By Jon Lee, Jens Vygen

This ebook constitutes the refereed lawsuits of the seventeenth foreign convention on Integer Programming and Combinatorial Optimization, IPCO 2014, held in Bonn, Germany, in June 2014. The 34 complete papers offered have been rigorously reviewed and chosen from 143 submissions. The convention is a discussion board for researchers and practitioners engaged on numerous features of integer programming and combinatorial optimization. the purpose is to provide fresh advancements in idea, computation, and functions in those components. The scope of IPCO is considered in a vast feel, to incorporate algorithmic and structural ends up in integer programming and combinatorial optimization in addition to revealing computational reviews and novel functions of discrete optimization to functional problems.

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**Additional resources for Integer Programming and Combinatorial Optimization: 17th International Conference, IPCO 2014, Bonn, Germany, June 23-25, 2014. Proceedings**

**Example text**

The most important problem we are leaving open is to exhibit a natural intractable pivoting rule. For example, establishing the following would be an important advance: On Simplex Pivoting Rules and Complexity Theory 23 Conjecture 3. Steepest descent is intractable. This looks quite challenging. Obviously, in such a proof much more will need to be encoded in the linear program (which, in the present proof, was of logarithmic complexity). The ultimate goal is a generic intractability proof that works for a large class of pivoting rules, thus delimiting the possibilities for a strongly polynomial algorithm.

Of Foundations of Computer Science, pp. 659–669 (1992) 19. : A simple min-cut algorithm. Journal of the ACM 44(4), 585–591 (1997) Integer Programs with Prescribed Number of Solutions and a Weighted Version of Doignon-Bell-Scarf ’s Theorem Iskander Aliev1 , Jes´ us A. be Abstract. In this paper we study a generalization of the classical feasibility problem in integer linear programming, where an ILP needs to have a prescribed number of solutions to be considered solved. We ﬁrst provide a generalization of the famous Doignon-Bell-Scarf theorem: Given an integer k, we prove that there exists a constant c(k, n), depending only on the dimension n and k, such that if a polyhedron {x : Ax ≤ b} contains exactly k integer solutions, then there exists a subset of the rows of cardinality no more than c(k, n), deﬁning a polyhedron that contains exactly the same k integer solutions.

A = (a1 , . . , an )T ∈ Zn>0 with gcd(a1 , . . , an ) = 1. For a positive integer k the k-Frobenius number Fk (a) Integer Programs with Prescribed Number of Solutions 39 is the largest number which cannot be represented in at least k diﬀerent ways as a non-negative integral combination of the ai ’s. Thus, putting A = aT , Fk (a) = max{b ∈ Z : IPA (b) is < k feasible}. When k = 1 this has been studied by a large number of authors and both the structure and algorithmic properties are well-understood.