An Exact Algorithm Exhibiting RS–RSB/Easy–Hard Correspondence for the Maximum Independent Set Problem

• DOI: 10.7566/jpsj.86.073001
• Publication Date: 2017-06-15T01:00:51Z
• Authors: Jun Takahashi; Satoshi Takabe; Koji Hukushima
• Keywords: FOS: Computer and information sciences; Statistical Mechanics (cond-mat.stat-mech); Computer Science - Data Structures and Algorithms; 0103 physical sciences; FOS: Physical sciences; Data Structures and Algorithms (cs.DS); Disordered Systems and Neural Networks (cond-mat.dis-nn); Condensed Matter - Disordered Systems and Neural Networks; 01 natural sciences; Condensed Matter - Statistical Mechanics

A recently proposed exact algorithm for the maximum independent set problem is analyzed. The typical running time improved exponentially in some parameter regions compared to simple binary search. also overcomes core transition point, where conventional leaf removal fails, and works up replica symmetry breaking (RSB) point. This suggests that a itself not enough hardness random problem, providing further evidence RSB being obstacle algorithms general.