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[nazev_en] => Stochastic Heuristic Methods for the Steiner Tree Problem in Graphs
[popis_en] => The Steiner tree problem in graphs (SPG) is concerned with connecting a subset of vertices at minimal cost. More precisely, given an undirected connected graph G=(V,E) with vertex set V, edge set E, nonnegative weights associated with the edges, and a subset B of V (called customer vertices or terminals), the problem is to find a subgraph, T, which connects the vertices in B so that the sum of the weights of the edges in T is minimized. It is obvious that the solution is always a tree and it is called a minimal Steiner tree for B in G. Applications of the SPG are frequently found in the layout of connection structures in networks and circuit design. Their common feature is that of connecting together a set of terminals (communications sites or circuits components) by a network of minimal total length. The contribution presents an application of stochastic heuristic methods in a combination with approximate algorithms and compares their effectiveness using standard benchmarks from OR-library.
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[popis] => Critical Path Method (CPM) is well known tool in project scheduling where time duration of activities and their precedence relationships are defined and resource capacities are not limited. In practice it usually is not satisfied. In spite of this, the CPM is a base of more general methods as PERT, solving the Resource Constrained Project Scheduling Problem (RCPSP), and Job Shop Scheduling Problem (JSSP) when it is represented by the disjunctive graph. RCPSP and JSSP are NP-hard problems and therefore it is necessary to solve them by heuristic methods. Here, with respect to high number of iterations, the effectiveness of the CPM calculations plays a substantial role. This contribution proposes a new implementation of the CPM using a lexicographical ordering of edges in network graphs and shows that its time complexity is lower than the time complexity of classical approaches. This conclusion is verified using the representative class of benchmarks.
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[citace_text] => ŠEDA, M. A New Implementation of the Critical Path Method Using Lexicographical Ordering of Edges. In Proceedings of the 35th Spring International Conference Modelling and Simulation of Systems MOSIS '01. Ostrava: MARQ Ostrava, 2001. 6 p. ISBN: 80-85988-57-7.
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author="Miloš {Šeda}",
title="Eppstein’s Proof of the Steiner Ratio for Rectilinear Steiner Trees is Mistaken and How to Correct it",
booktitle="Proceedings of the 7th International Conference on Soft Computing MENDEL 2001",
year="2001",
pages="7",
publisher="VUT FSI v Brně",
address="Brno",
isbn="80-214-1894-X"
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[citace_text] => ŠEDA, M. Computing Near-Optimal Solutions to the Network Steiner Tree Problem Using Approximate and Heuristic Techniques. In Proceedings of the 13th International Conference PROCESS CONTROL ‘01. Bratislava: KIRP CHTF STU Bratislava, 2001. 11 p. ISBN: 80-227-1542-5.
[citace_html] => ŠEDA, M. Computing Near-Optimal Solutions to the Network Steiner Tree Problem Using Approximate and Heuristic Techniques. In Proceedings of the 13th International Conference PROCESS CONTROL ‘01. Bratislava: KIRP CHTF STU Bratislava, 2001. 11 p. ISBN: 80-227-1542-5.
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[nazev_en] => Computing Near-Optimal Solutions to the Network Steiner Tree Problem Using Approximate and Heuristic Techniques
[popis_en] => This paper deals with the network Steiner tree problem. It proposes a mathematical model of this problem and its modification for including it in software package GAMS. As this optimisation tool is not able to find an optimum for larger instances in a reasonable amount of time we propose an approach that combines approximate and deterministic heuristic methods with stochastic heuristic techniques.
[klicova_slova_en] => minimum spanning tree, Steiner tree, approximate algorithm, stochastic heuristics
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