Using a Skewed Hamming Distance to Speed Up Deterministic Local Search

Schöning [13] presents a simple randomized algorithm for (d, k)-CSP problems with running time ( d(k−1) k )n poly(n). Here, d is the number of colors, k is the size of the constraints, and n is the number of variables. A derandomized version of this, given by Dantsin et al. [2], achieves a running time of ( dk k+1 )n poly(n), inferior to Schöning’s. We come up with a simple modification of the deterministic algorithm, achieving a running time of ( d(k−1) k · k d kd−1 ) n poly(n). Though not completely eleminating the gap, this comes very close to the randomized bound for all but very small values of d. Our main idea is to define a graph structure on the set of d colors to speed up local search.