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In board game playing, many endgames may be solved based on dynamic programming (DP) with value-to-go functions that evaluate each state towards final winning positions. We first identify all positions to win in one move; next, recognize the next set of positions to win in two moves; and then do so in three moves, and so on. In this way, the sets of constant values (moving towards winning) are produced...
For finding all-pairs shortest paths in a digraph of n nodes, the well-known Floyd-Warshall method yields a particular best path between each pair of nodes efficiently in running time O(n3) when there is no negative-cost cycle (and all ties are ignored). Such a digraph may be a model of a real-world transportation, communication, or road network; then, the information of alternative best routing (if...
We consider the problem for scheduling N jobs that are partitioned to F disjoint classes (or families) subject to changeover (or setup) times in order to minimize the total weighted completion time. We first identify a published inefficient forward dynamic programming (DP) procedure due to Potts (1991) that works in O(F2NF+d), where d is the number of different changeover values (d ≤ F2). We then...
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