Metric MAX-CUT is the problem of dividing a set of points in metric space into two parts so as to maximize the sum of the distances between points belonging to distinct parts. We show that metric MAX-CUT is NP-complete but has a polynomial time randomized approximation scheme.
A 78-approximation algorithm for metric Max TSP
β Scribed by Refael Hassin; Shlomi Rubinstein
- Publisher
- Elsevier Science
- Year
- 2002
- Tongue
- English
- Weight
- 66 KB
- Volume
- 81
- Category
- Article
- ISSN
- 0020-0190
No coin nor oath required. For personal study only.
β¦ Synopsis
We present a randomized approximation algorithm for the metric version of undirected Max TSP. Its expected performance guarantee approaches 7 8 as n β β, where n is the number of vertices in the graph.
π SIMILAR VOLUMES
We study approximation results for the Euclidean bipartite traveling salesman problem (TSP). We present the first worstcase examples, proving that the approximation guarantees of two known polynomial-time algorithms are tight. Moreover, we propose a new algorithm which displays a superior average ca
MAX SAT (the maximum s~tisfiability problem) is stated as follows: given a set of clauses with weights, find a truth assignment that maximizes the sum of the weights of the satisfied clauses. In this paper, we consider approxima~ tion algorithms for MAX SAT proposed by Goemans and Williamson and pze
We consider the problem of partitioning the node set of a graph into p equal sized subsets. The objective is to minimize the maximum length, over these subsets, of a minimum spanning tree. We show that no polynomial algorithm with bounded Ε½ 2 . error ratio can be given for the problem unless P s NP.
We prove upper and lower bounds on performance guarantees of approximation Ε½ . algorithms for the hierarchical MAX-SAT H-MAX-SAT problem. This problem is representative of a broad class of PSPACE-hard problems involving graphs, Boolean formulas, and other structures that are defined succinctly. Our