note

Placement and Routing for Tile-based Field-coupled Nanocomputing Circuits Is NP-complete (Research Note)

Authors:

Frank Sill Torres,

Rolf DrechslerAuthors Info & Claims

ACM Journal on Emerging Technologies in Computing Systems (JETC), Volume 15, Issue 3

Article No.: 29, Pages 1 - 10

https://doi.org/10.1145/3312661

Published: 22 April 2019 Publication History

Abstract

Field-coupled Nanocomputing (FCN) technologies provide an alternative to conventional CMOS-based computation technologies and are characterized by intriguingly low-energy dissipation. Accordingly, their design received significant attention in the recent past. FCN circuit implementations like Quantum-dot Cellular Automata (QCA) or Nanomagnet Logic (NML) have already been built in labs and basic operations such as inverters, Majority, AND, OR, and so on, are already available. The design problem basically boils down to the question of how to place basic operations and route their connections so that the desired function results while, at the same time, further constraints (related to timing, clocking, path lengths, etc.) are satisfied. While several solutions for this problem have been proposed, interestingly no clear understanding about the complexity of the underlying task exists thus far. In this research note, we consider this problem and eventually prove that placement and routing for tile-based FCN circuits is NP-complete. By this, we provide a theoretical foundation for the further development of corresponding design methods.

References

[1]

N. G. Anderson and S. Bhanja. 2014. Field-coupled Nanocomputing: Paradigms, Progress, and Perspectives (1st ed.). Springer, New York.

[2]

Valentina Arima, Matteo Iurlo, et al. 2012. Toward quantum-dot cellular automata units: Thiolated-carbazole linked bisferrocenes. Nanoscale 4, 3 (2012), 813--823.

[3]

Therese C. Biedl. 1996. Improved orthogonal drawings of 3-graphs. In Proceedings of the CCCG. 295--299.

Digital Library

[4]

C. A. T. Campos, A. L. P. Marciano, O. P. V. Neto, and F. S. Torres. 2016. USE: A universal, scalable, and efficient clocking scheme for QCA. Trans. Comput.-Aided Design 35, 3 (2016), 513--517.

Digital Library

[5]

Moon Jung Chung. 1987. O(n<sup>2.5</sup>) time algorithms for the subgraph homeomorphism problem on trees. J. Algor. 8, 1 (1987), 106--112.

Digital Library

[6]

L. De Moura and N. Bjørner. 2008. Z3: An efficient SMT solver. In Proceedings of the TACAS/ETAPS. 4.

Digital Library

[7]

I. Eichwald, A. Bartel, J. Kiermaier, S. Breitkreutz, G. Csaba, D. Schmitt-Landsiedel, and M. Becherer. 2012. Nanomagnetic logic: Error-free, directed signal transmission by an inverter chain. IEEE Trans. Magn. 48, 11 (2012), 4332--4335.

[8]

E. Fazzion, O. L. Fonseca, J. A. M. Nacif, O. P. V. Neto, A. O. Fernandes, and D. S. Silva. 2014. A quantum-dot cellular automata processor design. In Proceedings of the SBCCI.

Digital Library

[9]

Steven Fortune, John Hopcroft, and James Wyllie. 1980. The directed subgraph homeomorphism problem. Theor. Comput. Sci. 10, 2 (1980), 111--121.

[10]

Michael R. Garey and David S. Johnson. 1979. Computers and Intractability—A Guide to the Theory of NP-completeness. W. H. Freeman.

Digital Library

[11]

D. Giri, G. Causapruno, and F. Riente. 2018. Parallel and serial computation in nanomagnet logic: An overview. Trans. Very Large Scale Integr. 26, 8 (2018), 1427--1437.

[12]

D. Giri, M. Vacca, G. Causapruno, M. Zamboni, and M. Graziano. 2016. Modeling, design, and analysis of MagnetoElastic NML circuits. IEEE Trans. Nanotechnol. 15, 6 (Nov. 2016), 977--985.

Digital Library

[13]

K. Hennessy and C. S. Lent. 2001. Clocking of molecular quantum-dot cellular automata. J. Vac. Sci. Technol. B 19, 5 (2001), 1752--1755.

[14]

J. Huang, M. Momenzadeh, L. Schiano, M. Ottavi, and F. Lombardi. 2005. Tile-based QCA design using majority-like logic primitives. J. Emerg. Technol. Comput. 1, 3 (2005), 163--185.

