A greedy approximation algorithm for the group Steiner problem

A greedy approximation algorithm for the group Steiner problem

A combinatorial approximation algorithm for the group Steiner problem

In the group Steiner problem we are given a graph with edge weights w(e) and m subsets of vertices fg i g m i=1. Each subset g i is called a group and the vertices in S g i are called terminals. It is required to nd a minimum weight tree that contains at least one terminal from every group. We present the rst combinatorial poly-logarithmic ratio approximation for this problem when the input gra...

the algorithm for solving the inverse numerical range problem

برد عددی ماتریس مربعی a را با w(a) نشان داده و به این صورت تعریف می کنیم w(a)={x8ax:x ?s1} ، که در آن s1 گوی واحد است. در سال 2009، راسل کاردن مساله برد عددی معکوس را به این صورت مطرح کرده است : برای نقطه z?w(a)، بردار x?s1 را به گونه ای می یابیم که z=x*ax، در این پایان نامه ، الگوریتمی برای حل مساله برد عددی معکوس ارانه می دهیم.

A Practical Greedy Approximation for the Directed Steiner Tree Problem

The Directed Steiner Tree (DST) NP-hard problem asks, considering a directed weighted graph with n nodes and m arcs, a node r called root and a set of k nodes X called terminals, for a minimum cost directed tree rooted at r spanning X. The best known polynomial approximation ratio for DST is a O(k)-approximation greedy algorithm. However, a much faster k-approximation, returning the shortest pa...

A Primal-Dual Approximation Algorithm for the Steiner Connectivity Problem

We extend the primal-dual approximation technique of Goemans and Williamson to the Steiner connectivity problem, a kind of Steiner tree problem in hypergraphs. This yields a (k+1)-approximation algorithm for the case that k is the minimum of the maximal number of nodes in a hyperedge minus 1 and the maximal number of terminal nodes in a hyperedge. These results require the proof of a degree pro...