Approximating the tree and tour covers of a graph
Information Processing Letters
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Improved low-degree testing and its applications
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
A threshold of ln n for approximating set cover
Journal of the ACM (JACM)
On the hardness of approximating minimization problems
Journal of the ACM (JACM)
Approximation algorithms for directed Steiner problems
Journal of Algorithms
On approximability of the independent/connected edge dominating set problems
Information Processing Letters
A 2log2(n)-Approximation Algorithm for Directed Tour Cover
COCOA '09 Proceedings of the 3rd International Conference on Combinatorial Optimization and Applications
How to trim an MST: a 2-approximation algorithm for minimum cost tree cover
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part I
Multi-rooted greedy approximation of directed steiner trees with applications
WG'12 Proceedings of the 38th international conference on Graph-Theoretic Concepts in Computer Science
| Hi-index | 0.00 |
Given a directed graph G with non negative cost on the arcs, a directed tree cover of G is a rooted directed tree such that either head or tail (or both of them) of every arc in G is touched by T. The minimum directed tree cover problem (DTCP) is to find a directed tree cover of minimum cost. The problem is known to be NP-hard. In this paper, we show that the weighted Set Cover Problem (SCP) is a special case of DTCP. Hence, one can expect at best to approximate DTCP with the same ratio as for SCP. We show that this expectation can be satisfied in some way by designing a purely combinatorial approximation algorithm for the DTCP and proving that the approximation ratio of the algorithm is max{2, ln(D+)} with D+ is the maximum outgoing degree of the nodes in G.