Reduction of Hyperelliptic Curves in Residue Characteristic 2

Consider a hyperelliptic curve of genus g over a field K of characteristic zero. After extending K we can view it as a marked curve with its 2g+2 Weierstrass points. We present an explicit algorithm to compute the stable reduction of this marked curve for a valuation of residue characteristic 2 over a finite extension of K. In the cases g2 we work out relatively simple conditions for the structure of this reduction.