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ion. The abstractions in Gilpin et al. [6] range from k= 6 to k= 40 (the k is actually different in each round). The treeplex Q for the second player is also a uniform treeplex with similar characteristics. 6.5. Memory requirements. One particularly attractive feature of the EGT algorithm is the fact that the only operation performed on the matrix A is a(More)
We present a computational approach to the saddle-point formulation for the Nash equilibria of two-person, zero-sum sequential games of imperfect information. The algorithm is a first-order gradient method based on modern smoothing techniques for non-smooth convex optimization. The algorithm requires O(1/ ) iterations to compute an -equilibrium, and the(More)
We describe a specialized dynamic programming algorithm for factory crane scheduling. An innovative data structure controls the memory requirements of the state space and enables solution of problems of realistic size. The algorithm finds optimal space-time trajectories for two factory cranes or hoists that move along a single overhead track. Each crane is(More)
Fixed-width MDDs were introduced recently as a more refined alternative for the domain store to represent partial solutions to CSPs. In this work, we present a systematic approach to MDD-based constraint programming. First, we introduce a generic scheme for constraint propagation in MDDs. We show that all previously known propagation algorithms for MDDs can(More)
This thesis addresses three topics: solving the Nash Equilibrium problem for two-player zero-sum games presented in extensive form, constraint programming using multivalued decision diagrams and scheduling cranes in a factory. In the first chapter, we develop a first-order method based on a smoothing technique of Nesterov that allows us to solve problems(More)
We describe a heuristic algorithm for scheduling the movement of multiple factory cranes mounted on a common track. The cranes must complete a sequence of tasks at locations along the track without crossing paths, while adhering as closely as possible to a factory production schedule. The algorithm creates a decision tree of possible states of the crane(More)
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