# Lower bounds for solving undirected graph problems on VLSI

Conference paper

First Online:

## Abstract

We study VLSI solutions to the connected component problem on networks that have area too small to store all the edges of the graph for the entire computation. We give lower bounds on the time needed to solve this problem on such networks. The lower bounds use a new proof technique combining adversary strategy, information flow, and Kolmogorov complexity arguments. The lower bounds obtained for the connected components problem hold for a number of other undirected graph problems.

## Preview

Unable to display preview. Download preview PDF.

## References

- [AA]H. Abelson, P. Andreae, ‘Information Transfer and Area-Time Tradeoffs for VLSI Multiplication', CACM, Vol. 23, pp 20–23, Jan. 1980.Google Scholar
- [AK]M.J. Atallah, S.R. Kosaraju, ‘Graph Problems on a Mesh-Connected Processor Array', Proc. of the 14-th Ann. Symp. on Th. of Comp., pp 345–353, 1982.Google Scholar
- [BK]R.P. Brent, H.T. Kung, ‘The Area-Time Complexity of Binary Multiplication', JACM, Vol.28, pp 521–534, July 1981.Google Scholar
- [CM]B. Chazelle, L. Monier, ‘A Model of Computation for VLSI with Related Complexity Results', 13-th Ann. Symp. on Th. of Comp., pp 318–325, 1981.Google Scholar
- [FJ]G.N. Frederickson, D.B. Johnson, ‘Generalized Selection and Ranking: Sorted Matrices', Tech. Report of The Pennsylvania State University, CS-81-12, 1981.Google Scholar
- [GKT]L.J. Guibas, H.T. Kung, CD. Thompson, ‘Direct VLSI Implementations for Combinatorial Algorithms', Proc. of Conf. VLSI Tech. Design and Fabrication, Caltech 1979.Google Scholar
- [H1]S.E. Hambrusch, ‘The Complexity of Graph Problems on VLSI', Ph.D. thesis, The Pennsylvania State University, 1982.Google Scholar
- [H2]S.E. Hambrusch, ‘VLSI Algorithms for the Connected Components Problem', SIAM J. on Computing, Vol. 12, No. 2, May 1983.Google Scholar
- [J]J. Ja'sJa', ‘The VLSI Complexity of Graph Problems', Tech. Report of The Pennsylvania State University, CS-81-25, October 1981.Google Scholar
- [JK]J. Ja'sJa', V.K. Kumar, ‘Information Transfer in Distributed Computing with Applications to VLSI', Tech. Report of The Pennsylvania State University, CS-81-14, 1981.Google Scholar
- [KT]H.T. Kung, C.E. Leiserson, 'systolic Arrays for VLSI', appeared in Introduction to VLSI Systems', C. Mead, L. Conway, Addison-Wesley, pp 260–292, 1960.Google Scholar
- [LS]R.J. Lipton, R.S. Sedgewick, ‘Lower Bounds for VLSI', 13-th Ann. Symp. on Th. of Comp., pp 300–307, 1981.Google Scholar
- [LV]R.J. Lipton, J. Valdes, ‘Census Function: An Approach to VLSI Upper Bounds', Proc. of the 22-nd Ann. Symp. on Found. of Comp. Sc, pp 13–22, 1981.Google Scholar
- [MC]C. Mead, L. Conway, Introduction to VLSI Systems, Addison-Wesley, 1980.Google Scholar
- [NMB]D. Nath, S.N. Maheshwari, P.C.P. Bhatt, ‘Efficient VLSI Networks for Parallel Processing based on Orthogonal Trees', Techn. Report of the Indian Inst. of Techn., Delhi, April 1981.Google Scholar
- [P]W. Paul, ‘On Heads versus Tapes', 22-nd Ann. Symp. on Found, of Comp. Sc., pp 68–73, 1981.Google Scholar
- [PSS]W. Paul, J. Seiferas, J. Simon, ‘An Information Theoretic Approach to Time Bounds on On-line Computation', 12-th Ann. Symp. on Th. of Comp., pp 357–367, 1980.Google Scholar
- [PV]F.P. Preparata, J.E. Vuillemin, ‘The Cube Connected Cycles: a Versatile Network for Parallel Computation', Proc. of 20-th annual IEEE FOCS Conf., pp 140–147, 1979.Google Scholar
- [S]L. Snyder, ‘Overview of the CHiP Computer', in John P. Gray, VLSI 1981, pp 237–246, Academic Press, 1981.Google Scholar
- [T]C.D. Thompson, ‘Area-Time Complexity for VLSI', 11-th Ann. Symp, on Th. of Comp., pp B1–88, 1979.Google Scholar
- [V]J.E. Vuillemin, ‘A Combinatorial Limit to the Computing Power of VLSI Circuits', 21-st Ann. Symp. on Found. of Comp. Sc., pp 294–300, 1980.Google Scholar
- [Y]A. Yao, 'some Complexity Questions related to Distributed Computing', Proc. 11-th Ann. Symp. on Th. of Comp., pp 209–213, 1979.Google Scholar

## Copyright information

© Springer-Verlag Berlin Heidelberg 1983