A depth-first dynamic programming algorithm for the Tree Knapsack Problem

INFORMS Journal on Computing

Volumn 9, Issue 4, 1997, Pages 431-438

  Cho, Geon ^a   Shaw, Dong X ^b  

^a Chonnam National University   (South Korea)

^b SCHOOL OF INDUSTRIAL ENGINEERING   (United States)

Author keywords

Combinatorial optimization; Dynamic programming; Graphs; Networks; Tree

Indexed keywords

EID: 0002306254     PISSN: 10919856     EISSN: None     Source Type: Journal    
DOI: 10.1287/ijoc.9.4.431     Document Type: Article

References (12)

1. A. BALAKRISHNAN, T.L. MAGNANTI, and R.T. WONG, 1995. A Decomposition Algorithm for Local Access Telecommunications Network Expansion, Operations Research 43, 43-57.
2. D. BIENSTOCK, 1993. A Lot-Sizing Problem on Trees, Related to Network Design, Mathematics of Operations Research 18, 402-422.
3. G. CORNUEJOLS, G.L. NEMHAUSER, and L.A. WOLSEY, 1990. The Uncapacitated Facility Location Problem, in Discrete Location Theory, P.B. Mirchandani and R.L. Francis (eds.). John Wiley and Sons, New York.
4. M.R. GAREY and D.S. JOHNSON, 1979. Computers and Intractability: A Guide to the Theory of NP-Completeness, W.H. Freemand and Co., San Francisco.
5. O.H. IBARRA and C.E. KIM, 1978. Approximation Algorithms for Certain Scheduling Problems, Mathematics of Operations Research 3, 197-204.
6. D.S. JOHNSON and K.A. NIEMI, 1983. On Knapsacks, Partitions, and a New Dynamic Programming Technique for Trees, Mathematics of Operations Research 8, 1-14.
7. O. KARIV and S.L. HAKIMI, 1979. An Algorithmic Approach to Network Location Problems. II. The p-medians, SIAM Journal of Applied Mathematics 37, 539-555.
8. J.A. LUKES, 1974. Efficient Algorithm for the Partitioning of Trees, IBM Journal of Research and Development 18, 214-224.
9. D.X. SHAW, 1994. Reformulation and Column Generation for Several Telecommunications Network Design Problems, Proceedings of the 2nd International Telecommunication Conference, Nashville, TN.
10. D.X. SHAW and G. CHO, 1994. A Branch-and-Bound Procedure for the Tree Knapsack Problem, Technical Report, School of Industrial Engineering, Purdue University, West Lafayette, IN.
11. D.X. SHAW and G. CHO, 1994. Limited Column Generation for Local Access Telecommunication Network Expansion and Its Extension, Technical Report, School of Industrial Engineering, Purdue University, West Lafayette, IN.
12. D.X. SHAW, G. CHO, and H. CHANG, 1995. A Depth-First Dynamic Programming Procedure for the Extended Tree Knapsack Problem in Local Access Network Design, Technical Report, School of Industrial Engineering, Purdue University, West Lafayette, IN.