We propose a parallel tree search algorithm based on the idea of tree-decomposition in which different processors search different parts of the tree. This generic algorithm effectively searches irregular trees using an arbitrary number of processors without shared memory or centralized control. The algorithm is independent of the particular type of tree search, such as single-agent or two-player game, and independent of any particular processor allocation strategy. Uniprocessor depth-first and breadth-first search are special cases of this generic algorithm. The algorithm has been implemented for alpha-beta search in the game of Othello on a 32-node Hypercube multiprocessor.
Bei, Xiaohui (Tsinghua University) | Chen, Ning (Nanyang Technological University) | Hua, Xia (Nanyang Technological University) | Tao, Biaoshuai (Nanyang Technological University) | Yang, Endong (Nanyang Technological University)
We consider the classic cake cutting problem where one allocates a divisible cake to n participating agents. Among all valid divisions, fairness and efficiency (a.k.a. ~social welfare) are the most critical criteria to satisfy and optimize, respectively. We study computational complexity of computing an efficiency optimal division given the conditions that the allocation satisfies proportional fairness and assigns each agent a connected piece. For linear valuation functions, we give a polynomial time approximation scheme to compute an efficiency optimal allocation. On the other hand, we show that the problem is NP-hard to approximate within a factor of Ω 1/√ n for general piecewise constant functions, and is NP-hard to compute for normalized functions.
Multi-robot teams are useful in a variety of task allocation domains such as warehouse automation and surveillance. Robots in such domains perform tasks at given locations and specific times, and are allocated tasks to optimize given team objectives. We propose an efficient, satisficing and centralized Monte Carlo TreeSearch based algorithm exploiting branch and bound paradigm to solve the multi-robot task allocation problem with spatial, temporal and other side constraints. Unlike previous heuristics proposed for this problem, our approach offers theoretical guarantees and finds optimal solutions for some non-trivial data sets.
Reinforcement learning (RL) has been shown to be an effective paradigm for learning control policies for problems with discrete state spaces. For problems with continuous multidimensional state spaces, the results are less compelling. When these state spaces can be effectively discretized, traditional techniques can be applied. However, many interesting problems must be discretized into an infeasibly large number of states. In these cases, other techniques must be used.
Multiagent resource allocation under uncertainty raises various computational challenges in terms of efficiency such as intractability, communication cost, and preference representation. To date most approaches do not provide efficient solutions for dynamic environments where temporal constraints pose particular challenges. We propose two techniques to cope with such settings: auctions to allocate fairly according to preferences, and MDPs to address stochasticity. This research seeks to determine the ideal combination between the two methods to handle wide range of allocation problems with reduced computation and communication cost between agents.