Digital Library

[15]

Taleana R. Huff, Hatem Labidi, et al. 2017. Atomic white-out: Enabling atomic circuitry through mechanically induced bonding of single hydrogen atoms to a silicon surface. ACS Nano 11, 9 (2017), 8636--8642.

[16]

Alon Itai, Christos H. Papadimitriou, and Jayme Luiz Szwarcfiter. 1982. Hamilton paths in grid graphs. SIAM J. Comput. 11, 4 (1982), 676--686.

Digital Library

[17]

M. Kianpour and R. Sabbaghi-Nadooshan. 2014. A novel quantum-dot cellular automata CLB of FPGA. J. Comput. Electron. 13, 3 (2014), 709--725.

Digital Library

[18]

Andrea S. LaPaugh and Ronald L. Rivest. 1980. The subgraph homeomorphism problem. J. Comput. Syst. Sci. (1980), 133--149.

[19]

C. S. Lent and P. D. Tougaw. 1997. A device architecture for computing with quantum dots. Proc. IEEE 85, 4 (1997), 541--557.

[20]

Andrzej Lingas and Martin Wahlen. 2009. An exact algorithm for subgraph homeomorphism. J. Discrete Algor. 7, 4 (2009), 464--468.

Digital Library

[21]

Jiří Matoušek and Robin Thomas. 1992. On the complexity of finding iso-and other morphisms for partial k-trees. Discrete Math. 108, 1--3 (1992), 343--364.

Digital Library

[22]

R. K. Nath, B. Sen, and B. K. Sikdar. 2017. Optimal synthesis of QCA logic circuit eliminating wire-crossings. IET-Circ. Dev. Syst. 11, 3 (2017), 201--208.

[23]

Tobias Nipkow, Lawrence C. Paulson, and Markus Wenzel. 2002. Isabelle/HOL: A Proof Assistant for Higher-order Logic. Vol. 2283. Springer Science 8 Business Media.

[24]

S. Perri and P. Corsonello. 2012. New methodology for the design of efficient binary addition circuits in QCA. Trans. Nanotechnol. 11, 6 (2012), 1192--1200.

Digital Library

[25]

Wolfgang Porod, Gary H. Bernstein, György Csaba, Sharon X. Hu, Joseph Nahas, Michael T. Niemier, and Alexei Orlov. 2014. Nanomagnet Logic. Springer, Berlin, 21--32.

[26]

D. A. Reis, C. A. T. Campos, T. R. Soares, O. P. V. Neto, and F. S. Torres. 2016. A methodology for standard cell design for QCA. In Proceedings of the ISCAS.

[27]

Arman Roohi, Ronald F. DeMara, and Navid Khoshavi. 2015. Design and evaluation of an ultra-area-efficient fault-tolerant QCA full adder. Microelectron. J. 46, 6 (2015), 531--542.

Digital Library

[28]

S. Srivastava, S. Sarkar, and S. Bhanja. 2009. Estimation of upper bound of power dissipation in QCA circuits. IEEE Trans. Nanotechnol. 8, 1 (Jan. 2009), 116--127.

Digital Library

[29]

J. Timler and C. S. Lent. 2002. Power gain and dissipation in quantum-dot cellular automata. J. Appl. Phys. 91, 2 (2002), 823--831.

[30]

Frank Sill Torres, Marcel Walter, Robert Wille, Daniel Große, and Rolf Drechsler. 2018a. Synchronization of clocked field-coupled circuits. In Proceedings of the IEEE-NANO. 1--4.

[31]

Frank Sill Torres, Robert Wille, Philipp Niemann, and Rolf Drechsler. 2018b. An energy-aware model for the logic synthesis of quantum-dot cellular automata. IEEE Trans. Comput.-Aided Design 37, 12 (Dec. 2018), 3031--3041.

[32]

Frank Sill Torres, Robert Wille, Marcel Walter, Philipp Niemann, Daniel Große, and Rolf Drechsler. 2018c. Evaluating the impact of interconnections in quantum-dot cellular automata. In Proceedings of the DSD. 649--656.

[33]

A. Trindade, R. S. Ferreira, J. A. M. Nacif, D. Sales, and O. P. V. Neto. 2016. A placement and routing algorithm for quantum-dot cellular automata. In Proceedings of the SBCCI.

