20th International Symposium on Mathematical Programming TA02 Tuesday, 10:30am - 12:00pm ■ TA01 Marriott - Chicago A Geometric Methods for Approximation Algorithms Cluster: Approximation Algorithms Invited Session Chair: Cliff Stein, Columbia University, 326 S W Mudd Building, 500 W. 120th Street, New York, NY, 10027,
[email protected] 1 - Geometric Rounding: Theory and Application Dongdong Ge, Stanford University, Terman 328, Stanford, 94305, United States of America,
[email protected], Jiawei Zhang, Yinyu Ye We develop a new dependent randomized rounding method for approximation of optimization problems with integral assignment constraints. The core of the method is a simple, intuitive, and computationally efficient geometric rounding that simultaneously rounds multiple points in a multi-dimensional simplex to its vertices. Using this method we obtain in a systematic way known as well as new results for a series of combinatorial optimization problems. 2 - Understanding the Limits of Semidefinite Programming through Unique Games Prasad Raghavendra, University of Washington, #4, 5856 Alderson Street, Pittsburgh, PA, 15217, United States of America,
[email protected], David Steurer Assuming the Unique games conjecture (UGC), recent work has demonstrated that a simple semidefinite programming relaxation yields the best approximation for large classes of combinatorial optimization problems like constraint satisfaction problems. In this work, we show that irrespective of the truth of UGC, introducing additional constraints