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Abstract: : We describe a series of optimizations to Dreyfus and Wagner's dynamic program for finding a Steiner minimal tree on a graph. Our interest is in finding rectilinear Steiner minimal trees on k pins, for which the Dreyfus and Wagner algorithm runs in O(k 2 3 k ) time. The original, unoptimized, code was hopelessly I/O-bound for k ? 17, even on a workstation with 16 megabytes of main memory. Our optimized code runs twenty times faster than the original code. It is not I/O-bound even when run ... (Update)
Context of citations to this paper: More
...nodes of the tree. This allows us to use the same structure to model the memory hierarchy, which in our experience [AABCH91, TAC92, ACFS93] is crucially important for developing high performance programs. 3 Choosing a Specific Model A three step approach can be used...
...programming algorithm of Dreyfus and Wagner [3] which has time complexity O(n 2 3 n ) when applied to G. Thomborson, Alpern, and Carter [12] present some improvements to the Dreyfus Wagner algorithm that do not change the algorithm s time complexity, but do improve its...
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BibTeX entry: (Update)
C. D. Thomborson, B. Alpern, and L. Carter, Rectilinear Steiner tree minimization on a workstation, in Proceedings of the DIMACS Workshop on Computational Support for Discrete Mathematics, 1992. http://citeseer.ist.psu.edu/thomborson92rectilinear.html More
@incollection{ thomborson94rectilinear,
author = "C. D. Thomborson and B. Alpern and L. Carter",
title = "Rectilinear {Steiner} tree minimization on a workstation",
booktitle = "Computational Support for Discrete Mathematics",
volume = "15",
publisher = "American Mathematical Society",
address = "Providence, Rhode Island",
editor = "N. Dean and G. E. Shannon",
pages = "119--136",
year = "1994",
url = "citeseer.ist.psu.edu/thomborson92rectilinear.html" }
Citations (may not include all citations):113 output complexity of sorting and related problems (context) - Aggarwal, Vitter et al. - 1988
87 Random number generators: Good ones are hard to find (context) - Park, Miller - 1988
82 A Model for Hierarchical Memory (context) - Aggarwal, Alpern et al. - 1987
82 Hierarchical Memory with Block Transfer (context) - Aggarwal, Chandra et al. - 1987
68 The rectilinear Steiner tree problem is NP-complete (context) - Garey, Johnson - 1977
66 On Steiner's problem with rectilinear distance (context) - Hanan - 1966
54 complexity: The Red-Blue Pebble Game (context) - Hong, Kung - 1981
50 The Steiner problem in graphs (context) - Dreyfus, Wagner - 1972
35 Efficient and portable combined random number generators (context) - L'Ecuyer - 1988
35 Uniform memory hierarchies (context) - Alpern, Carter et al. - 1990
35 Permuting information in idealized two-level storage (context) - Floyd - 1972
30 Algorithms for parallel memory i: Two-level memories - Vitter, Shriver - 1990
14 A faster approximation algorithm for the Steiner problem in .. (context) - Wu, Widmayer et al. - 1986
14 approximation algorithm for the Steiner problem on networks .. (context) - Zelikovsky - 1991
12 Fast heuristic algorithms for rectilinear Steiner trees (context) - Richards - 1989
11 Speeding up dynamic programming - Eppstein, Galil et al. - 1988
11 Use of Steiner's problem in suboptimal routing in rectilinea.. (context) - Lee, Bose et al. - 1976
8 Rectilinear Steiner trees: Efficient special-case algorithms (context) - Aho, Garey et al. - 1977
7 Two probabilistic results on rectilinear Steiner trees (context) - Bern - 1986
7 Algorithms for parallel memory ii: Hierarchical multi-level .. - Vitter, Shriver - 1990
6 An approximation algorithm for the Steiner tree problem (context) - Berman, Ramaiyer - 1991
6 Optimal and suboptimal solution algorithms for the wiring pr.. (context) - Yang, Wing - 1972
5 algorithm for suboptimal rectilinear Steiner trees (context) - Hwang, log - 1979
5 Algorithms for special cases of rectilinear Steiner trees (context) - Agarwal, Shing - 1990
4 heuristic algorithm for the rectilinear Steiner minimal tree.. (context) - Smith, Lee et al. - 1980
4 Probabilistic partitioning algorithms for the rectilinear St.. (context) - Koml'os, Shing - 1985
3 Using partitioning and clustering techniques to generate rec.. (context) - Deneen, Dezell - 1990
3 A greedy heuristic for the rectilinear Steiner tree problem (context) - Bern, de Carvalho - 1987
3 Heuristic algorithms for rectilinear Steiner trees (context) - Servit - 1981
2 Suboptimal algorithm for a wire routing problem (context) - Yang, Wing - 1972
2 Computing a rectilinear Steiner minimal tree in n O (context) - Thomborson, Deneen et al. - 1987
1 A plane-sweep algorithm for rectilinear Steiner trees with d.. (context) - Deneen, Shute - 1990
1 New algorithms for the rectilinear Steiner tree problem (context) - Ho, Vijayan et al. - 1990
1 Design Automation and Fault Tolerant Computing (context) - Hwang, Steiner - 1978
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