give polynomial-time algorithms for two special cases of the Steiner problem: (1) the underlying network is planar and all terminals lie within a bounded number of "layers" of a single face, and (2) the problem is the rectilinear Steiner problem and the number of rectilinear convex hulls in the entire "onion" of convex hulls is bounded. Our algorithms build on well-known dynamic programming algorithms. For the second problem, we also use some geometric arguments.

Marshall W. Bern | Daniel Bienstock

[1] Warren D. Smith. Studies in computational geometry motivated by mesh generation , 1989 .

[2] Pawel Winter,et al. Steiner problem in networks: A survey , 1987, Networks.

[3] M. Hanan,et al. On Steiner’s Problem with Rectilinear Distance , 1966 .

[4] S. E. Dreyfus,et al. The steiner problem in graphs , 1971, Networks.

[5] J. S. Provan. Convexity and the Steiner tree problem , 1988, Networks.

[6] Clyde L. Monma,et al. Send-and-Split Method for Minimum-Concave-Cost Network Flows , 1987, Math. Oper. Res..

[7] Marshall W. Bern,et al. Faster exact algorithms for steiner trees in planar networks , 1990, Networks.

[8] Clark Thomborson,et al. Computing a Rectilinear Steiner Minimal Tree in nO(sqrt(n)) Time , 1987, Parallel Algorithms and Architectures.

[9] J. Scott Provan. An Approximation Scheme for Finding Steiner Trees with Obstacles , 1988, SIAM J. Comput..

[10] David S. Johnson,et al. Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[11] Clyde L. Monma,et al. On the Complexity of Covering Vertices by Faces in a Planar Graph , 1988, SIAM J. Comput..