  Clustering of dark matter halos has been shown to depend on halo properties
beyond mass such as halo concentration, a phenomenon referred to as halo
assembly bias. Standard halo occupation models (HOD) in large scale structure
studies assume that halo mass alone is sufficient in characterizing the
connection between galaxies and halos. Modeling of galaxy clustering can face
systematic effects if the number of galaxies within a halo is correlated with
other halo properties. Using the Small MultiDark-Planck high resolution
$N$-body simulation and the clustering measurements of the Sloan Digital Sky
Survey (SDSS) DR7 main galaxy sample, we investigate the extent to which the
concentration-dependence of halo occupation can be constrained. Furthermore, we
study how allowing for the concentration dependence can improve our modeling of
galaxy clustering.
  Our constraints on HOD with assembly bias suggest that satellite population
is not correlated with halo concentration at fixed halo mass. At fixed halo
mass, our constraints favor lack of correlation between the occupation of
centrals and halo concentration in the most luminous samples ($M_{\rm
r}<-21.5,-21$), and modest correlation in the $M_{\rm r}<-20.5,-20, -19.5$
samples. We show that in comparison with abundance-matching mock catalogs, our
findings suggest qualitatively similar but modest levels of the impact of halo
assembly bias on galaxy clustering. The effect is only present in the central
occupation and becomes less significant in brighter galaxy samples.
Furthermore, by performing model comparison based on information criteria, we
find that in most cases, the standard mass-only HOD model is still favored by
the observations.
