Directed Steiner Tree and the Lasserre Hierarchy
نویسنده
چکیده
Known results: • Generalizes Set Cover, (Non-Metric / Multi-level) Facility Location, Group Steiner Tree • Ω(log2− n)-hard (Halperin, Krauthgamer ’03) • |X| -apx in poly by sophisticated greedy algo (Zelikovsky ’97) • O(log |X|)-apx in nO(log |X|) time by more sophisticated greedy algo (Charikar, Chekuri, Cheung, Goel, Guha and Li ’99) • LP’s have integrality gap Ω( √ k) already for 5 layers; existing attempts fail (Alon, Moitra, Sudakov ’12).
منابع مشابه
Directed Steiner Tree and the Lasserre Hierarchy
The goal for the DIRECTED STEINER TREE problem is to find a minimum cost tree in a directed graph G = (V ,E ) that connects all terminals X to a given root r . It is well known that modulo a logarithmic factor it suffices to consider acyclic graphs where the nodes are arranged in l ≤ log |X | levels. Unfortunately the natural LP formulation has a Ω( p |X |) integrality gap already for 5 levels....
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عنوان ژورنال:
- CoRR
دوره abs/1111.5473 شماره
صفحات -
تاریخ انتشار 2011