A 1.5-approximation algorithm for augmenting edge-connectivity of a graph
نویسندگان
چکیده
We present a 1.5-approximation algorithm for the following NP-hard problem: given a connected graph G = (V, E) and an edge set E on V disjoint to E , find a minimum size subset of edges F ⊆ E such that (V, E ∪ F ) is 2-edge-connected. Our result improves and significantly simplifies the approximation algorithm with ratio 1.875 + ε of Nagamochi.
منابع مشابه
A simplified 1.5-approximation algorithm for augmenting edge-connectivity of a graph
The Tree Augmentation Problem(TAP) is given a connected graph G = (V, E) and an edge set E on V disjoint to E , find a minimum size subset of edges F ⊆ E such that (V, E ∪ F ) is 2-edge-connected. In [5] and [6] a 1.8 and 1.5 approximation were given for the problem. The proof of the 1.5 was cut into two papers, as our proof then was very complex and very long. In the current paper we present a...
متن کاملA Survey on Complexity of Integrity Parameter
Many graph theoretical parameters have been used to describe the vulnerability of communication networks, including toughness, binding number, rate of disruption, neighbor-connectivity, integrity, mean integrity, edgeconnectivity vector, l-connectivity and tenacity. In this paper we discuss Integrity and its properties in vulnerability calculation. The integrity of a graph G, I(G), is defined t...
متن کاملA 1.5-approximation algorithm for augmenting edge-connectivity of a graph from 1 to 2
We consider the following NP-hard problem: given a connected graph G = (V, E) and an edge set E on V disjoint to E , find a minimum size subset of edges F ⊆ E such that (V, E ∪ F ) is 2-edge-connected. In [4] we presented a 1.8 approximation for the problem. In this paper we improve the ratio to 1.5. ∗Preliminary version appeared in APPROX 2001, LNCS 2129, pp. 90-101, 2001. †Dept. of Electrical...
متن کاملSufficient conditions for maximally edge-connected and super-edge-connected
Let $G$ be a connected graph with minimum degree $delta$ and edge-connectivity $lambda$. A graph ismaximally edge-connected if $lambda=delta$, and it is super-edge-connected if every minimum edge-cut istrivial; that is, if every minimum edge-cut consists of edges incident with a vertex of minimum degree.In this paper, we show that a connected graph or a connected triangle-free graph is maximall...
متن کاملOn the edge-connectivity of C_4-free graphs
Let $G$ be a connected graph of order $n$ and minimum degree $delta(G)$.The edge-connectivity $lambda(G)$ of $G$ is the minimum numberof edges whose removal renders $G$ disconnected. It is well-known that$lambda(G) leq delta(G)$,and if $lambda(G)=delta(G)$, then$G$ is said to be maximally edge-connected. A classical resultby Chartrand gives the sufficient condition $delta(G) geq frac{n-1}{2}$fo...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2001