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By J. Ian Munro, Robert Sedgewick, Dorothea Wagner, Wojciech Szpankowski
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Extra info for Proc. 10th workshop on algorithm engineering, 5th workshop on analytic algorithmics and combinatorics
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In the section thereafter, we provide polyhedral and algorithmic comparison to the known Gsec formulation. In Section 4, we describe the resulting Branchand-Cut algorithm in order to deal with the exponential ILP size. We conclude the paper with the extensive experimental study in Section 5, where we compare our algorithm with the state-of-the-art metaheuristics for the KCT. 1 Transformation into the k-Cardinality Arborescence Problem. Let D = (VD , AD ) be a directed graph with a distinguished root vertex r ∈ VD and arc costs ca for all arcs a ∈ AD .
This solution is feasible for the LP-relaxation of less, as experimentally shown in [22] for PCST and is GUCut, but infeasible for DCut. 14) speeds up the algorithm tremendously, as they 4 Branch-and-Cut Algorithm do not have to be separated explicitly by the BranchBased on our DCut formulation, we developed and im- and-Cut algorithm. plemented a Branch-and-Cut algorithm. 15) xrj ≤ 1 − yi ∀i, j ∈ V, i < j. considering a certain subset of all constraints. , identify constraints of the full adjacent to the root is the one with the smallest possible constraint set which the current solution violates.
We would like to thank Peter cal approach: SHARC steps up the hierarchy at the be- Sanders and Dominik Schultes for interesting discusginning of the query, runs a strongly goal-directed query sions on contraction and arc-flags. We also thank Daniel on the highest level and automatically steps down the Karch for implementing classic Arc-Flags. Finally, we hierarchy as soon as the search is approaching the target thank Moritz Hilger for running a preliminary expericell. As a result we are able to perform queries as fast ment with his new centralized approach.