Evidence of Exponential Speed-Up in the Solution of Hard Optimization Problems

Figure 2

Simulation time comparison between incomplete solvers CCLS and DeciLS against our solver, Falcon, for the balanced and constrained delta-Max-E3SAT. A threshold of of unsatisfiable clauses has been set. We have then tested how long CCLS, DeciLS, and our solver Falcon take to overcome this limit with increasing number of variables. All calculations have been performed on a single thread of an Intel Xeon E5-2680 v3 with 128 Gb DRAM shared on 24 threads. The local solvers require an exponentially increasing time to reach that limit already visible at a few hundred variables for the CCLS and a few thousands for the DeciLS. Our solver has been tested up to variables and required order of seconds for that maximum number of variables. We show also the estimate of time that would have been required these local solvers to run up to variables. The estimated time (dashed and dashed-dotted lines) has been calculated using a linear regression of the versus the number of variables.