úÎ#KöA      !"#$%&'()*+,-./0123456789:;<=>?@None:<=DQRT  None:<=DQRT      None:<=DQRT  None:<=DQRT .Minimal distance algebraETODO The two Ints are the indices of the nodes and could be replaced?/IMaximum edge probability following the probabilities generated from the EdgeProb grammar.0KThis should give the correct order of nodes independent of the underlying  Set1 First or  Set1 Last because the  (From:.To) system is agnostic over these.1KThis should give the correct order of nodes independent of the underlying  Set1 First or  Set1 Last because the  (From:.To) system is agnostic over these.2 Before using aInside the  ScoreMatrix` needs to be scaled appropriately! Due to performance reasons we don't want to do this within aInside.3!Run the minimal distance algebra.jThis produces one-boundary sets. Meaning that for each boundary we get the total distance within the set.6 Given the Set1 produced in forwardMinDist14 we can now extract the co-optimal paths using the  Set1 -> () index change.QTODO do we want this one explicitly or make life easy and just extract from all forwardMinDist1 paths?7IReturn the minimal distance and provide a list of co-optimal backtraces.8(Extract the individual partition scores.9)Run the maximal edge probability grammar.= Given the Set1 produced in forwardMinDist14 we can now extract the co-optimal paths using the  Set1 -> () index change.QTODO do we want this one explicitly or make life easy and just extract from all forwardMinDist1 paths?!"#$%&'()*+,-./0123456789:;<=>?!"#$%&'()*+,-./0123456789:;<=>?./+,-012*)('&%$#"!3456789:;<=>?!"#$%&'()*+,-./0123456789:;<=>?A          !"#$%&'()*+,-./012343ShortestPathProblems-0.0.0.1-8r9tnzaiVr8FNHFWezSi4m ShortestPath.SHP.Grammar.MinDist#ShortestPath.SHP.Grammar.EdgeProbIO!ShortestPath.SHP.Grammar.EdgeProbShortestPath.SHP.Edge.MinDist SigMinDistedgefinimptynodehgMinDist$D:R:SigCombiningSigMinDistSigMinDist&$fProductCombiningSigMinDistSigMinDist)$fProductBacktrackingSigMinDistSigMinDist SigEdgeProb gEdgeProb&D:R:SigCombiningSigEdgeProbSigEdgeProb($fProductCombiningSigEdgeProbSigEdgeProb+$fProductBacktrackingSigEdgeProbSigEdgeProbBTULBT1LBTUBT1PFLULTS1LPFUTS1PathBTBTnodeBTedgeaMinDist aMaxEdgeProbaPathBTaPrettyaInsideforwardMinDist1backtrackMinDist1 pathbtMinDist runCoOptDist runMinDistboundaryPartFunforwardMaxEdgeProbFirstforwardMaxEdgeProbLastpathbtMaxEdgeProbFirstpathbtMaxEdgeProbLastrunMaxEdgeProbFirstrunMaxEdgeProbLasttest $fShowPathBT