A better approximation ratio for the minimum k-edge-connected spanning subgraph problem

Conference · Sun Jun 01 04:00:00 EDT 1997

OSTI ID:471720

Fernandes, C G ^[1]

---

1. Georgia Institute of Technology, Atlanta, GA (United States)

Consider the minimum k-edge-connected spanning subgraph problem: given a positive integer k and a k-edge-connected graph G, find a k-edge-connected spanning subgraph of G with minimum number of edges. This problem is known to be NP-complete. Khuller and Raghavachari presented the first algorithm with a performance ratio smaller than 2 for all k. They proved an upper bound of 1.85 for the performance ratio of their algorithm. We improve their analysis, proving that the performance ratio of their algorithm is smaller than 1.7 for large enough k, and that it is at most 1.75 for all k. Our analysis improves the best known ratios for any fixed k {ge} 4, in particular, for k = 4 from 1.75 to 1.65, and for k = 5 from 1.733... to 1.68. Last, we show that the minimum k-edge-connected spanning subgraph problem is MAX SNP-hard, even for k = 2.

• OSTI ID: 471720
• Report Number(s): CONF-970142--; CNN: Contract 200975/92-7
• Country of Publication: United States
• Language: English

Related Subjects

99 GENERAL AND MISCELLANEOUS
ALGORITHMS
DIAGRAMS
NETWORK ANALYSIS
PERFORMANCE