Computing directed Minimum Spanning Tree (DMST) is a fundamental problem in graph theory. It applied wide spectrum of fields from computer network and communication protocol design to revenue maximization social networks syntactic parsing Natural Language Processing. State-of-the-art solutions are online algorithms that compute DMST for given root. For multi-query requirements, the algorithm in...

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) ...

Given a directed graph G with non negative cost on the arcs, a directed tree cover of G is a 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 sp...

We introduce a single-valued solution concept, the so-called average covering tree value, for the class of transferable utility games with limited communication structure represented by a directed graph. The solution is the average of the marginal contribution vectors corresponding to all covering trees of the directed graph. The covering trees of a directed graph are those (rooted) trees on th...

A directed spanning tree in a directed graph G = (V,A) is a spanning tree such that no two arcs share their tails. In this paper, we propose an algorithm for listing all directed spanning trees of G. Its time and space complexities are O(|A| + ND(|V |, |A|)) and O(|A|+DS(|V |, |A|)), where D(|V |, |A|) and DS(|V |, |A|) are the time and space complexities of the data structure for updating the ...

The Matrix-Forest Theorem the number of C>'-UUiiJL<hv.UA. obtained A J-cycle in G, for J ~ is a directed For any node i, an i-rooted tree in we mean a tree where one outgoing which has none. In other in the tree, the path between j and i in the tree directed towards tree is sometimes called an "in-directed arborescence".) If the tree reaches all the nodes m it is an i-rooted tree. For any node ...