Daisuke Hatano

Dynamic SAT with decision change costs: formalization and solutions

We address a dynamic decision problem in which decision makers must pay some costs when they change their decisions along the way. We formalize this problem as Dynamic SAT (DynSAT) with decision change costs, whose goal is to find a sequence of models that minimize the aggregation of the costs for changing variables. We provide two solutions to solve a specific case of this problem. The first uses a Weighted Partial MaxSAT solver after we encode the entire problem as a Weighted Partial MaxSAT problem. The second solution, which we believe is novel, uses the Lagrangian decomposition technique that divides the entire problem into sub-problems, each of which can be separately solved by an exact Weighted Partial MaxSAT solver, and produces both lower and upper bounds on the optimal in an anytime manner. To compare the performance of these solvers, we experimented on the random problem and the target tracking problem. The experimental results show that a solver based on Lagrangian decomposition performs better for the random problem and competitively for the target tracking problem.

Computational Aspects of the Preference Cores of Supermodular Two-Scenario Cooperative Games

In a cooperative game, the utility of a coalition of players is given by the characteristic function, and the goal is to find a stable value division of the total utility to the players. In real-world applications, however, multiple scenarios could exist, each of which determines a characteristic function, and which scenario is more important is unknown. To handle such situations, the notion of multi-scenario cooperative games and several solution concepts have been proposed. However, computing the value divisions in those solution concepts is intractable in general. To resolve this issue, we focus on supermodular two-scenario cooperative games in which the number of scenarios is two and the characteristic functions are supermodular and study the computational aspects of a major solution concept called the preference core. First, we show that we can compute a value division in the preference core of a supermodular two-scenario game in polynomial time. Then, we reveal the relations among preference cores with different parameters. Finally, we provide more efficient algorithms for deciding the nonemptiness of the preference core for several specific supermodular two-scenario cooperative games such as the airport game, multicast tree game, and a special case of the generalized induced subgraph game.