A new bound for the 2-edge connected subgraph problem
- Sandia National Labs., Albuquerque, NM (United States)
- Carnegie Mellon Univ., Pittsburgh, PA (United States)
Given a complete undirected graph with non-negative costs on the edges, the 2-Edge Connected Subgraph Problem consists in finding the minimum cost spanning 2-edge connected subgraph (where multi-edges are allowed in the solution). A lower bound for the minimum cost 2-edge connected subgraph is obtained by solving the linear programming relaxation for this problem, which coincides with the subtour relaxation of the traveling salesman problem when the costs satisfy the triangle inequality. The simplest fractional solutions to the subtour relaxation are the 1/2-integral solutions in which every edge variable has a value which is a multiple of 1/2. The authors show that the minimum cost of a 2-edge connected subgraph is at most four-thirds the cost of the minimum cost 1/2-integral solution of the subtour relaxation. This supports the long-standing 4/3 Conjecture for the TSP, which states that there is a Hamilton cycle which is within 4/3 times the cost of the optimal subtour relaxation solution when the costs satisfy the triangle inequality.
- Research Organization:
- Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
- Sponsoring Organization:
- USDOE, Washington, DC (United States)
- DOE Contract Number:
- AC04-94AL85000
- OSTI ID:
- 671991
- Report Number(s):
- SAND-98-0820C; CONF-980633-; ON: DE98004529; BR: DP0102052; CNN: Grant NSF DMS9509581; Grant NSF CCR-9625297; TRN: AHC2DT07%%150
- Resource Relation:
- Conference: 6. conference on integer programming and combinatorial optimization, Houston, TX (United States), 22-24 Jun 1998; Other Information: PBD: Apr 1998
- Country of Publication:
- United States
- Language:
- English
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