Cell flipping in permutation diagrams

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


Permutation diagrams have been used in circuit design to model a set of single point nets crossing a channel, where the minimum number of layers needed to realize the diagram equals the clique number ω(G) of its permutation graph, the value of which can be calculated in O(n log n) time. We consider a generalization of this model motivated by "standard cell" technology in which the numbers on each side of the channel are partitioned into consecutive subsequences, or cells, each of which can be left unchanged or flipped (i.e., reversed). We ask, for what choice of fiippings will the resulting clique number be minimum or maximum. We show that when one side of the channel is fixed (no flipping), an optimal flipping for the other side can be found in O(n log n) time for the maximum clique number. We prove that the general problem is NP-complete for the minimum clique number and O(n 2) for the maximum clique number. Moreover, since the complement of a permutation graph is also a permutation graph, the same complexity results hold for the independence number.

Original languageEnglish
Title of host publicationSTACS 98 - 15th Annual Symposium on Theoretical Aspects of Computer Science, Proceedings
Number of pages10
StatePublished - 1998
Externally publishedYes
Event15th Annual Symposium on Theoretical Aspects of Computer Science, STACS 98 - Paris, France
Duration: 25 Feb 199827 Feb 1998

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume1373 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference15th Annual Symposium on Theoretical Aspects of Computer Science, STACS 98

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science


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