Inapproximability of Hypergraph Vertex Cover and Applications to Scheduling Problems
نویسندگان
چکیده
Assuming the Unique Games Conjecture (UGC), we show optimal inapproximability results for two classic scheduling problems. We obtain a hardness of 2 − ε for the problem of minimizing the total weighted completion time in concurrent open shops. We also obtain a hardness of 2 − ε for minimizing the makespan in the assembly line problem. These results follow from a new inapproximability result for the Vertex Cover problem on k-uniform hypergraphs that is stronger and simpler than previous results. We show that assuming the UGC, for every k ≥ 2, the problem is inapproximable within k − ε even when the hypergraph is almost k-partite.
منابع مشابه
The Inapproximability of Non NP-hard Optimization Problems
The inapproximability of non NP-hard optimization problems is investigated. Techniques are given to show that problems Log Dominating Set and Log Hypergraph Vertex Cover cannot be approximated to a constant ratio in polynomial time unless the corresponding NP-hard versions are also approximable in deterministic subexponential time. A direct connection is established between non NP-hard problems...
متن کاملNew Results in the Theory of Approximation Fast Graph Algorithms and Inapproximability
For several basic optimization problems, it is NP-hard to find an exact solution. As a result, understanding the best possible trade-off between the running time of an algorithm and its approximation guarantee, is a fundamental question in theoretical computer science, and the central goal of the theory of approximation. There are two aspects to the theory of approximation : (1) efficient appro...
متن کاملStrong Inapproximability Results on Balanced Rainbow-Colorable Hypergraphs
Consider a K-uniform hypergraph H = (V,E). A coloring c : V → {1, 2, . . . , k} with k colors is rainbow if every hyperedge e contains at least one vertex from each color, and is called perfectly balanced when each color appears the same number of times. A simple polynomialtime algorithm finds a 2-coloring if H admits a perfectly balanced rainbow k-coloring. For a hypergraph that admits an almo...
متن کاملInapproximability of H-Transversal/Packing
Given an undirected graph G = (VG, EG) and a fixed pattern graph H = (VH , EH) with k vertices, we consider the H-Transversal and H-Packing problems. The former asks to find the smallest S ⊆ VG such that the subgraph induced by VG \ S does not have H as a subgraph, and the latter asks to find the maximum number of pairwise disjoint k-subsets S1, ..., Sm ⊆ VG such that the subgraph induced by ea...
متن کاملThe Quest for Strong Inapproximability Results with Perfect Completeness
The Unique Games Conjecture (UGC) has pinned down the approximability of all constraint satisfaction problems (CSPs), showing that a natural semidefinite programming relaxation offers the optimal worst-case approximation ratio for any CSP. This elegant picture, however, does not apply for CSP instances that are perfectly satisfiable, due to the imperfect completeness inherent in the UGC. For th...
متن کامل