Digital Library

[34]

V. Vankamamidi, M. Ottavi, and F. Lombardi. 2008. Two-dimensional schemes for clocking/timing of QCA circuits. Trans. Comput.-Aided Design 27, 1 (2008), 34--44.

Digital Library

[35]

E. Varga, M. T. Niemier, G. Csaba, G. H. Bernstein, and W. Porod. 2013. Experimental realization of a nanomagnet full adder using slanted-edge magnets. IEEE Trans. Magn. 49, 7 (July 2013), 4452--4455.

[36]

Marcel Walter, Robert Wille, Daniel Große, Frank Sill Torres, and Rolf Drechsler. 2018. An exact method for design exploration of quantum-dot cellular automata. In Proceedings of the DATE. 503--508.

[37]

Marcel Walter, Robert Wille, Frank Sill Torres, Daniel Große, and Rolf Drechsler. 2019. Scalable design for field-coupled nanocomputing circuits. In Proceedings of the ASP-DAC.

Digital Library

[38]

Robert A. Wolkow, Lucian Livadaru, et al. 2014. Silicon Atomic Quantum Dots Enable Beyond-CMOS Electronics. Springer-Verlag, 33--58.

Cited By

Drewniok JWalter MHang Ng SWalus KWille R(2024)On-the-fly Defect-Aware Design of Circuits based on Silicon Dangling Bond Logic2024 IEEE 24th International Conference on Nanotechnology (NANO)10.1109/NANO61778.2024.10628962(30-35)Online publication date: 8-Jul-2024
https://doi.org/10.1109/NANO61778.2024.10628962
Hofmann SWalter MWille R(2024)A* is Born: Efficient and Scalable Physical Design for Field-coupled Nanocomputing2024 IEEE 24th International Conference on Nanotechnology (NANO)10.1109/NANO61778.2024.10628808(80-85)Online publication date: 8-Jul-2024
https://doi.org/10.1109/NANO61778.2024.10628808
Walter MDrewniok JHofmann SHien BWille R(2024)The Munich N anotech Toolkit (MNT)2024 IEEE 24th International Conference on Nanotechnology (NANO)10.1109/NANO61778.2024.10628747(454-459)Online publication date: 8-Jul-2024
https://doi.org/10.1109/NANO61778.2024.10628747
Show More Cited By

Index Terms

Placement and Routing for Tile-based Field-coupled Nanocomputing Circuits Is NP-complete (Research Note)
1. Theory of computation
  1. Computational complexity and cryptography

Recommendations

Simultaneous analog placement and routing with current flow and current density considerations
DAC '13: Proceedings of the 50th Annual Design Automation Conference

Current-flow and current-density are two major considerations for placement and routing of analog layout synthesis. The current-flow constraints are specified to the critical nets with monotonic current/signal paths to reduce parasitic impacts. The ...
Device Layer-Aware Analytical Placement for Analog Circuits
ISPD '19: Proceedings of the 2019 International Symposium on Physical Design

The layouts of analog/mixed-signal (AMS) integrated circuits (ICs) are dramatically different from their digital counterparts. AMS circuit layouts usually include a variety of devices, including transistors, capacitors, resistors, and inductors. A ...
Near Zero-Energy Computation Using Quantum-Dot Cellular Automata

Near zero-energy computing describes the concept of executing logic operations below the (k_BT ln 2) energy limit. Landauer discussed that it is impossible to break this limit as long as the computations are performed in the conventional, non-reversible ...

Comments

Information & Contributors

Information

Published In

cover image ACM Journal on Emerging Technologies in Computing Systems

ACM Journal on Emerging Technologies in Computing Systems Volume 15, Issue 3

July 2019

160 pages

ISSN:1550-4832

EISSN:1550-4840

DOI:10.1145/3327966

Editor:
Yuan Xie
University of California, Santa Barbara, USA

Issue’s Table of Contents

Copyright © 2019 ACM.

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

Publisher

Association for Computing Machinery

New York, NY, United States

Journal Family

ACM Journals for the Design of Smart and Connected Systems

Publication History

Published: 22 April 2019

Accepted: 01 February 2019

Revised: 01 February 2019

Received: 01 June 2018

Published in JETC Volume 15, Issue 3

Permissions

Request permissions for this article.

