Features

New in 5.3

• MatrixGames calculates optimal strategies for two-person zero-sum games. The optimal strategy is in general a mixed one, where players 1 and 2 independently pick decisions (alternatives) si and tj, with probability xi and yj, respectively. Such optimal mixed strategies always exist. Payment to a player will be less if he deviates from his optimal strategy whereas the other player sticks to his optimal strategy (Nash equilibrium).

General Features

• Implemented a new routine DualSimplex that solves linear constrained problems with the dual simplex method
• Representation of graph routines graphically
• Linear optimization: revised simplex with sensitivity analysis and branch-and-bound methods
• Shortest-path tasks: one-to-all and all-to-all shortest connections on a graph
• Graph algorithms: calculations of flows on a graph
• Combinatorial optimization and heuristics: several routines that can be used to solve assignment, traveling salesman, and other problems and can be used for implementation of additional effective heuristics
• Documentation fully compatible with Mathematica 7

• Completely new branch of problems: graph algorithms
• MaximumFlow: calculates the maximum flow on a network defined by a list of links from a source node to a sink node
• MinCostsFlow: calculates the minimum costs flow on a network from a source node to a sink node, at given net flow
• MininmalSpanningTree: calculates a minimal spanning tree of a network with not directed links; the algorithm of Prim is implemented
• BiConnectComp: calculates the list of articulation points and the biconnected components of a graph given by its link list
• StronglyConnectedComponents: calculates a list of subsets of nodes ("block nodes") each inducing a strongly connected component of the directed graph
• TopologicalOrdering: calculates a reordered list of nodes if topological ordering is possible; an empty is returned otherwise
• LCShortestPath: calculates the shortest path in a network defined through a list of links; negative weights are allowed as long as no negative cycles arise