New structural approach to integer programming : a survey

Structure theory of set addition, Astérisque, no. 258 (1999), 22 p.

@incollection{AST_1999__258__341_0,
     author = {Chaimovich, Mark},
     title = {New structural approach to integer programming : a survey},
     booktitle = {Structure theory of set addition},
     editor = {Deshouilliers Jean-Marc and Landreau Bernard and Yudin Alexander A.},
     series = {Ast\'erisque},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {258},
     year = {1999},
     zbl = {0987.90060},
     mrnumber = {1701209},
     language = {en},
     url = {archive.numdam.org/item/AST_1999__258__341_0/}
}

Chaimovich, Mark. New structural approach to integer programming : a survey, dans Structure theory of set addition, Astérisque, no. 258 (1999), 22 p. http://archive.numdam.org/item/AST_1999__258__341_0/

Bibliographie

[1] Alon N. and Freiman G. A., On Sums of Subsets of a Set of Integers, Combinatorica, 8, 1988, 305-314. | Article | MR 981887 | Zbl 0666.10035

[2] Balas E. and Zemel E., An Algorithm for Large Zero-One Knapsack Problems, Operations Research, 28, 1980, 1130-1154. | Article | MR 589676 | Zbl 0449.90064

[3] Buzytsky P. and Freiman G. A., Analytical Methods in Integer Programming,Moscow, ZEMJ., (Russian), 48 pp., 1980.

[4] Chaimovich M., An Efficient Algorithm for the Subset-Sum Problem, a manuscript, 1988.

[5] Chaimovich M., Subset-Sum Problems with Different Summands : Computation, Discrete Applied Mathematics, 27, 1990, 277-282. | Article | MR 1058951 | Zbl 0709.90082

[6] Chaimovich M., Solving a Value-Independent Knapsack Problem with the Use of Methods of Additive Number Theory, Congressus Numerantium, 72, 1990, 115-123. | MR 1041813 | Zbl 0695.90065

[7] Chaimovich M., Fast Exact and Approximate Algorithms for $k$ -Partition and Scheduling Independent Tasks, Discrete Mathematics, 114, 1993, 87-103. | Article | MR 1217744 | Zbl 0776.68054

[8] Chaimovich M., On Solving Dense $n$ -Dimensional Subset-Sum Problem, Congressus Numerantium, 84, 1992, 41-50. | MR 1152100 | Zbl 0759.90071

[9] Chaimovich M., Analytical Methods of Number Theory in Integer Programming, Ph. D. Thesis, Tel-Aviv University, Israel, 1991.

[10] Chaimovich M., Freiman G. and Galil Z., Solving Dense Subset-Sum Problem by Using Analytical Number Theory, J. of Complexity, 5, 1989, 271-282. | Article | MR 1018019 | Zbl 0686.68030

[11] Erdős P. and Freiman G., On Two Additive Problems,J. Number Theory, 34, 1990, 1-12. | Article | MR 1039762 | Zbl 0697.10047

[12] Freiman G. A., An Analytical Method of Analysis of Linear Boolean Equations, Ann. New York Acad. Sci., 337, 1980, 97-102. | Article | MR 624284 | Zbl 0459.05013

[13] Freiman G. A., What is the Structure of $K$ if $K + K$ is Small ?, in Lecture Notes in Mathematics, 1240, 1987, 109-134. | MR 894508 | Zbl 0625.10045

[14] Freiman G. A., On Extremal Additive Problems of Paul Erdős, ARS Combinatoria, 26B, 1988, 93-114. | MR 990542 | Zbl 0666.10009

[15] Freiman G. A., Subset-Sum Problem with Different Summands, Congressus Numerantium, 70, 1990, 207-215. | MR 1041604 | Zbl 0701.90068

[16] Freiman G. A., On Solvability of a System of Two Boolean Linear Equations, The Proceedings of the Number Theory Conference, New York, 1989. | MR 1420205 | Zbl 0860.11013

[17] Freiman G. A., New Analytical Results in Subset-Sum Problem, Discrete Mathematics, 114, 1993, 205-218. | Article | MR 1217753 | Zbl 0849.11015

[18] Galil Z. and Margalit O., An Almost Linear-Time Algorithm for the Dense Subset-Sum Problem, SIAM J. of Computing, 20, 1991, 1157-1189. | Article | MR 1135754 | Zbl 0736.68041

[19] Jeroslow R. G., Trivial Integer Programs Unsolvable by Branch and Bound, Mathematical Programming, 6, 1974, 105-109. | Article | MR 345630 | Zbl 0283.90035

[20] Lipkin E., On Representation of $r$ -Powers by Subset-Sums, Acta Arithmetica, LII, 1989, 353-366. | Article | EuDML 206208 | MR 1030087 | Zbl 0691.10042

[21] Sahni S. K., Algorithms for Scheduling Independent Tasks, J. ACM, 23, 1976, 116-127. | Article | MR 434399 | Zbl 0326.68024

[22] Sárkőzy A., Finite Addition Theorems II, J. Number Theory, 48, 1994, 197-218. | Article | MR 1285539 | Zbl 0808.11011