Reasonable breadth-biased

A+ algorithms are A algorithms (as studied by Nilsson) satisfying two additional constraints which magnify the breadth aspect of a graph search. Use of A+ algorithms is perhaps most plausible when it is desirable to generate alternative goal nodes on optimal paths. There are two principal results for A+ algorithms. First, if A(1) and A(2) are A+ algorithms and A(2) is as well informed as A(1) then A(2) expands no more nodes than A1 does. Second, if an A+ algorithm is modified so as to return a set of optimal paths and the monotone condition is satisfied, the A+ algorithm returns a set of solutions consisting of an optimal path to each goal node on an optimal path.