Finding 2-edge connected spanning subgraphs
نویسنده
چکیده
This paper studies the NP-hard problem of /nding a minimum size 2-edge connected spanning subgraph (2-ECSS). An algorithm is given that on an r-edge connected input graph G=(V; E) /nds a 2-ECSS of size at most |V |+(|E|−|V |)=(r−1). For r-regular, r-edge connected input graphs for r = 3, 4, 5 and 6, this gives approximation guarantees of 4 ; 4 3 ; 11 8 and 7 5 , respectively. c © 2003 Elsevier B.V. All rights reserved.
منابع مشابه
Approximate Minimum 2-Connected Subgraphs in Weighted Planar Graphs
We consider the problems of finding the minimum-weight 2-connected spanning subgraph in edge-weighted planar graphs and its variations. We first give a PTAS for the problem of finding minimum-weight 2-edge-connected spanning subgraphs where duplicate edges are allowed. Then we present a new greedy spanner construction for edge-weighted planar graphs. From this we derive quasi-polynomial time ap...
متن کاملFinding k-Connected Subgraphs with Minimum Average Weight
We consider the problems of finding k-connected spanning subgraphs with minimum average weight. We show that the problems are NP-hard for k > 1. Approximation algorithms are given for four versions of the minimum average edge weight problem: 1. 3-approximation for k-edge-connectivity, 2. O(logk) approximation for k-node-connectivity 3. 2+ approximation for k-node-connectivity in Euclidian graph...
متن کاملOn Finding Minimal Two-Connected Subgraphs
Wepresent e cient parallel algorithms for the problems of nding a minimal2-edge-connected spanning subgraph of a 2-edge-connected graph and nding a minimalbiconnected spanning subgraph of a biconnected graph. The parallel algorithms run in polylog time using a linear number of PRAM processors. We also give linear time sequential algorithms for minimally augmenting a spanning tree into a 2-edge-...
متن کاملApproximation Schemes for Minimum 2-Connected Spanning Subgraphs in Weighted Planar Graphs
We present new approximation schemes for various classical problems of finding the minimum-weight spanning subgraph in edgeweighted undirected planar graphs that are resistant to edge or vertex removal. We first give a PTAS for the problem of finding minimum-weight 2-edge-connected spanning subgraphs where duplicate edges are allowed. Then we present a new greedy spanner construction for edge-w...
متن کاملSeries-parallel subgraphs of planar graphs
In this paper we show that every 3-connected (3-edge-connected) planar graph contains a 2-connected (respectively, 2-edge-connected) spanning partial 2-tree (seriesparallel) graph. In contrast, a recent result by [4] implies that not all 3-connected graphs contain 2-edge-connected series-parallel spanning subgraphs.
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:
- Oper. Res. Lett.
دوره 32 شماره
صفحات -
تاریخ انتشار 2004