Every recursive call returns a list of all (partial) solutions found (where a solution respects (v) by construction), and the calling code then checks each returned solution for the tail for topological connectedness with the current solution for the head (cf. Algorithm 2, line 32).
These quantities are being processed by Algorithm 2. The first is |M|, the number of candidates of a source edge, and the second is |T|, the number of returned solutions for the tail.
To obtain the average number of returned solutions for the tail for one of the experiments with a fixed route length, an observed total must be divided by the number of locations, 1,000, and also by the respective route length n.
Open image in new window Fig. 11 Total number of returned solutions for the tail, standardised with respect to 1,000 successfully matched random line locations, with various numbers of segments, respectively.
Secondly, the total number of returned solutions for the tail during all recursive calls to Algorithm 2, has been observed for the first series of experiments with 1,000 lineear locations each, but such that only the positives contributed to this total count.
In every other pooled set, the strict ratchets returned solutions for the largest percentage of protein trees, while the unconstrained runs were least successful in recovering edit paths.
Existing sampling-based path planners on manifolds focus on finding a feasible solution, but they do not optimize the quality of the path in any sense and, thus, the returned solution is usually not adequate for direct execution.
Only the permissive reference tree ratchet did not recover most-parsimonious edit paths for every protein tree of size 4 10, failing to return a solution for 12 out of 796 ten-taxon protein trees.
The main contribution of this paper is a design method for allocation rules that return solutions in the core or ε-core of the game under delayed information on the coalitions' values, and therefore the resulting allocation rule is called robust.
Therefore, although DPCPE is not guaranteed to return the optimal solution, it usually returns solutions that work better in practice for the BFs algorithm than directly using the database with no preprocessing (Section 6.6).
