关于满Steiner树问题的一个近似算法An Approximation Algorithm about Full Steiner Tree Problem
罗美菊,赵传立,唐恒永
摘要(Abstract)：
满Steiner树问题(TST)是求解一个正则点都是叶子的最小Steiner树问题.Fabio Viduani Martinez等人给出了此问题的近似算法,它的性能比为2ρ-ρ/(3ρ-2)≈2.52,而目前求解Steiner树问题的近似算法的性能比,最小值约为1.550.对满Steiner树问题给出了一个近似算法,并将它的性能比改进为2ρ-3ρ/(6ρ-2)≈2.463.
关键词(KeyWords)： 满Steiner树;近似算法;最小Steiner树
基金项目(Foundation): 国家自然科学基金资助项目(10471096)
作者(Author): 罗美菊,赵传立,唐恒永
DOI: 10.16393/j.cnki.37-1436/z.2006.05.002
参考文献(References)：
- [1]Karp R.Reducibility among combinatorial problems[J].Com-plexity Computer Computations,1972:85-103.
- [2]Garey M,Graham R,Johnson D.The complexity of computingSteiner minimal trees[J].SIAM Journal on Applied Mathe-matics 32,1977:835-859.
- [3]Garey M,Johnson D.The rectilinear Steiner problem is NP-complete[J].SIAM Journal on Applied Mathematics 32,1977:826-834.
- [4]Ausiello G,Crescenzi P,Gambosi G,et al.Marchetti-Spac-camelai A,Protasi M.Complexity and Approximation—Com-binatorial Optimization Problems and Their ApproximabilityProperties[J].Springer Verlag,1999.
- [5]Robins G,Zelikovsky A.Improved Steiner tree approximationin graphs[J].Proceedings of the 11th Annual ACMSIAMSymposium on Discrete Algorithms,2000:770-779.
- [6]Lu C L,Tang C Y.The full Steiner tree problem[J].Theo-retical ComputerScience,2003,306:55-67.
- [7]Drake D E,Hougardy S.On approximation algorithms forthe terminal Steiner tree problem[J].Information ProcessingLetters,2004,89(1):15-18.
- [8]Fuchs B.A note on the terminal Steiner tree problem[J].In-formation Processing Letters,2003,87:219-220.
- [9]Lin G,Xue G.On the terminal Steiner tree problem[J].In-formation Processing Letters,2002,84:103-107.
- [10]Lu C L,Tang C Y.The full Steiner tree problem[J].Theo-retical Computer Science,2003:55-67.
- [11]Lin G H,Xue G L.On the terminal Steiner tree problem[J].Information Processing Letters,2002:103-107.
- [12]Fuchs B.A note on the terminal Steiner tree problem[J].Information Processing Letters,2003:219-220.
- [13]Chen T H,Lu C L,Tang C Y.On the full and bottleneckfull Steiner tree problems[J].2003:122-129.
- [14]Drake D E,Hougardy S.On approximation algorithms forthe terminal Steiner tree problem[J].Information ProcessingLetters,2004,89(1):15-18.