Eigenvalue, Quadratic Programming and Semidefinite Programming Bounds for Graph Partitioning Problems

Graph Partitioning;Semidefinite Programming;eigenvalue bounds;Combinatorics and Optimization

Wang, Ningchuan

University of Waterloo

关键词: Graph Partitioning;    Semidefinite Programming;    eigenvalue bounds;    Combinatorics and Optimization;   

Others  :  https://uwspace.uwaterloo.ca/bitstream/10012/8760/1/Wang_Ningchuan.pdf

瑞士|英语

来源: UWSPACE Waterloo Institutional Repository

【 摘 要 】

The Graph Partitioning problems are hard combinatorial optimization problems. We are interested in both lower bounds and upper bounds. We introduce several methods including basic eigenvalue and projected eigenvalue techniques, convex quadratic programming techniques, and semidefinite programming (SDP). In particular, we show that the SDP relaxation is equivalent to and arises from the Lagrangian relaxation for a particular quadratically constrained quadratic model. Moreover, the bounds obtained by the eigenvalue techniques are good and cheap.