Optimal Euler Circuit of Maximum Contiguous Cost

Yu QIAO  Makoto YASUHARA  

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E90-A   No.1   pp.274-280
Publication Date: 2007/01/01
Online ISSN: 1745-1337
DOI: 10.1093/ietfec/e90-a.1.274
Print ISSN: 0916-8508
Type of Manuscript: PAPER
Category: Graphs and Networks
Keyword: 
Optimal Euler Circuit,  Euler circuit,  graph theory,  contiguous cost,  NP-complete,  approximation algorithm,  

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Summary: 
This paper introduces a new graph problem to find an Optimal Euler Circuit (OEC) in an Euler graph. OEC is defined as the Euler circuit that maximizes the sum of contiguous costs along it, where the contiguous cost is assigned for each of the two contiguous edges incident to a vertex. We prove that the OEC problem is NP-complete. A polynomial time algorithm will be presented for the case of a graph without vertex of degree greater than 4, and for the general case, a 1/4-approximation polynomial time algorithm will be proposed.