Complexity of approximating the oriented diameter of chordal graphs
نویسندگان
چکیده
The oriented diameter of a bridgeless connected undirected (bcu ) graph G is the smallest diameter among all the diameters of strongly connected orientations of G. We study algorithmic aspects of determining the oriented diameter of a chordal graph. We (a) construct a linear-time approximation algorithm that, for a given chordal bcu graph G, finds a strongly connected orientation of G with diameter at most one plus twice the oriented diameter of G; (b) prove that, for every k 2 and k 61⁄4 3, to
منابع مشابه
Complement of Special Chordal Graphs and Vertex Decomposability
In this paper, we introduce a subclass of chordal graphs which contains $d$-trees and show that their complement are vertex decomposable and so is shellable and sequentially Cohen-Macaulay.
متن کاملTree Spanners on Chordal Graphs: Complexity, Algorithms, Open Problems
A tree t-spanner T in a graph G is a spanning tree of G such that the distance in T between every pair of vertices is at most t times their distance in G. The Tree t-Spanner problem asks whether a graph admits a tree t-spanner, given t. We substantially strengthen the hardness result of Cai and Corneil [SIAM J. Discrete Math. 8 (1995) 359– 387] by showing that, for any t ≥ 4, Tree t-Spanner is ...
متن کاملTree spanners on chordal graphs: complexity and algorithms
A tree t-spanner T in a graph G is a spanning tree of G such that the distance in T between every pair of vertices is at most t times their distance in G. The TREE t-SPANNER problem asks whether a graph admits a tree t-spanner, given t. We substantially strengthen the hardness result of Cai and Corneil (SIAM J. Discrete Math. 8 (1995) 359–387) by showing that, for any t¿ 4, TREE t-SPANNER is NP...
متن کاملDistributed Computing of Efficient Routing Schemes in Generalized Chordal Graphs
Efficient algorithms for computing routing tables should take advantage of the particular properties arising in large scale networks. There are in fact at least two properties that any routing scheme must consider: low (logarithmic) diameter and high clustering coefficient. High clustering coefficient implies the existence of few large induced cycles. Therefore, we propose a routing scheme that...
متن کاملTreewidth for Graphs with Small Chordality
A graph G is k-chordal, if it does not contain chordless cycles of length larger than k. The chordality Ic of a graph G is the minimum k for which G is k-chordal. The degeneracy or the width of a graph is the maximum min-degree of any of its subgraphs. Our results are the following: ( 1) The problem of treewidth remains NP-complete when restricted to graphs with small maximum degree. (2) An upp...
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:
- Journal of Graph Theory
دوره 45 شماره
صفحات -
تاریخ انتشار 2004