Skip to main content
U.S. Department of Energy
Office of Scientific and Technical Information

A New Bound for the Ration Between the 2-Matching Problem and Its Linear Programming Relaxation

Journal Article · · Mathematical Programming

Consider the 2-matching problem defined on the complete graph, with edge costs which satisfy the triangle inequality. We prove that the value of a minimum cost 2-matching is bounded above by 4/3 times the value of its linear programming relaxation, the fractional 2-matching problem. This lends credibility to a long-standing conjecture that the optimal value for the traveling salesman problem is bounded above by 4/3 times the value of its linear programming relaxation, the subtour elimination problem.

Research Organization:
Sandia National Labs., Albuquerque, NM (US); Sandia National Labs., Livermore, CA (US)
Sponsoring Organization:
US Department of Energy (US)
DOE Contract Number:
AC04-94AL85000
OSTI ID:
9490
Report Number(s):
SAND99-1971J
Journal Information:
Mathematical Programming, Journal Name: Mathematical Programming
Country of Publication:
United States
Language:
English

Similar Records

A new bound for the 2-edge connected subgraph problem
Conference · Tue Mar 31 23:00:00 EST 1998 · OSTI ID:671991

Steiner problem in graphs: Lagrangean relaxation and strong valid inequalities
Conference · Fri Dec 30 23:00:00 EST 1994 · OSTI ID:36244

The cost-constrained traveling salesman problem
Technical Report · Mon Oct 01 00:00:00 EDT 1990 · OSTI ID:6223080