Approximating k-outconnected Subgraph Problems

نویسندگان

  • Joseph Cheriyan
  • Tibor Jordán
  • Zeev Nutov
چکیده

We present approximation algorithms and structural results for problems in network design. We give improved approximation algorithms for nding min-cost k-outconnected graphs with either a single root or multiple roots for (i) uniform costs, and (ii) metric costs. The improvements are obtained by focusing on single-root k-outconnected graphs and proving (i) a version of Mader's critical cycle theorem and (ii) an extension of a splitting oo theorem by Bienstock et al.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Approximating Minimum Power Edge-Multi-Covers

Given a graph with edge costs, the power of a node is the maximum cost of an edge incident to it, and the power of a graph is the sum of the powers of its nodes. Motivated by applications in wireless networks, we consider the following fundamental problem in wireless network design. Given a graph G = (V,E) with edge costs and degree bounds {r(v) : v ∈ V }, the Minimum-Power Edge-Multi-Cover (MP...

متن کامل

Minimum Power Connectivity Problems

Given a (directed or undirected) graph with costs on the edges, the power of a node is the maximum cost of an edge leaving it, and the power of the graph is the sum of the powers of its nodes. Motivated by applications for wireless networks, we consider some fundamental network design problems under the power minimization criteria. Let G = (V, E) be a graph with edge-costs {ce : e ∈ E} and let ...

متن کامل

An O(log k)-approximation algorithm for the k-vertex connected subgraph problem

We present an O(log n · log k)-approximation algorithm for the problem of finding k-vertex connected spanning subgraph of minimum cost, where n is the number of vertices in the input graph, and k is the connectivity requirement. Our algorithm works for both directed and undirected graphs. The best known approximation guarantees for this problems are O(ln k · min{ √ k, n n−k ln k}) by Kortsarz a...

متن کامل

On extremal k-outconnected graphs

Let G be a minimally k-connected graph with n nodes and m edges. Mader proved that if n ≥ 3k− 2 then m ≤ k(n− k), and for n ≥ 3k− 1 an equality is possible if, and only if, G is the complete bipartite graph Kk,n−k. Cai proved that if n ≤ 3k − 2 then m ≤ b(n + k)2/8c, and listed the cases when this bound is tight. In this paper we prove a more general theorem, which implies similar results for m...

متن کامل

Approximating Maximum Subgraphs without Short Cycles

We study approximation algorithms, integrality gaps, and hardness of approximation, of two problems related to cycles of “small” length k in a given (undirected) graph. The instance for these problems consists of a graph G = (V, E) and an integer k. The k-Cycle Transversal problem is to find a minimum edge subset of E that intersects every k-cycle. The k-Cycle-Free Subgraph problem is to find a...

متن کامل

ذخیره 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 نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 1998