2 research outputs found
Bicoloring Random Hypergraphs
We study the problem of bicoloring random hypergraphs, both numerically and
analytically. We apply the zero-temperature cavity method to find analytical
results for the phase transitions (dynamic and static) in the 1RSB
approximation. These points appear to be in agreement with the results of the
numerical algorithm. In the second part, we implement and test the Survey
Propagation algorithm for specific bicoloring instances in the so called
HARD-SAT phase.Comment: 14 pages, 10 figure
Polynomial iterative algorithms for coloring and analyzing random graphs
We study the graph coloring problem over random graphs of finite average
connectivity . Given a number of available colors, we find that graphs
with low connectivity admit almost always a proper coloring whereas graphs with
high connectivity are uncolorable. Depending on , we find the precise value
of the critical average connectivity . Moreover, we show that below
there exist a clustering phase in which ground states
spontaneously divide into an exponential number of clusters. Furthermore, we
extended our considerations to the case of single instances showing consistent
results. This lead us to propose a new algorithm able to color in polynomial
time random graphs in the hard but colorable region, i.e when .Comment: 23 pages, 10 eps figure