Tow algorithms for finding a minimal ratio hamiltonian cycle in a network

References

• Chritofides , N. 1975 . Graph Theory: An Algorithmic Approach , London : Academic Press .
   Google Scholar
• Dinkelbach , W. 1979 . On nonlinear fraction programming . Management Science , 13 : 490 – 498 .
   Google Scholar
• Gary , M.R. and Johnson , D.S. 1979 . Computers and Intractibility , San Francisco : W.H. Freeman .
   Google Scholar
• Hansen , P. 1980 . “ Bicriterion path problems ” . In Multiple Criteria Decision Making: Theory and Applications , Edited by: Fandel , G. and Gal , T. Vol. 177 , 109 – 127 . Heidelberg : Springer . Lecture Notes in Economics and in Mathematical Systems
   Google Scholar
• Ibaraki , T. 1983 . Parametric approaches to fractional problems . Mathematical Programming , 26 : 345 – 362 .
   Web of Science ®Google Scholar
• lawler , E.L. 1976 . Combinatoral Optimization: Networks and Matroids , New York : Hold, Rinehart and Wiston .
   Google Scholar
• Lawler E.L. Lenstra J.K. Kan A.H.G.R. Shmoys D.B. The Traveling Salesman Problem John Wiley and Sons Ltd New Work 1985
   Google Scholar
• Liu , C.L. 1977 . Elements of Discreate Mathematics , New York : McGraw–Hill .
   Google Scholar
• Megiddo , N. 1979 . Combinatorial Optimization with rational objective functions . Mathematics of Operations Research , 4 : 414 – 424 .
   Google Scholar
• Megiddo , N. 1983 . Applying prarllel computation algorithms in design of serial algorithms . Journal of the ACM , 30 : 852 – 865 .
   Google Scholar
• Nilsson N.J. Problem-Solving Methods in Artifical Intelligence McGraw-Hill New York 1971
   Google Scholar
• Pearl , J. 1984 . Heuristics: Intelligent Search Strategies for Computer Problem Solving , Reading, MA : Addison–Wesley .
   Google Scholar
• Radzik , T. 1993 . “ Parametric flows, weighted means of cuts, and fractional combinatorial optimization. in ” . In Complexity in Numerical Optimization , Edited by: Paralos , P.M. 351 – 386 . World Scientific Publishing Co. .
   Google Scholar
• Schiable , S. and Ibarki , T. 1983 . Fractional Programming . European Journaal of Operation Research , 12 : 325 – 338 .
   Google Scholar
• Tung , C.T. 1983 . Finding a path with minium cost to time ratio in a network . Asia–pacific Journmal of Operatation Research , 3 : 43 – 52 .
   Google Scholar
• Verma , V. and Puri , M.C. 1990 . On Wolf’ method for solving linear fraction programming problem . Opsearch , 27 : 176 – 179 .
   Google Scholar
• Tung , C.T.,. , Chan , G.H. and Chew , K.L. 1987 . Finding a minimal ratio elementary path in a network . Asia-Pacific Journal of Operational Research , 4 : 151 – 157 .
   Google Scholar
• Wolf , H. 1985 . A Pramermetric method for solving the linear fraction programming problems . Operations Research , 33 : 835 – 841 .
   Web of Science ®Google Scholar