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....
متن کاملLinear Programming Hierarchies Suffice for Directed Steiner Tree
We demonstrate that ` rounds of the Sherali-Adams hierarchy and 2` rounds of the Lovász-Schrijver hierarchy suffice to reduce the integrality gap of a natural LP relaxation for Directed Steiner Tree in `-layered graphs from Ω( √ k) to O(` · log k) where k is the number of terminals. This is an improvement over Rothvoss’ result that 2` rounds of the considerably stronger Lasserre SDP hierarchy r...
متن کاملOn The Integrality Gap of Directed Steiner Tree Problem
In the Directed Steiner Tree problem, we are given a directed graph G = (V,E) with edge costs, a root vertex r ∈ V , and a terminal set X ⊆ V . The goal is to find the cheapest subset of edges that contains an r-t path for every terminal t ∈ X. The only known polylogarithmic approximations for Directed Steiner Tree run in quasi-polynomial time and the best polynomial time approximations only ac...
متن کاملSolving a tri-objective convergent product network using the Steiner tree
Considering convergent product as an important manufacturing technology for digital products, we integrate functions and sub-functions using a comprehensive fuzzy mathematical optimization process. To form the convergent product, a web-based fuzzy network is considered in which a collection of base functions and sub-functions configure the nodes and each arc in the network is to be a link betwe...
متن کاملSteiner Transitive-Closure Spanners of Low-Dimensional Posets
Given a directed graph G = (V,E) and an integer k ≥ 1, a Steiner k-transitive-closure-spanner (Steiner k-TC-spanner) of G is a directed graph H = (VH , EH) such that (1) V ⊆ VH and (2) for all vertices v, u ∈ V , the distance from v to u in H is at most k if u is reachable from v in G, and ∞ otherwise. Motivated by applications to property reconstruction and access control hierarchies, we conce...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- CoRR
دوره abs/1111.5473 شماره
صفحات -
تاریخ انتشار 2011