In the directed minimum spanning tree problem (DMST, also called weight arborescence), we are given a weighted graph, and root node r. Our goal is to construct minimum-weight tree, rooted at r oriented outwards. We present first sub-quadratic DMST algorithm in distributed $${\mathsf {CONGEST}}$$ network model, where messages exchanged between nodes bounded size. consider three versions of model...

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...

This paper investigates the complexity of self-stabilizing mutual exclusion protocols for distributed systems, where processors communicate through shared memory according to a strongly connected directed communication graph. Tchuente's approach of covering a network with one directed cycle is taken as point of departure. This protocol requires O(n 2n) states per processor together with some pr...

Tree-Embedding is one of the most powerful techniques in the area of approximation algorithms as it reduces many diffcult problems like group Steiner tree (GST) on general graphs into amenable tree intances. However, the developments on tree-embedding are pertained only to undirected graphs, thus rendering it useless against problems on directed graphs like directed Steiner tree (DST) and its g...

For a tree T , the graph X is T -decomposable if there exists a partition of the edge set of X into isomorphic copies of T . In 1963, Ringel conjectured that K2m+1 can be decomposed by any tree with m edges. Graham and Häggkvist conjectured more generally that every 2m-regular graph can be decomposed by any tree with m edges. Fink showed in 1994 that for any directed tree T with m arcs, the dir...