A polynomial time approximation scheme for rectilinear Steiner minimum tree construction in the presence of obstacles

Jian Liu; Ying Zhao; Eugene Shragowitz; George Karypis

doi:10.1109/ICECS.2002.1046286

A polynomial time approximation scheme for rectilinear Steiner minimum tree construction in the presence of obstacles

Jian Liu, Ying Zhao, Eugene Shragowitz, George Karypis

Computer Science and Engineering

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

9 Scopus citations

Abstract

One problem in VLSI physical designs is to route multi-terminal nets in the presence of obstacles. This paper presents a polynomial time approximation scheme for construction of a rectilinear Steiner minimum tree in the presence of obstacles. Given any m rectangular obstacles, n nodes and ε>0, the scheme finds a (1 + ε) - approximation to the optimum solution in the time n^o(1/ε), providing an alternative of previous heuristics Remark: m is assumed to be a constant, otherwise when we solve the sub-problem in a brute force manner, we cannot declare that it can be solved in constant time.

Original language	English (US)
Title of host publication	ICECS 2002 - 9th IEEE International Conference on Electronics, Circuits and Systems
Pages	781-784
Number of pages	4
DOIs	https://doi.org/10.1109/ICECS.2002.1046286
State	Published - 2002
Event	9th IEEE International Conference on Electronics, Circuits and Systems, ICECS 2002 - Dubrovnik, Croatia Duration: Sep 15 2002 → Sep 18 2002

Publication series

Name	Proceedings of the IEEE International Conference on Electronics, Circuits, and Systems
Volume	2

Other

Other	9th IEEE International Conference on Electronics, Circuits and Systems, ICECS 2002
Country/Territory	Croatia
City	Dubrovnik
Period	9/15/02 → 9/18/02

Keywords

Approximation algorithm
Guillotine cut
PTAS
Rectilinear steiner minimum tree in presence of obstacles
VLSI routing

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10.1109/ICECS.2002.1046286

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Liu, J., Zhao, Y., Shragowitz, E., & Karypis, G. (2002). A polynomial time approximation scheme for rectilinear Steiner minimum tree construction in the presence of obstacles. In ICECS 2002 - 9th IEEE International Conference on Electronics, Circuits and Systems (pp. 781-784). Article 1046286 (Proceedings of the IEEE International Conference on Electronics, Circuits, and Systems; Vol. 2). https://doi.org/10.1109/ICECS.2002.1046286

A polynomial time approximation scheme for rectilinear Steiner minimum tree construction in the presence of obstacles. / Liu, Jian; Zhao, Ying; Shragowitz, Eugene et al.
ICECS 2002 - 9th IEEE International Conference on Electronics, Circuits and Systems. 2002. p. 781-784 1046286 (Proceedings of the IEEE International Conference on Electronics, Circuits, and Systems; Vol. 2).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Liu, J, Zhao, Y, Shragowitz, E & Karypis, G 2002, A polynomial time approximation scheme for rectilinear Steiner minimum tree construction in the presence of obstacles. in ICECS 2002 - 9th IEEE International Conference on Electronics, Circuits and Systems., 1046286, Proceedings of the IEEE International Conference on Electronics, Circuits, and Systems, vol. 2, pp. 781-784, 9th IEEE International Conference on Electronics, Circuits and Systems, ICECS 2002, Dubrovnik, Croatia, 9/15/02. https://doi.org/10.1109/ICECS.2002.1046286

Liu J, Zhao Y, Shragowitz E, Karypis G. A polynomial time approximation scheme for rectilinear Steiner minimum tree construction in the presence of obstacles. In ICECS 2002 - 9th IEEE International Conference on Electronics, Circuits and Systems. 2002. p. 781-784. 1046286. (Proceedings of the IEEE International Conference on Electronics, Circuits, and Systems). doi: 10.1109/ICECS.2002.1046286

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abstract = "One problem in VLSI physical designs is to route multi-terminal nets in the presence of obstacles. This paper presents a polynomial time approximation scheme for construction of a rectilinear Steiner minimum tree in the presence of obstacles. Given any m rectangular obstacles, n nodes and ε>0, the scheme finds a (1 + ε) - approximation to the optimum solution in the time no(1/ε), providing an alternative of previous heuristics Remark: m is assumed to be a constant, otherwise when we solve the sub-problem in a brute force manner, we cannot declare that it can be solved in constant time.",

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A polynomial time approximation scheme for rectilinear Steiner minimum tree construction in the presence of obstacles

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