On full Steiner trees in unit disk graphs
نویسندگان
چکیده
Given an edge-weighted graph G = (V,E) and a subset R of V , a Steiner tree of G is a tree which spans all the vertices in R. A full Steiner tree is a Steiner tree which has all the vertices of R as its leaves. The full Steiner tree problem is to find a full Steiner tree of G with minimum weight. In this paper we consider the full Steiner tree problem when G is a unit disk graph. We present a 20-approximation algorithm for the full Steiner tree problem in G. As for λ-precise unit disk graphs we present a (10 + 1 λ)-approximation algorithm, where λ is the length of the shortest edge in G.
منابع مشابه
A (4 + ǫ)-Approximation for the Minimum-Weight Dominating Set Problem in Unit Disk Graphs
We present a (4 + ǫ)-approximation algorithm for the problem of computing a minimum-weight dominating set in unit disk graphs, where ǫ is an arbitrarily small constant. The previous best known approximation ratio was 5+ǫ. The main result of this paper is a 4-approximation algorithm for the problem restricted to constant-size areas. To obtain the (4 + ǫ)-approximation algorithm for the unrestric...
متن کاملNode-weighted Steiner tree approximation in unit disk graphs
Given a graph G = (V ,E) with node weight w : V → R+ and a subset S ⊆ V , find a minimum total weight tree interconnecting all nodes in S. This is the node-weighted Steiner tree problem which will be studied in this paper. In general, this problem is NP-hard and cannot be approximated by a polynomial time algorithm with performance ratio a lnn for any 0 < a < 1 unless NP ⊆ DTIME(nO(logn)), wher...
متن کاملApproximating Full Steiner Tree in a Unit Disk Graph
Given an edge-weighted graph G = (V,E) and a subset R of V , a Steiner tree of G is a tree which spans all the vertices in R. A full Steiner tree is a Steiner tree which has all the vertices of R as its leaves. The full Steiner tree problem is to find a full Steiner tree of G with minimum weight. In this paper we present a 20-approximation algorithm for the full Steiner tree problem when G is a...
متن کاملA PTAS for Node-Weighted Steiner Tree in Unit Disk Graphs
The node-weighted Steiner tree problem is a variation of classical Steiner minimum tree problem. Given a graph G = (V,E) with node weight function C : V → R and a subset X of V , the node-weighted Steiner tree problem is to find a Steiner tree for the set X such that its total weight is minimum. In this paper, we study this problem in unit disk graphs and present a (1+ε)-approximation algorithm...
متن کاملMinimum Steiner Trees in Normed Planes
A minimum Steiner tree for a given set X of points is a network interconnecting the points of X having minimum possible total length. In this note we investigate various properties of minimum Steiner trees in normed planes, i.e., where the "unit disk" is an arbitrary compact convex centrally symmetric domain D having nonempty interior. We show that if the boundary of D is strictly convex and di...
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:
- Comput. Geom.
دوره 48 شماره
صفحات -
تاریخ انتشار 2015