A heuristic for the Steiner problem in graphs
نویسندگان
چکیده
In this paper, we present a heuristic for the Steiner problem in graphs (SPG) along with some experimental results. The heuristic is based on an approach similar to Prim’s algorithm for the minimum spanning tree. However, in this approach, arcs are associated with preference weights which are used to break ties among alternative choices of shortest paths occurring during the course of the algorithm. The preference weights are calculated according to a global view which takes into consideration the effect of all the regular nodes, nodes to be connected, on determining the choice of an arc in the solution tree.
منابع مشابه
1.757 and 1.267 - Approximation Algorithms for the Network and Rectilinear Steiner Tree Problems
The Steiner tree problem requires to nd a shortest tree connecting a given set of terminal points in a metric space. We suggest a better and fast heuristic for the Steiner problem in graphs and in rectilinear plane. This heuristic nds a Steiner tree at most 1.757 and 1.267 times longer than the optimal solution in graphs and rectilinear plane, respectively.
متن کاملMETA-HEURISTIC ALGORITHMS FOR MINIMIZING THE NUMBER OF CROSSING OF COMPLETE GRAPHS AND COMPLETE BIPARTITE GRAPHS
The minimum crossing number problem is among the oldest and most fundamental problems arising in the area of automatic graph drawing. In this paper, eight population-based meta-heuristic algorithms are utilized to tackle the minimum crossing number problem for two special types of graphs, namely complete graphs and complete bipartite graphs. A 2-page book drawing representation is employed for ...
متن کاملNordhaus-Gaddum type results for the Harary index of graphs
The emph{Harary index} $H(G)$ of a connected graph $G$ is defined as $H(G)=sum_{u,vin V(G)}frac{1}{d_G(u,v)}$ where $d_G(u,v)$ is the distance between vertices $u$ and $v$ of $G$. The Steiner distance in a graph, introduced by Chartrand et al. in 1989, is a natural generalization of the concept of classical graph distance. For a connected graph $G$ of order at least $2$ ...
متن کاملTighter Bounds for Graph Steiner Tree Approximation
The classical Steiner tree problem in weighted graphs seeks a minimum weight connected subgraph containing a given subset of the vertices (terminals). We present a new polynomialtime heuristic that achieves a best-known approximation ratio of 1 + ln 3 2 ≈ 1.55 for general graphs, and best-known approximation ratios of ≈ 1.28 for quasi-bipartite graphs (i.e., where no two non-terminals are adjac...
متن کاملImproved Minimum Spanning Tree Heuristics for Steiner Tree problem in graph
The minimum Steiner tree problem, a classical combinatorial optimization problem with a long history, is a NP-complete problem. Due to its wide application, study of heuristic algorithm about Steiner tree problem has important practical and theoretical significance. In this paper we first review one of the existing algorithms for solving the Steiner problem in graphs, Minimum Spanning Tree Heur...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Comp. Opt. and Appl.
دوره 6 شماره
صفحات -
تاریخ انتشار 1996