8,167 research outputs found

    A note on the lower bound for online strip packing

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    This note presents a lower bound of 3/2+33/62.4573/2+\sqrt{33}/6 \approx 2.457 on the competitive ratio for online strip packing. The instance construction we use to obtain the lower bound was first coined by Brown, Baker and Katseff (1980). Recently this instance construction is used to improve the lower bound in computer aided proofs. We derive the best possible lower bound that can be obtained with this instance construction

    The generalized sports competition problem

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    Consider a sports competition among various teams playing against each other in pairs (matches) according to a previously determined schedule. At some stage of the competition one may ask whether a particular team still has a (theoretical) chance to win the competition. The computational complexity of this question depends on the way scores are allocated according to the outcome of a match. For competitions with at most 33 different outcomes of a match the complexity is already known. In practice there are many competitions in which more than 33 outcomes are possible. We determine the complexity of the above problem for competitions with an arbitrary number of different outcomes. Our model also includes competitions that are asymmetric in the sense that away playing teams possibly receive other scores than home playing teams. \u

    Matching games: the least core and the nucleolus

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    A matching game is a cooperative game defined by a graph G=(V,E)G=(V,E). The player set is VV and the value of a coalition SVS \subseteq V is defined as the size of a maximum matching in the subgraph induced by SS. We show that the nucleolus of such games can be computed efficiently. The result is based on an alternative characterization of the least core which may be of independent interest. The general case of weighted matching games remains unsolved. \u

    A simple dual ascent algorithm for the multilevel facility location problem

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    We present a simple dual ascent method for the multilevel facility location problem which finds a solution within 66 times the optimum for the uncapacitated case and within 1212 times the optimum for the capacitated one. The algorithm is deterministic and based on the primal-dual technique. \u

    An improved local search algorithm for 3-SAT

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    We slightly improve the pruning technique presented in Dantsin et. al. (2002) to obtain an O(1.473n)\mathcal{O}^*\left(1.473^n\right) algorithm for 3-SAT

    The new FIFA rules are hard: Complexity aspects of sports competitions

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    Consider a soccer competition among various teams playing against each other in pairs (matches) according to a previously determined schedule. At some stage of the competition one may ask whether a particular team still has a (theoretical) chance to win the competition. The complexity of this question depends on the way scores are allocated according to the outcome of a match. For example, the problem is polynomially solvable for the ancient FIFA rules (2:0 resp. 1:1) but becomes NP-hard if the new rules (3:0 resp. 1:1) are applied. We determine the complexity of the above problem for all possible score allocation rules. \u

    Space related scientific and technical investigations Final progress report, 1 Sep. 1967 - 29 Feb. 1968

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    Research projects in low temperature physics, solid state physics, atomic physics, comet physics, and physics of space related flow problem

    Note on the game chromatic index of trees

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    We study edge coloring games defining the so-called game chromatic index of a graph. It has been reported that the game chromatic index of trees with maximum degree Δ=3\Delta = 3 is at most Δ+1\Delta + 1. We show that the same holds true in case Δ6\Delta \geq 6, which would leave only the cases Δ=4\Delta = 4 and Δ=5\Delta = 5 open. \u

    The generalized minimum spanning tree problem

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    We consider the Generalized Minimum Spanning Tree Problem denoted by GMSTP. It is known that GMSTP is NP-hard and even finding a near optimal solution is NP-hard. We introduce a new mixed integer programming formulation of the problem which contains a polynomial number of constraints and a polynomial number of variables. Based on this formulation we give an heuristic solution, a lower bound procedure and an upper bound procedure and present the advantages of our approach in comparison with an earlier method. We present a solution procedure for solving GMST problem using cutting planes

    An approximation algorithm for the generalized minimum spanning tree problem with bounded cluster size

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    Given a complete undirected graph with the nodes partitioned into m node sets called clusters, the Generalized Minimum Spanning Tree problem denoted by GMST is to find a minimum-cost tree which includes exactly one node from each cluster. It is known that the GMST problem is NP-hard and even finding a near optimal solution is NP-hard. We give an approximation algorithm for the Generalized Minimum Spanning Tree problem in the case when the cluster size is bounded by ρ\rho. In this case, the GMST problem can be approximated to within 2ρ\rho
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