  This paper presents a general framework for generating greedy algorithms for
solving convex constraint satisfaction problems for sparse solutions by mapping
the satisfaction problem into one of graph traversal on a rooted tree of
unknown topology. For every pre-walk of the tree an initial set of generally
dense feasible solutions is processed in such a way that the sparsity of each
solution increases with each generation unveiled. The specific computation
performed at any particular child node is shown to correspond to an embedding
of a polytope into the polytope received from that nodes parent. Several issues
related to pre-walk order selection, computational complexity and tractability,
and the use of heuristic and/or side information is discussed. An example of a
single-path, depth-first algorithm on a tree with randomized vertex reduction
and a run-time path selection algorithm is presented in the context of sparse
lowpass filter design.
