  We present a new class of algorithms for performing valence-bond quantum
Monte Carlo of quantum spin models. Valence-bond quantum Monte Carlo is a T=0
Monte Carlo method based on sampling of a set of operator-strings that can be
viewed as forming a tree-like structure. The algorithms presented here utilize
the notion of a worm that moves up and down this tree and changes the
associated operator-string. In quite general terms we derive a set of equations
whose solutions correspond to a new class of algorithms. As specific examples
of this class of algorithms we focus on two cases. The bouncing worm algorithm,
for which updates are always accepted by allowing the worm to bounce up and
down the tree and the driven worm algorithm, where a single parameter controls
how far up the tree the worm reaches before turning around. The latter
algorithm involves only a single bounce where the worm turns from going up the
tree to going down. The presence of the control parameter necessitates the
introduction of an acceptance probability for the update.
