An optimal time algorithm for minimum linear arrangement of chord graphs

  • Authors:

  • Pariya Raoufi;Habib Rostami;Hessam Bagherinezhad

  • Affiliations:

  • Computer Engineering Department, School of Engineering, Persian Gulf University of Bushehr, Bushehr 75168, Iran and School of Computing Science, Simon Fraser University, Canada;Computer Engineering Department, School of Engineering, Persian Gulf University of Bushehr, Bushehr 75168, Iran;Computer Engineering Department, School of Engineering, Persian Gulf University of Bushehr, Bushehr 75168, Iran and Computer Engineering Department, Sharif University of Technology, Tehran, Iran

  • Venue:
  • Information Sciences: an International Journal
  • Year:
  • 2013

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Abstract

A linear arrangement @f of an undirected graph G=(V,E) with |V|=n nodes is a bijective function @f:V-{0,...,n-1}. The cost function is cost(G,@f)=@?"u"v"@?"E|(@f(u)-@f(v))| and opt(G)=min"@?"@fcost(G,@f). The problem of finding opt(G) is called minimum linear arrangement (MINLA). The Minimum Linear Arrangement is an NP-hard problem in general. But there are some classes of graphs optimally solvable in polynomial time. In this paper, we show that the label of each node equals to the reverse of binary representation of its id in the optimal arrangement. Then, we design an O(n) algorithm to solve the minimum linear arrangement problem of Chord graphs.