A Branch-and-Price Approach for the Maximum Weight Independent Set Problem Deepak Warrier (deepakwarrier@hotmail.com) Wilbert E. Wilhelm (wilhelm@tamu.edu ) 1 Jeffrey S. Warren (j-warren@tamu.edu ) Illya V. Hicks (ivhicks@tamu.edu ) Department of Industrial Engineering Texas A&M University TAMUS 3131 College Station, TX 77843-3131 March 9, 2005 Revised May 31, 2005 August 22, 2005 Abstract The maximum weight independent set problem (MWISP) is one of the most well-known and well- studied problems in combinatorial optimization. This paper presents a novel approach to solve MWISP exactly by decomposing the original graph into vertex-induced sub-graphs. The approach solves MWISP for the original graph by solving MWISP on the sub-graphs in order to generate columns for a branch-and-price framework. The authors investigate different implementation techniques that can be associated with the approach and offer computational results to identify the strengths and weaknesses of each implementation technique. Key Words Branch and price, maximum weight independent set problem, Dantzig-Wolfe Decomposition, vertex partitioning, inheritly decomposable graphs 1 Communicating author 1