Finding hidden Hamiltonian cycles

Andrei Z. Broder; Alan M. Friezet; Eli Shamirt

doi:10.1145/103418.103442

Finding hidden Hamiltonian cycles

Andrei Z. Broder, Alan M. Friezet, Eli Shamirt

Einstein Institute of Mathematics

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

12 Scopus citations

Abstract

Consider a random graph G composed of a Hamiltonian cycle on n labeled vertices and dn random edges that "hide" the cycle. Is it possible to unravel the structure, that is, to efficiently find a Hamiltonian cycle in G? We describe an O(dn³) steps algorithm A for this purpose, and prove that it succeeds almost surely. Part one of A properly covers the "trouble spots" of G by a collection of disjoint paths. (This is the hard part to analyze.) Part two of A extends this cover to a full cycle by the rotation-extension technique which is already classical for such problems.

Original language	English
Title of host publication	Proceedings of the 23rd Annual ACM Symposium on Theory of Computing, STOC 1991
Publisher	Association for Computing Machinery
Pages	182-189
Number of pages	8
ISBN (Electronic)	0897913973
DOIs	https://doi.org/10.1145/103418.103442
State	Published - 3 Jan 1991
Event	23rd Annual ACM Symposium on Theory of Computing, STOC 1991 - New Orleans, United States Duration: 5 May 1991 → 8 May 1991

Publication series

Name	Proceedings of the Annual ACM Symposium on Theory of Computing
Volume	Part F130073
ISSN (Print)	0737-8017

Conference

Conference	23rd Annual ACM Symposium on Theory of Computing, STOC 1991
Country/Territory	United States
City	New Orleans
Period	5/05/91 → 8/05/91

Bibliographical note

Publisher Copyright:
© 1991 ACM.

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10.1145/103418.103442

Cite this

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abstract = "Consider a random graph G composed of a Hamiltonian cycle on n labeled vertices and dn random edges that {"}hide{"} the cycle. Is it possible to unravel the structure, that is, to efficiently find a Hamiltonian cycle in G? We describe an O(dn3) steps algorithm A for this purpose, and prove that it succeeds almost surely. Part one of A properly covers the {"}trouble spots{"} of G by a collection of disjoint paths. (This is the hard part to analyze.) Part two of A extends this cover to a full cycle by the rotation-extension technique which is already classical for such problems.",

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Broder, AZ, Friezet, AM & Shamirt, E 1991, Finding hidden Hamiltonian cycles. in Proceedings of the 23rd Annual ACM Symposium on Theory of Computing, STOC 1991. Proceedings of the Annual ACM Symposium on Theory of Computing, vol. Part F130073, Association for Computing Machinery, pp. 182-189, 23rd Annual ACM Symposium on Theory of Computing, STOC 1991, New Orleans, United States, 5/05/91. https://doi.org/10.1145/103418.103442

Finding hidden Hamiltonian cycles. / Broder, Andrei Z.; Friezet, Alan M.; Shamirt, Eli.
Proceedings of the 23rd Annual ACM Symposium on Theory of Computing, STOC 1991. Association for Computing Machinery, 1991. p. 182-189 (Proceedings of the Annual ACM Symposium on Theory of Computing; Vol. Part F130073).

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

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AB - Consider a random graph G composed of a Hamiltonian cycle on n labeled vertices and dn random edges that "hide" the cycle. Is it possible to unravel the structure, that is, to efficiently find a Hamiltonian cycle in G? We describe an O(dn3) steps algorithm A for this purpose, and prove that it succeeds almost surely. Part one of A properly covers the "trouble spots" of G by a collection of disjoint paths. (This is the hard part to analyze.) Part two of A extends this cover to a full cycle by the rotation-extension technique which is already classical for such problems.

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Finding hidden Hamiltonian cycles

Abstract

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