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Page 6627 of Mathematical Reviews Vol. , Issue 99j [page]

1999 Mathematical Reviews  
F. (5-MELB-EE; Parkville) A polynomial time algorithm for rectilinear Steiner trees with terminals constrained to curves. (English summary) Networks 33 (1999), no. 2, 145-155.  ...  In this paper, we show that there is a polynomial time algorithm for solving the rectilinear Steiner prob- lem for the case where terminals are constrained to lie on almost any fixed set of simple disjoint  ... 

Page 9754 of Mathematical Reviews Vol. , Issue 2003m [page]

2003 Mathematical Reviews  
Anna Rycerz (Krakow) 2003m:90106 90C27 90C60 Thomas, Doreen A. (5-MELB-UBI; Parkville) ; Weng, Jia F. (5-MELB-UBI; Parkville) Polynomial time algorithms for the rectilinear Steiner tree problem.  ...  Moreover, a polynomial-time approximation with performance ratio 2+ e for ¢ > 0 is found by using a local search technique.  ... 

Angle-Restricted Steiner Arborescences for Flow Map Layout

Kevin Buchin, Bettina Speckmann, Kevin Verbeek
2014 Algorithmica  
To capture these properties, our angle-restricted Steiner arborescences, or flux trees, connect several targets to a source with a tree of minimal length whose arcs obey a certain restriction on the angle  ...  they form with the source.  ...  We give an exact polynomial time algorithm that computes optimal spiral trees for input instances with this property.  ... 
doi:10.1007/s00453-013-9867-z fatcat:amro4knwtnafnktxd7fiwbzc6m

Angle-Restricted Steiner Arborescences for Flow Map Layout [article]

Kevin Buchin, Bettina Speckmann, Kevin Verbeek
2011 arXiv   pre-print
To capture these properties, our angle-restricted Steiner arborescences, or flux trees, connect several targets to a source with a tree of minimal length whose arcs obey a certain restriction on the angle  ...  they form with the source.  ...  We give an exact polynomial time algorithm that computes optimal spiral trees for input instances with this property.  ... 
arXiv:1109.3316v1 fatcat:6uocrwf5offmbccmaz6hwpwelm

Spanning trees short or small [article]

R. Ravi, R. Sundaram, Madhav V. Marathe, S. S. Ravi, Daniel J. Rosenkrantz
1994 arXiv   pre-print
A simple technique is used to provide a polynomial-time solution for finding k-trees of minimum diameter.  ...  Polynomial-time exact solutions are also presented for the class of decomposable graphs which includes trees, series-parallel graphs, and bounded bandwidth graphs, and for points on the boundary of a convex  ...  for points in the plane extends to the rectilinear case too.  ... 
arXiv:math/9409222v1 fatcat:4kgvq4vomzevhnqfoznyouhf5m

A simultaneous routing tree construction and fanout optimization algorithm

Amir H. Salek, Jinan Lou, Massoud Pedram
1998 Proceedings of the 1998 IEEE/ACM international conference on Computer-aided design - ICCAD '98  
The algorithm, which is based on dynamic programming, generates a rectilinear Steiner tree routing solution containing appropriately sized and placed buffers.  ...  This paper presents an optimal algorithm for solving the problem of simultaneous fanout optimization and routing tree construction for an ordered set of critical sinks.  ...  John Lillis of the University of Illinois at Chicago for providing the implementation of the PTREE algorithm and for helpful discussions about the complexity of PTREE.  ... 
doi:10.1145/288548.289098 dblp:conf/iccad/SalekLP98 fatcat:hf7gy3dzqfhmpb3fmzsjel4pna

MERLIN

Amir H. Salek, Jinan Lou, Massoud Pedram
1999 Proceedings of the 36th ACM/IEEE conference on Design automation conference - DAC '99  
The output is a hierarchical buffered rectilinear Steiner routing tree that connects the driver of a net to its sink nodes.  ...  Using a novel bottom-up construction algorithm and a local neighborhood search strategy, this method finds the best solution of the problem in an exponential size solution subspace in polynomial time.  ...  buffered routing tree structures with buffers located on the routing Steiner points, • generating and propagating three-dimensional curves to allow trade-off between required time and total buffer area  ... 
doi:10.1145/309847.309982 dblp:conf/dac/SalekLP99 fatcat:fnvz7ey2sjhtnlbcbdnjddjsyq

Multi-level Steiner Trees

Reyan Ahmed, Joseph Watkins, Alexander Wolff, Patrizio Angelini, Faryad Darabi Sahneh, Alon Efrat, David Glickenstein, Martin Gronemann, Niklas Heinsohn, Stephen G. Kobourov, Richard Spence
2019 ACM Journal of Experimental Algorithmics  
In the classical Steiner tree problem, one is given an undirected, connected graph G = (V, E) with non-negative edge costs and a set of terminals T ⊆ V .  ...  We first present two natural heuristics with approximation factor O(k). Based on these, we introduce a composite algorithm that requires 2 k Steiner tree computations.  ...  the notion of multi-level graphs to related problems (such as the node-weighted Steiner tree problem).  ... 
doi:10.1145/3368621 fatcat:xrb473shhrdu7axlsa2qrradp4

