Counting and enumeration complexity with application to multicriteria scheduling

t'Kindt, Vincent; Bouibede-Hocine, Karima; Esswein, Carl

doi:10.1007/s10288-005-0063-0

Cited by 13 publications

(2 citation statements)

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“…However, when the goal is to find a set of solutions instead of a single one, it may well be the case that the requested output is exponential in the given input. The computational complexity of bicriteria problems has been addressed in Garey and Johnson [17], T'Kindt et al [35], Fukuda [16] and the references contained therein. Here, we will argue that it is unlikely that there is a polynomial algorithm for finding all efficient points of SubtreeE.…”

Section: Problem Subtreeementioning

confidence: 99%

Balancing profits and costs on trees

et al. 2012

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We consider a rooted tree graph with costs associated with the edges and profits associated with the vertices. Every subtree containing the root incurs the sum of the costs of its edges, and collects the sum of the profits of its nodes; the goal is the simultaneous minimization of the total cost and maximization of the total profit. This problem is related to the TSP with profits on graphs with a tree metric. We analyze the problem from a biobjective point of view. We show that finding all extreme supported efficient points can be done in polynomial time. The problem of finding all efficient points, however, is harder; we propose a practical FPTAS for solving this problem. Some special cases are considered where the particular profit/cost structure or graph topology allows the efficient points to be found in polynomial time. Our results can be extended to more general graphs with distance matrices satisfying the Kalmanson conditions

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Section: Problem Subtreeementioning

confidence: 99%

Balancing profits and costs on trees

et al. 2012

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“…The classification of list‐generating algorithms to be described below in Definition 3 is based on a proposal due to Johnson , Yannakakis and Papadimitriou (1988), for problems in which the size of the output may be exponentially larger than the size of the input such as, for instance, the problem of listing all maximal independent sets of a graph, or all vertices of a polyhedron (see also Dyer 1983 or Lawler , Lenstra and Rinnooy Kan 1980, for related concepts. A similar approach is encountered in the study of the complexity of counting and enumerating solutions of multicriteria problems (see T'kindt Bouibede‐Hocine and Esswein (2005) for a thorough treatment.…”

Section: Solving the Optimization Version Of High Multiplicity Schementioning

confidence: 99%

Multiplicity and complexity issues in contemporary production scheduling

Brauner¹,

Crama²,

Grigoriev³

et al. 2007

Statistica Neerlandica

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High multiplicity scheduling problems arise naturally in contemporary production settings where manufacturers combine economies of scale with high product variety. Despite their frequent occurrence in practice, the complexity of high multiplicity problems -as opposed to classical, single multiplicity problems -is in many cases not well understood. In this paper, we discuss various concepts and results that enable a better understanding of the nature and complexity of high multiplicity scheduling problems. The paper extends the framework presented in Brauner et al. (2005) for single machine, non preemptive high multiplicity scheduling problems, to more general classes of problems.

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