Download Integer Programming and Combinatorial Optimization: 17th by Jon Lee, Jens Vygen PDF

By Jon Lee, Jens Vygen

This ebook constitutes the refereed lawsuits of the seventeenth overseas convention on Integer Programming and Combinatorial Optimization, IPCO 2014, held in Bonn, Germany, in June 2014. The 34 complete papers provided have been rigorously reviewed and chosen from 143 submissions. The convention is a discussion board for researchers and practitioners engaged on a number of features of integer programming and combinatorial optimization. the purpose is to offer fresh advancements in thought, computation, and functions in those parts. The scope of IPCO is considered in a wide feel, to incorporate algorithmic and structural leads to integer programming and combinatorial optimization in addition to revealing computational reviews and novel functions of discrete optimization to useful problems.

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

Example text

For μ ∈ R define the parametric edge costs fμ (e) = μc1e + c2e . We suppose that there exists an interval [α, β] where all fμ (e) are positive. Here Lemma 1 and Step 3 of Algorithm 2 are no longer applicable and thus, Theorem 1 does hold in this case. Using ideas in [11] and avoiding unnecessary subdivisions of the interval [α, β], we obtain a strongly polynomial bound. The next result is also non-constructive (proof omitted). Theorem 2 Assume that the parametric edge costs fμ (e) are positive for all μ ∈ [α, β].

10 that the parametric complexity is polynomial in this case. However, if iii) is relaxed, the proof of his theorem implies that the parametric complexity is O(|V |19 log |V | log Cmax ), where Cmax is the maximum cost over all edges. This is surprising since the parametric function f is the minimum of the parametric functions of O(|V |) minimum s–t cut problems (by fixing s and letting t vary over the other nodes), each of which could have an exponential number of breakpoints. In this paper we give a much smaller, strongly polynomial upper bound on the parametric complexity of minimum cut, which leads to a strongly polynomial time algorithm for parametric global minimum cut, and hence a strongly polynomial time algorithm for the multicriteria version.

De Loera, and Q. Louveaux Corollary 1. Consider the knapsack problem aT x = b associated with a = (a1 , . . , an )T ∈ Zn>0 with gcd(a1 , . . , an ) = 1. For a fixed positive integer k and fixed n the k-Frobenius number can be computed in polynomial time. The paper is organized as follows.

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