Abstract
Using an algebra of paths we present abstract algebraic derivations for two problem classes concerning graphs, viz. layer oriented traversal and computing sets of Hamiltonian paths. In the first case, we are even able to abstract to the very general setting of Kleene algebras. Applications include reachability and a shortest path problem as well as topological sorting and finding maximum cardinality matchings.
This research was partially funded by Esprit Working Group 8533 — NADA: New Hardware Design Methods
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
References
A.V. Aho, J.E. Hopcroft, J.D. Ullman: The design and analysis of computer algorithms. Reading, Mass.: Addison Wesley 1974
R. Berghammer: unpublished manuscript
Biggs: Discrete Mathematics. Oxford: Clarendon Press 1989
T. Brunn: Deduktiver Entwurf und funktionale Programmierung von Graphenalgorithmen. Institut für Informatik, Universität Augsburg, Diplomarbeit, August 1997
J.H. Conway: Regular algebra and finite machines. London: Chapman and Hall 1971
S.C. Kleene: Introduction to metamathematics. New York: van Nostrand 1952
B. Möller: Relations as a program development language. In: B. Möller (ed.): Constructing programs from specifications. Proc. IFIP TC2/WG 2.1 Working Conference on Constructing Programs from Specifications, Pacific Grove, CA, USA, 13–16 May 1991. Amsterdam: North-Holland 1991, 373–397
B. Möller: Derivation of graph and pointer algorithms. In: B. Möller, H.A. Partsch, S.A. Schuman (eds.): Formal program development. Proc. IFIP TC2/WG2.1 State of Art Seminar, Rio de Janeiro, Jan. 1992. Lecture Notes in Computer Science 755. Berlin: Springer 1993, 123–160
B. Möller: Assertions and recursions. In: G. Dowek, J. Heering, K. Meinke, B. Möller (eds.): Higher order algebra, logic and term rewriting. Second International Workshop, Paderborn, Sept. 21–22, 1995. Lecture Notes in Computer Science 1074. Berlin: Springer 1996, 163–184
B. Möller: Typed Kleene algebras. Institut für Informatik, Universität Augsburg, Technical Report 1998-3, April 1998
B. Möller, M. Russling: Shorter paths to graph algorithms. In: R.S. Bird, C.C. Morgan, J.C.P. Woodcock (eds.): Mathematics of Program Construction. Lecture Notes in Computer Science 669. Berlin: Springer 1993, 250–268. Extended version: Science of Computer Programming 22, 157–180 (1994)
M. Russling: Deriving a class of layer-oriented graph algorithms. Science of Computer Programming 26, 117–132 (1996).
M. Russling: Deriving general schemes for classes of graph algorithms. Augsburger Mathematisch-Naturwissenschaftliche Schriften, Band 13 (1996).
G. Schmidt, T. Ströhlein: Relations and graphs. Discrete Mathematics for Computer Scientists. EATCS Monographs on Theoretical Computer Science. Berlin: Springer 1993
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1998 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Brunn, T., Möller, B., Russling, M. (1998). Layered graph traversals and Hamiltonian path problems — An algebraic approach. In: Jeuring, J. (eds) Mathematics of Program Construction. MPC 1998. Lecture Notes in Computer Science, vol 1422. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0054287
Download citation
DOI: https://doi.org/10.1007/BFb0054287
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-64591-7
Online ISBN: 978-3-540-69345-1
eBook Packages: Springer Book Archive