The number of vertices of degree k in a minimally k-edge-connected graph
Journal of Combinatorial Theory Series B
Biconnectivity approximations and graph carvings
Journal of the ACM (JACM)
Approximation algorithms for finding highly connected subgraphs
Approximation algorithms for NP-hard problems
Approximating Minimum-Size k-Connected Spanning Subgraphs via Matching
SIAM Journal on Computing
A 5/4-approximation algorithm for minimum 2-edge-connectivity
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Special edges, and approximating the smallest directed k-edge connected spanning subgraph
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
SIAM Journal on Discrete Mathematics
Approximating the smallest k-edge connected spanning subgraph by LP-rounding
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Max-Weight Integral Multicommodity Flow in Spiders and High-Capacity Trees
Approximation and Online Algorithms
k-edge-connectivity: approximation and LP relaxation
WAOA'10 Proceedings of the 8th international conference on Approximation and online algorithms
Approximating the smallest 2-vertex connected spanning subgraph of a directed graph
ESA'11 Proceedings of the 19th European conference on Algorithms
On the maximum size of a minimal k-edge connected augmentation
Journal of Combinatorial Theory Series B
A rounding by sampling approach to the minimum size k-arc connected subgraph problem
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part I
Hi-index | 0.00 |
We present the best known algorithms for approximating the minimum cardinality undirected k-edge connected spanning subgraph. For simple graphs our approximation ratio is 1 + 1/2k + O(1/k2). The more precise version of our bound requires k ≥ 7, and for all such k it improves the longstanding bound of Cheriyan and Thurimella, 1 + 2/(k + 1) [2]. The improvement comes in two steps: First we show that for simple k-edge connected graphs, any laminar family of degree k sets is smaller than the general bound (n(1 + 3/k + O(1/k√k)) versus 2n). This immediately implies that iterated rounding improves the bound of [2]. Our second step improves iterated rounding by finding good edges for rounding. For multigraphs our approximation ratio is 1 + 21/11k k. This improves the previous bound 1 + 2/k [6]. It is of interest since it is known that for some constant c 0, an approximation ratio ≤ 1 + c/k implies P = NP. Our approximation ratio extends to the minimum cardinality Steiner network problem, where k denotes the average vertex demand. The algorithm exploits rounding properties of the first two linear programs in iterated rounding.