Request Permissions

Check for updates

Author Tags

Qualifiers

Note
Research
Refereed

Contributors

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

19
Total Citations
View Citations
196
Total Downloads

Downloads (Last 12 months)11
Downloads (Last 6 weeks)2

Reflects downloads up to 09 Jan 2025

Other Metrics

View Author Metrics

Citations

Cited By

Drewniok JWalter MHang Ng SWalus KWille R(2024)On-the-fly Defect-Aware Design of Circuits based on Silicon Dangling Bond Logic2024 IEEE 24th International Conference on Nanotechnology (NANO)10.1109/NANO61778.2024.10628962(30-35)Online publication date: 8-Jul-2024
https://doi.org/10.1109/NANO61778.2024.10628962
Hofmann SWalter MWille R(2024)A* is Born: Efficient and Scalable Physical Design for Field-coupled Nanocomputing2024 IEEE 24th International Conference on Nanotechnology (NANO)10.1109/NANO61778.2024.10628808(80-85)Online publication date: 8-Jul-2024
https://doi.org/10.1109/NANO61778.2024.10628808
Walter MDrewniok JHofmann SHien BWille R(2024)The Munich N anotech Toolkit (MNT)2024 IEEE 24th International Conference on Nanotechnology (NANO)10.1109/NANO61778.2024.10628747(454-459)Online publication date: 8-Jul-2024
https://doi.org/10.1109/NANO61778.2024.10628747
Hofmann SWalter MServadei LWille R(2024)Thinking Outside the Clock: Physical Design for Field-coupled Nanocomputing with Deep Reinforcement Learning2024 25th International Symposium on Quality Electronic Design (ISQED)10.1109/ISQED60706.2024.10528711(1-8)Online publication date: 3-Apr-2024
https://doi.org/10.1109/ISQED60706.2024.10528711
Hofmann SWalter MWille R(2023)Post-Layout Optimization for Field-coupled NanotechnologiesProceedings of the 18th ACM International Symposium on Nanoscale Architectures10.1145/3611315.3633247(1-6)Online publication date: 18-Dec-2023
https://dl.acm.org/doi/10.1145/3611315.3633247
Hofmann SWalter MWille R(2023)Scalable Physical Design for Silicon Dangling Bond Logic: How a 45° Turn Prevents the Reinvention of the Wheel2023 IEEE 23rd International Conference on Nanotechnology (NANO)10.1109/NANO58406.2023.10231278(872-877)Online publication date: 2-Jul-2023
https://doi.org/10.1109/NANO58406.2023.10231278
Walter MHien BWille R(2023)Versatile Signal Distribution Networks for Scalable Placement and Routing of Field-coupled Nanocomputing Technologies2023 IEEE Computer Society Annual Symposium on VLSI (ISVLSI)10.1109/ISVLSI59464.2023.10238604(1-6)Online publication date: 20-Jun-2023
https://doi.org/10.1109/ISVLSI59464.2023.10238604
Walter MNg SWalus KWille ROshana R(2022)Hexagons are the bestagonsProceedings of the 59th ACM/IEEE Design Automation Conference10.1145/3489517.3530525(739-744)Online publication date: 23-Aug-2022
https://doi.org/10.1145/3489517.3530525
Li YXie GHan QLi XLi GZhang BPeng F(2022)Field-Coupled Nanocomputing Placement and Routing With Genetic and A* AlgorithmsIEEE Transactions on Circuits and Systems I: Regular Papers10.1109/TCSI.2022.319745069:11(4619-4631)Online publication date: Nov-2022
https://doi.org/10.1109/TCSI.2022.3197450
Gassoumi ITouil LMtibaa A(2022)Design of efficient binary-coded decimal adder in QCA technology with a regular clocking schemeComputers and Electrical Engineering10.1016/j.compeleceng.2022.107999101:COnline publication date: 1-Jul-2022
https://dl.acm.org/doi/10.1016/j.compeleceng.2022.107999
Show More Cited By

View Options

Login options

Check if you have access through your login credentials or your institution to get full access on this article.

Full Access

Get this Article

View options

PDF

View or Download as a PDF file.

eReader

View online with eReader.

HTML Format

View this article in HTML Format.

Media

Figures

Other

Tables

View Issue’s Table of Contents