Performance optimization of VLSI interconnect layout

Jason Cong, Lei He, Cheng-Kok Koh, Patrick H. Madden
1996 Integration  
This paper presents a comprehensive survey of existing techniques for interconnect optimization during the VLSI physical design process, with emphasis on recent studies on interconnect design and optimization  ...  interconnects, including the algorithms for total wire length minimization, critical path length minimization, and delay minimization; (ii) device and interconnect sizing, including techniques for efficient  ...  For a problem with n vertices, we can construct a Voronoi diagram [45] to constrain the number of edges to be considered by the two algorithms to be linear with n.  ... 
doi:10.1016/s0167-9260(96)00008-9 fatcat:jt7444lufzaf5hxi7vg22qvvue

Hierarchical buffered routing tree generation

A.H. Salek, J. Lou, M. Pedram
2002 IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems  
The final output is a buffered rectilinear Steiner routing tree that connects the driver of a net to its sink nodes.  ...  This paper presents a solution to the problem of performance-driven buffered routing tree generation for VLSI circuits.  ...  ACKNOWLEDGEMENTS The authors wish to thank Dr. John Lillis of the University of Illinois at Chicago for helpful discussions and comments. ACKNOWLEDGEMENTS The authors wish to thank Dr.  ... 
doi:10.1109/43.998627 fatcat:ng7y37avvnao5eqbdxzwkvvliy

MESH GENERATION AND OPTIMAL TRIANGULATION [chapter]

MARSHALL BERN, DAVID EPPSTEIN
1992 Lecture Notes Series on Computing  
We discuss algorithms both for the optimization of triangulations on a xed set of vertices and for the placement of new vertices (Steiner points).  ...  The ip algorithm terminates after O(n 2 ) ips. Proof: We use the lifting relation between DTs and convex hulls.  ...  This material spans a spectrum from purely theoretical results (for example, Chazelle's linear-time triangulation algorithm), through a middle ground (our own work on Steiner triangulations), to practical  ... 
doi:10.1142/9789814355858_0002 fatcat:zjlfgakee5df7nihosmpeuhco4

MESH GENERATION AND OPTIMAL TRIANGULATION [chapter]

MARSHALL BERN, DAVID EPPSTEIN
1995 Lecture Notes Series on Computing  
We discuss algorithms both for the optimization of triangulations on a xed set of vertices and for the placement of new vertices (Steiner points).  ...  The ip algorithm terminates after O(n 2 ) ips. Proof: We use the lifting relation between DTs and convex hulls.  ...  This material spans a spectrum from purely theoretical results (for example, Chazelle's linear-time triangulation algorithm), through a middle ground (our own work on Steiner triangulations), to practical  ... 
doi:10.1142/9789812831699_0003 fatcat:ec6436f5i5bszheuiherz452ae

Recent advances in VLSI layout

E.S. Kuh, T. Ohtsuki
1990 Proceedings of the IEEE  
The influence of computer-aided physical design will continue to be felt in the future; for example, in further popularizing the sea-of-gates and building-block design styles.  ...  The latter is becoming an interesting research topic along with other hardware accelerators and specialpurpose engines.  ...  Unfortunately, the Steiner problem is NP complete. There exist simple heuristic algorithms, however, and for n 5 5 the rectilinear Steiner tree is easily found [MI.  ... 
doi:10.1109/5.52212 fatcat:ffytetht4relvc3td7j54r4neu

Who witnesses The Witness? Finding witnesses in The Witness is hard and sometimes impossible [article]

Zachary Abel, Erik D. Demaine , Jayson Lynch MIT EECS Department, Department of Mathematics, University of Kaiserslautern)
2019 arXiv   pre-print
path" for terminals on the boundary of an embedded planar graph in polynomial time.  ...  On the positive side, we give a polynomial-time algorithm for monomino clues, by reducing to hexagon clues on the boundary of the puzzle, even in the presence of broken edges, and solving "subset Hamiltonian  ...  Acknowledgments We thank Jason Ku and Quanquan Liu for helpful discussions related to this paper.  ... 
arXiv:1804.10193v4 fatcat:po3hxbl3hfg5lhnauu4uau7gsa

14th International Symposium on Mathematical Programming

1990 Mathematical programming  
If we use a decomposition approach in order to solve a minimization problem we often get an objective function in such a w a y that its domain dom 6 = n is not given explicitely to us.  ...  to the well known serious steps und null steps of bundle methods a third type of steps is used to generate the model of dom .  ...  in quasi-polynomial incremental time for any function f given by a quasi-polynomial-time oracle.  ... 
doi:10.1007/bf01580875 fatcat:3jtclwmntzgjxkqs5uecombdaa
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